The Physics Of Particle Detectors Dan Green

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The Physics of Particle Detectors
This text provides a comprehensive introduction to the physical principles and design of parti-
cle detectors, covering all major detector types in use today. The book begins with a reprise of
the size and energy scales involved in different physical processes. It then considers non-destruc-
tive methods, including the photoelectric effect, photomultipliers, scintillators, Cerenkov and
transition radiation, scattering and ionization and the use of magnetic fields in drift and wire
chambers. A complete chapter is devoted to silicon detectors. In the final part of the book, the
author discusses destructive measurement techniques including Thomson and Compton scat-
tering, Bremsstrahlung and calorimetry. Throughout the book, emphasis is placed on explain-
ing the physical principles on which detection is based, and showing, by considering appropriate
examples, how those principles are best utilized in real detectors. This approach also reveals the
limitations that are intrinsic to different devices.
DAN GREEN received his Ph.D. from the University of Rochester in 1969. He was a post-doc at
Stony Brook from 1969 to 1972 and worked at the Intersecting Storage Rings (ISR) at CERN.
His next appointment was as an Assistant Professor at Carnegie Mellon University from 1972
to 1978 during which time he was also Spokesperson of a BNL Baryonium Experiment. He has
been a Staff Scientist at Fermilab from 1979 to the present, and has worked in a wide variety of
roles on experiments both at Fermilab and elsewhere. He worked on the DO Experiment as Muon
Group Leader from 1982 to 1990 and as B Physics Group Co-Convener from 1990 to 1994. He
led the US Compact Muon Solenoid (CMS) Collaboration as Spokesperson for the US groups
working at the Large Hadron Collider (LHC) at CERN. At Fermilab, he was Physics
Department Deputy Head from 1984 to 1986 and Head from 1986 to 1990. From 1993 to present
he has served as the CMS Department Head in the Particle Physics Division.

CAMBRIDGE MONOGRAPHS ON
PARTICLE PHYSICS,
NUCLEAR PHYSICS AND COSMOLOGY
12
General Editors: T. Ericson, P. V. Landshoff
1. K. Winter (ed.): Neutrino Physics
2. J. F. Donoghue, E. Golowich and B. R. Holstein: Dynamics of the Standard Model
3. E. Leader and E. Predazzi: An Introduction to Gauge Theories and Modern Particle
Physics, Volume 1: Electroweak Interactions, the 'New Particles' and the Parton Model
4. E. Leader and E. Predazzi: An Introduction to Gauge Theories and Modern Particle
Physics, Volume 2: CP- Violation, QCD and Hard Processes
5. C. Grupen: Particle Detectors
6. H. Grosse and A. Martin: Particle Physics and the Schrodinger Equation
7. B. Andersson: The Lund Model
8. R. K. Ellis, W J. Stirling and B. R. Webber: QCD and Collider Physics
9. I. I. Bigi and A. I. Sanda: CP Violation
10. A. V. Manohar and M. B. Wise: Heavy Quark Physics
11. R. K. Bock, H. Grote, R. Friihwirth and M. Regier: Data Analysis Techniques for High-
Energy Physics, Second edition
12. D. Green: The Physics of Particle Detectors

PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE
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© Cambridge University Press 2000
This book is in copyright. Subjccllo talllloryexceplion
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First published 2000
Printed in the United Kingdom at the University Press, Cambridge
Type/ace Times New Roman MT 11114 pI System QuarkXPress™ [SE]
A catalogue record/or this book is available/rom the British Library
Library 0/ Congress Cataloguing in Publication data
Green, Dan.
The physics of particle detectors I Dan Green.
p. em. - ( ambridge monographs on panicle physics,
nuclear physics, and cosmology ; 12)
lnclude.~ bibliographiC<ll references and index.
ISBN 0 521 662265 (hardback)
I. Nuclear counters. I. Title. II. Series.
QC787.C6 G67 2000
539.7'7-dc21 99-053251
ISBN 0 521 66226 5 hardback

Contents
Acknowledgments
I Introduction
1 Size, energy, cross section
1.1 Units
1.2 Planck constant
1.3 Electromagnetic units
1.4 Coupling constants
1.5 Atomic energy scales
1.6 Atomic size
1.7 Atomic spin effects
1.8 Cross section and mean free path
1.9 Partial waves and differential cross section
1.10 Nuclear scales of energy and size
1.11 Nuclear cross section
1.12 Photon cross section
Exercises
References
II Non-destructive measurements
IIA Time and velocity
2 The photoelectric effect, photomultipliers, scintillators
2.1 Interaction Hamiltonian
2.2
2.3
2.4
2.5
2.6
2.7
2.8
Transition amplitude and cross section
The angular distribution
The photomultiplier tube
Time of flight
Scintillators and light collection
Gain and time structure
Wavelength shifting
vii
page Xlll
1
5
5
6
6
12
12
15
17
17
19
22
23
25
27
28
29
29
31
31
32
38
38
39
41
43
47

Vlll
2.9
Contents
Coincidence logic and deadtime
Exercises
References
3 Cerenkov radiation
3.1 Units
3.2
3.3
3.4
3.5
3.6
3.7
3.8
Index of refraction
Optical theorem
Conducting medium and skin depth
Plasma frequency
Two 'derivations' of the Cerenkov angle
A 'derivation' of the frequency spectrum
Examples and numerical values
Exercises
References
4 Transition radiation
4.1 Cerenkov radiation for a finite length radiator
4.2 Interference effects
4.3 The vacuum phase shift
4.4 The frequency spectrum
4.5 Dependence on yand saturation
4.6 TRD foil number and thickness
4.7 TRD data
Exercises
References
fiB Scattering and ionization
5 Elastic electromagnetic scattering
5.1 Single scattering off a nucleus
5.2 The scattering cross section
5.3 Feynman diagrams
5.4 Relativistic considerations
5.5 Multiple scattering
5.6 The radiation length
5.7 Small angle, three dimensional multiple scattering
5.8 Maximum momentum transfer
5.9 Energy transfer
5.10 Delta rays
5.11 Other force laws
Exercises
References
50
53
53
55
55
58
59
59
61
62
69
70
73
74
75
75
77
79
79
81
83
85
85
87
89
91
91
93
94
95
96
97
98
100
103
103
104
105
105

Contents
6 Ionization
6.1 Energy loss
6.2
6.3
6.4
6.5
6.6
6.7
6.8
Minimum ionizing particle
Velocity dependence
Range
Radioactive sources
The logarithmic dependence and relativistic rise
Fluctuations
The critical energy
Exercises
References
lie Position and momentum
7 Magnetic fields
7.1 Solenoidal fields
7.2
7.3
Dipole fields - fringe fields
Particle motion in a uniform field
7.4 Momentum measurement and error
7.5 Exact solutions - Cartesian and cylindrical coordinates
7.6 Particle beam and quadrupole magnets
7.7 The quadrupole doublet
Exercises
References
8 Drift and diffusion in materials, wire chambers
8.1 Thermal and drift velocity
8.2 Mobility
8.3
8.4
8.5
8.6
8.7
8.8
8.9
Pulse formation in 'unity gain' detectors
Diffusion and the diffusion limit
Motion in E and B fields, with and without collisions
Wire chamber electrostatics
Pulse formation in a wire chamber
Mechanical considerations
The induced cathode signal
Exercises
References
9 Silicon detectors
9.1 Impact parameter and secondary vertex
9.2 Band gap, intrinsic semiconductors and ionization
9.3 The silicon diode fields
9.4 The silicon diode: signal formation at depletion
ix
106
106
107
108
111
115
117
119
121
125
125
127
129
129
130
133
135
138
140
146
148
150
151
151
153
154
158
161
165
167
169
172
175
175
177
177
181
182
186

x Contents
9.5 Noise sources - thermal and shot noise 190
9.6 Filtering and the 'equivalent noise charge' 194
9.7 Front end transistor noise 196
9.8 Total noise charge 197
9.9 Hybrid silicon devices 199
Exercises 200
References 201
ill Destructive measurements 203
IliA Radiation 203
10 Radiation and photon scattering 205
10.1 Non-relativistic radiation 205
10.2 Thomson scattering 207
10.3 Thomson scattering off objects with structure 209
10.4 Relativistic photon scattering 210
10.5 Compton scattering 211
10.6 Relativistic acceleration 213
10.7 Circular and linear acceleration 216
10.8 Angular distribution 217
10.9 Synchrotron radiation 219
10.10 Synchrotron applications 221
10.11 Photon emission kinematics 224
10.12 Photon frequency spectrum 224
10.13 Bremsstrahlung and pair production 225
10.14 The radiation length 227
10.15 Pair production by photons 229
10.16 Pair production by charged particles 230
10.17 Strong and electromagnetic interaction probabilities 231
Exercises 231
References 232
IIIB Energy measurements 235
11 Electromagnetic calorimetry 237
11.1 Radiation length and critical energy 237
11.2 The electromagnetic cascade 238
11.3 Energy -linearity and resolution 241
11.4 Profiles and single cascades 243
11.5 Sampling devices 245
11.6 Fully active devices 247
11.7 Transverse energy flow 251
11.8 Calibration methods 254
Exercises 256
References 257

Contents xi
12 Hadronic calorimetry 258
12.1 Properties of single hadronic interactions 259
12.2 The hadronic cascade - neutrals 262
12.3 Binding energy effects 264
12.4 Energy resolution 266
12.5 Profiles and single cascades 268
12.6 e/h and the 'constant term' 273
12.7 Transverse energy flow 278
12.8 Radiation damage 280
12.9 Energy leakage 281
12.lO Neutron radiation fields 284
12.11 Neutron detection 286
Exercises 288
References 289
IV The complete set of measurements 291
13 Summary 293
13.1 Fundamental particles 293
13.2 Detection of fundamental particles 294
13.3 General purpose detectors 298
13.4 The jumping off point 300
References 301
Appendices 303
A Kinematics 305
B Quantum bound states and scattering cross section 311
C The photoelectric effect 317
D Connecting cables 320
E The emission of Cerenkov radiation 324
F Motion in a constant magnetic field 328
G Non-relativistic motion in combined constant E and B fields 331
H Signal generation in a silicon diode for point ionization 333
I Ideal operational amplifier circuits 336
J Statistics introduction 342
K Monte Carlo models 348
Glossary of symbols 353
Index 357

Acknowledgments
This book represents a distillation of 30 years of experimental experience. The
author cannot possibly individually acknowledge all the colleagues who
'taught him the business' of experimental high energy physics. Suffice it to say
that he is indebted to a multitude.The input of the students who were subjected
to lectures consisting of parts of this text was often incisive and thought pro-
voking. The enthusiasm and dedication of Ms. Terry Grozis in assembling the
final document from inaudible tapes, scraps of paper and marginal digressions
were also of inestimable value. Dr. John Womersley and Dr. Adam Para are
thanked for a critical reading of the text and for valuable suggestions. Finally,
the students subjected to a full course of lectures in the summer of 1997 gave
very valuable criticism.
xiii

Part I
Introduction
The subject of particle detectors covers those devices by which the existence
and attributes of particles in a detecting medium is made manifest to us. The
full and complete understanding of these devices requires a good under-
standing of basic physics. Without that knowledge we are simply 'mechanics'
without the capacity to advance the state of the art of detector technology. On
the other hand, a rigorous understanding from first principles is also not an
optimal approach. The 'useful' understanding of a given device proceeds from
an understanding of what approximations to full rigor are possible. That
understanding can only come from experience and it is the purpose of this
volume to communicate that experience. The aim of this text is to steer a per-
ilous course between the purely descriptive and the purely theoretical.
The role of detectors can be visualized by assuming that an interesting inter-
action occurs at a point in space and time. From that point several secondary
particles of different masses are emitted with various angles and momenta as
shown in Fig. 1.1. It is the job of the detector designer to measure the time of
interaction, t, and the vector momenta, p., and masses, M., of those emitted
1 I
particles. The text is organized so as to show the ensemble of tools available to
the designer. Typically, mathematical detail and topics outside the main scope
of the text are relegated to the Appendices.
A list of the topics covered is given in the Table of Contents. The first chapter
is an introduction devoted to a numerical description of the appropriate size,
energy scales, and cross sections for different processes. The numerical data
given in the tables of Chapter 1will constantly be referred to in later chapters.
There then follow eight chapters on 'non-destructive' measurements, or
those which do not appreciably change the measured particle's position or
momentum. The first subtopic concerns the measurement of time and veloc-
ity. Chapter 2 starts with the basic physics of the photoelectric effect and
leads into photomultiplier tubes, scintillator and time of flight measurement.

2
1
A
Introduction
Fig. 1.1. A schematic representation of the reaction A +B~ 1+2+3+4 +5+6. The
reaction is specified when the vector momentum and mass of each particle is deter-
mined.
Chapter 3 describes velocity measurement by way of the emission of optical
photons in the Cerenkov process. Chapter 4 follows with a discussion of the
closely related emission of x-ray photons in transition radiation which also
determines the velocity of a particle.
The second sUbtopic within non-destructive readout first lays the physics
groundwork of elastic scattering in Chapter 5. Chapter 6 then covers the
application of single scattering to scattering offatomic electrons and the result-
ing energy loss. Detection of the energy lost is the physical basis of many of the
techniques used in charged particle detection. The third sUbtopic then follows
up with the non-destructive measurement of the position and momentum of
charged particles. Chapter 7 contains a derivation of the particle trajectory
in a magnetic field and the consequent measurement of momentum. Those
measurements have intrinsic limitations which are explored first in Chapter 8
in studying diffusion in gases and wire chambers. Chapter 9 looks at faster and
higher spatial resolution silicon detectors for more accurate position measure-
ments.
The text then switches to destructive measurements, where the particle to be
measured loses a significant fraction of its energy or is fully absorbed in the
detector. First, in Chapter 10, the physics foundation is laid by exploring radia-
tion and photon scattering. Then these concepts are applied in exploring the
topic of destructive energy measurements. Chapter 11 describes measurements
of electron and photon energy, while Chapter 12 describes the measurement of
the energy of strongly interacting particles.
Finally, a general-purpose high energy physics detector using all the previ-
ously described techniques is sketched in Chapter 13. The concept of multiple
redundant measurements is introduced and several examples are given.

Introduction 3
The full set of material in the text is suitable for a one year course. If a one
semester course is desired, the algebraic details in the Appendices can be
skipped as well as Chapter 1, the first half of Chapter 2 and Chapters 5, 6, and
10 assuming that no supplementary physics background was required.
Note that the subjects covered in the text are strongly limited to detectors
themselves. Exceptions are a brief description of coincidence circuits in
Chapter 2 and front end noise processing in Chapter 9. These brief forays were
made since these special topics were tightly connected to the detectors them-
selves. However, there is no other discussion of front end electronics, trigger
systems, data acquisition, or computer programming. In addition, the vital
area of detector modeling and Monte Carlo techniques is only sketched in
Appendix K. Probability theory and statistical analysis appear only briefly in
Appendix 1. References to these vital areas are given at the end of the text for
readers who want to go beyond the scope of this volume.
The aim of this text is to describe the full ensemble of particle detectors from
first principles. The goal is to strike a balance between simply presenting the
final result and a full and rigorous derivation and thus to extract the relevant
physics in a clear fashion. Intuition and order of magnitude numerical esti-
mates are stressed throughout in an attempt to communicate the insights gar-
nered from experience.
Ah, but a man's reach should exceed his grasp, or what's a heaven
for?
Robert Browning
Curiosity is, in great and generous minds, the first passion and the
last.
Dr Samuel Johnson, 1750
General references - A
Mechanics, electricity and magnetism and quantum mechanics
[1] The Feynman Lectures in Physics, R. Feynman, R. Leighton, and M. Sands,
Addison-Wesley Publishing Co., Inc. (1963).
[2] Classical Mechanics, H. Goldstein, Addison-Wesley Publishing Co., Inc. (1950).
[3] Classical Electricity and Magnetism, W.K.H. Panofsky and M. Phillips, Addison-
Wesley Publishing Co., Inc. (1962).
[4] Quantum Mechanics, E. Merzbacher, John Wiley & Sons, Inc. (1961).
General references - B
Textbooks on particle detectors
[1] Detectors/or Particle Radiation, K. Kleinknecht, Cambridge University Press
(1987).

4 Introduction
[2] Experimelltal Techniques in High Energy Physics, T. Ferbel, Addison-Wesley
Publishing Co. Inc. 1987).
[3] instrumenta.tion ill High Energy Physics, Ed. F. Sauli, World Scientific Publishing
Co. (1992).
[4] Inslrumel11otion in Elementary Particle Physics, Ie. Anjos, D. Hartill, F. Sauli,
and M. Sheaf. Rio de Janeiro 1990, World Scientific Publishing Co. (1992).
[5J Instrumentation in Elemelltary P(lI·ticle Physics, e.W Fabjan and IE. Pilcher,
Trieste 1987, World Scientific Publi lung Co. (1988).
[6] e.w. Pabjan and H.E Fi her Particle detectors', Rep. Prog. Phys. 43 1003
(1980).

1
Size, energy, cross section
Beauty depends on size as well as symmetry.
Aristotle
Energy is eternal delight.
William Blake
Textbooks on detectors often jump directly into a description of the devices
themselves. The relevant descriptive formulae are then simply given without
derivation and readers are instead referred to the relevant texts. A comple-
mentary approach is taken here. A 'derivation' of the relevant physics is always
attempted first. Armed with the derivations, the reader is then introduced to the
detector where the approximations which are made are explained along with
the reasons why they are valid. In order to contain the length of the text, all
'derivations' are heuristic and thus either compressed or left to the Appendices.
Numerical examples are given at regular intervals in order that the reader be
firmly connected to real devices and have a firm grasp of the appropriate orders
of magnitude. We note that 'intuition' is largely the result of experience. The
judgement that allows a simplifying approximation to be made usually comes
with an appreciation of orders of magnitude of the quantities involved. In this
text, that hard won 'intuition' is, it is hoped, passed on to the student.
Detectors function by causing a particle to interact with some detecting
medium. For example, a charged particle might ionize a gas in a device and the
freed charge might be collected as an electrical signal localized in time, a
'pulse', on a detector electrode. To characterize the detector it is fundamental
to understand the probability of interaction of the particle with the device. The
aim of Chapter 1 is to provide the basic numerical data needed to later
characterize the interaction probability of the different particles which we wish
to detect.
1.1 Units
It is traditional in high energy physics to work in dimensionless units where h
and c are defined to be equal to 1. In those units momentum (pc), energy (8),
mass (mc2
), inverse time (hit) and inverse length (he/x) all have the same
5

6 1 Size, energy, cross section
dimensions, which we take to be energy. Units for energy are taken to be the
electron volt, where one electron volt, eV, is the energy, I:lU, gained by an elec-
tron of charge e, in dropping through a potential difference, I:lV, of 1 volt,
I:lU= el:l V. A tabulation of many of the physical quantities used throughout
the text is given in Table 1.1[1]. In that table, the speed of light, the Planck con-
stant, the electron charge, the masses of elementary particles, the fine-structure
constant, the classical electron radius, the Compton wavelength of the electron
etc. are gathered together in electron volt and in MKS units. This table and
Table 1.2 contain sufficient numerical information for the needs of this text.
Kinematics, the constraints imposed by energy-momentum conservation, are
worked out in Appendix A.
1.2 Planck constant
In going from the dimensionless calculations of high energy physics to dimen-
sional quantities, it is necessary to know the Planck constant and be able to use
it. (See Table 1.1.)
he = 0.2 GeV fm=2000eV A
1GeV = 10g
eV
1A = 10 - 8cm = 10nm
1fm = 10- 13cm
(1.1)
The Planck constant is given for two different distance scales, the angstrom
and the fermi. Those two distance scales are characteristic of the size of an
atom and the size of a nucleus respectively. The conversion of size to energy
leads us to the immediate conclusion that nuclear energy scales are GeV
whereas atomic energy scales are of order a few electron volts. The ratio of one
angstrom to one fermi is 100000 to 1.
1.3 Electromagnetic units
In the body of the text we will most often use CGS units in symbolic manipUla-
tions and we will freely convert back and forth to MKS units. It is a fact of life
that practicing physicists must acquire a facility with both systems of units
since experimentalists have connections to both theory and engineering. (See
the beginning of Chapter 3 for a full explanation.) We will later explicitly give
a prescription for converting between MKS and CGS units.

Table 1.1. Fundamental physical constants
Quantity Symbol, equation Value Uncert. (ppm)
Speed of light in vacuum c 299792458 ms- I exacta
Planck constant h 6.626075 5(40) X 10-34 Js 0.60
Planck constant, reduced h=h/27T 1.054572 66(63) X 10-34 Js 0.60
= 6.5821220(20) X 10-22 MeV s 0.30
Electron charge magnitude e 1.60217733(49) X10-19 C=4.803 206 8(l5) X 10-10 esu 0.30,0.30
Conversion constant he 197.327053(59) MeV fm 0.30
Conversion constant (he)2 0.38937966(23) GeV2 mbam 0.59
Electron mass me 0.51099906(15) MeV/c2= 9.l09 389 7(54) X10- 31 kg 0.30,0.59
Proton mass mp 938.272 31(28) MeV/c2= 1.672 623 1(10) X 10-27 kg 0.30,0.59
= 1.007 276 470(12) u= 1836.l52 701(37) m. 0.012,0.020
Deuteron mass md 1875.613 39(57)MeV/c2 0.30
Unified atomic mass unit (u) (mass 1
2C atom)/12 = (lg)/(NA mol) 931.49432(28) MeV/c2= 1.660 540 2(10) X 10- 27 kg 0.30,0.59
Permittivity of free space
EO } E /-t = 11c2
8.854187817 . . . X 10-12 F m- I exact
Permeability of free space /-to 0 0 47TX 10- 7N A-2= 12.566 370 614 . . . X 10-7N A-2 exact
Fine-structure constant a= e2/47TEohe 11137.0359895(61/ 0.045
Classical electron radius re =e2/47TEomcc2 2.817940 92(38) X10-15 m 0.13
Electron Compton wavelength lI. =li/m e=r a-I
c c c
3.861 59323(35) X 10-13 m 0.089
Bohr radius (mnucleus = 00) a", = 47TEoh2/mee2 = r.a-2 0.529 177 249(24) X 10-10 m 0.045
Wavelength of 1 eVle particle hc/e 1.239 84244(37) X10-6 m 0.30
Rydberg energy heR", = mee4/2(47Teo)2h2= mec2a212 13.605698 1(40) eV 0.30
Thomson cross section (TT=87T~/3 0.65524616(18) bam 0.27
Bohr magneton /-La = eli/2mc 5.78838263(52) X10-11 MeV T-I 0.089
Nuclear magneton f-LN = eli/2mp 3.15245166(28) X 10-14 MeV T-I 0.089
Electron cyclotron freq.lfield w~c/B=e/me 1.75881962(53) X10" rad S-I T-' 0.30
Proton cyclotron freq.lfield £UP
cyc/B = e/mp 9.578 8309(29) X1Q1 rad S-I T-I 0.30

Quantity
Gravitational constant
Standard grav. accel., sea level
Avogadro constant
Boltzmann constant
Molar volume, ideal gas at STP
Wien displacement law constant
Stefan-Boltzmann constant
Fermi coupling constant
Weak mixing angle
W = boson mass
zO boson mass
Strong coupling constant
Table 1.1. (cont.)
Symbol, equation Value
GN
6.672 59(85) X 10-11 m3kg-1 S-2
=6.70711(86) X 10-39 lie (GeV/d)-2
g 9.80665 m S-2
NA 6.022 1367(36) X 1023 mol-1
k 1.380658(12) X 10-23 J K-l
=8.617385(73) X 10-5 eV K-l
N Ak(273.15 K)/(101325 Pa) 22.41410(19) X 10-3 m3 mol-1
b=AmaxT 2.897756(24) X 10-3 m K
u= -rr2/(.4/601i3d 5.67051(19) X 10-8 W m-2K-4
G!(lie)3 1.16639(2) X 10-5 GeV-2
sin28(Mz) (MS) 0.2319(5)
mw 80.22(26) GeV/c2
mz 91.187(7) GeV/c2
as(mz) 0.116(5)
e= 2.718281828459045235 y= 0.577215 664901532861
Uncert. (ppm)
128
128
exact
0.59
8.5
8.4
8.4
8.4
34
20
2200
3200
77
43000
1 in=0.0254 m
1 A=1O nm
-rr= 3.141592653 589793238
1 G=IO-4 T 1 eV= 1.60217733(49) X 10-19 J kTat 300 K=[38.68149(33W1 eV
1 barn=1O-28m2
Notes:
1 dyne = 10-5 N
1 erg= 10-7 J
1 eV/d= 1.78266270(54) X 10-36 kg
2.99792458 X 109 esu = 1C
0°C=273.15 K
1 atmosphere = 760 torr= 101325 Pa
a The meter is defined to be the length of path traveled by light in vacuum in 11299792458 s. See B. W Petley, Nature 303,373 (1983).
b At Q2=0. At Q2=m~ the value is approximately 11128.
Source: From Ref. 1.1.
Table 1.2. Atomic and nuclear properties ofmaterials
Nuclear Nuclear Nuclear Nuclear dEldxlmin
total inelastic collision interaction Radiation length Density Refractive
(MeV)
cross cross length length Xo (glcml) index n
section section A-r AI
glcm2
(glcm2) (cm) () is for gas () is (n-I) X 1Q6
Material Z A O'T (bam) 0'1 (bam) (glcm2) (glcm2) () is for gas () is for gas (gle) for gas
H2gas 1.01 0.0387 0.033 43.3 50.8 (4.103) 61.28 865 (0.0838) [0.090] [140]
H2 (B.C., 26K) 1.01 0.0387 0.033 43.3 50.8 4.045 61.28 865 0.0708 1.112
D2 2.01 0.073 0.061 45.7 54.7 (2.052) 122.6 757 0.162 [0.177] 1.128
He 2 4.00 0.133 0.102 49.9 65.1 (1.937) 94.32 755 0.125 [0.178] 1.024 [35]
Li 3 6.94 0.211 0.157 54.6 73.4 1.639 82.76 ISS 0.534
Be 4 9.01 0.268 0.199 55.8 75.2 1.594 65.19 35.3 1.848
C 6 12.01 0.331 0.231 60.2 86.3 1.745 42.70 18.8 2.265
N2 7 14.01 0.379 0.265 61.4 87.8 (1.825) 37.99 47.0 0.808 [1.25] 1.205[300]
°2 8 16.00 0.420 0.292 63.2 91.0 (1.801) 34.24 30.0 1.14 [1.43] 1.22 [266]
Ne 10 20.18 0.507 0.347 66.1 96.6 (1.724) 28.94 24.0 1.207 [0.900] 1.092 [67]
Al 13 26.98 0.634 0.421 70.6 106.4 1.615 24.01 8.9 2.70
Si 14 28.09 0.660 0.440 70.6 106.0 1.664 21.82 9.36 2.33
Ar 18 39.95 0.868 0.566 76.4 117.2 (1.519) 19.55 14.0 1.40 [1.782] 1.233 [283]
Ti 22 47.88 0.995 0.637 79.9 124.9 1.476 16.17 3.56 4.54
Fe 26 55.85 1.120 0.703 82.8 131.9 1.451 13.84 1.76 7.87
Cu 29 63.55 1.232 0.782 85.6 134.9 1.403 12.86 1.43 8.96
Ge 32 72.59 1.365 0.858 88.3 140.5 1.371 12.25 2.30 5.323
Sn SO 118.69 1.967 1.21 100.2 163 1.264 8.82 1.21 7.31
Xe 54 131.29 2.120 1.29 102.8 169 (1.255) 8.48 2.77 3.057 [5.858] [705]
W 74 183.85 2.767 1.65 110.3 185 1.145 6.76 0.35 19.3
Pt 78 195.08 2.861 1.708 113.3 189.7 1.129 6.54 0.305 21.45
Pb 82 207.19 2.960 1.77 116.2 194 1.123 6.37 0.56 11.35
U 92 238.03 3.378 1.98 117.0 199 1.082 6.00 =0.32 =18.95

Table 1.2. (cont.)
Nuclear Nuclear dEldxlmin
collision interaction
(MeV)
Radiation length
length length
glcm2 Xo
A-r Al (glcm2) (cm)
Material (glcm2) (glcm2) () is for gas () is for gas
Air, (20°C, I atm), [STPJ 62.0 90.0 (1.815) 36.66 [30 420J
Hp 60.1 84.9 1.991 36.08 36.1
CO2 62.4 90.5 (1.819) 36.2 [1831OJ
Shielding concrete 67.4 99.9 1.711 26.7 10.7
Borosilicate glass (Pyrex) 66.2 97.6 1.695 28.3 12.7
Si02(fused quartz) 67.0 99.2 1.697 27.05 11.7
Methane (CH,J 54.7 74.0 (2.417) 46.5 [64850J
Ethane (C2H6) 55.73 75.71 (2.304) 45.66 [34035J
Propane (C)Hs) (2.262)
Isobutane «CHl)2CHCHl) 56.3 77.4 (2.239) 45.2 [16930J
Octane, liquid (CHl(CH2)6CH) 2.123
Paraffin wax (CH/CH2)nCHl' (n}=25) 2.087
Nylon, type 6 1.974
Polycarbonate (Lexan) 1.886
Polyethylene terephthlate (Mylar) (C5
H4
O) 60.2 85.7 1.848 39.95 28.7
Polyethylene (monomer CH2= CH2) 56.9 78.8 2.076 44.8 "'47.9
Polyimide film (Kapton) 1.820
Polymethylmethacrylate (Lucite, Plexiglas) 59.2 83.6 1.929 40.55 "'34.4
(monomer (CH2= C(CH3)C02CH3
»
Polystyrene, scintillator (monomer C6H5
CH= CH2) 58.4 82.0 1.936 43.8 42.4
Polytetrafluoroethylene (Teflon) (monomer CF2= CF2) 1.671
Polyvinyltoluene, scintillator
1.956
(monomer 2-CH3
C6H4
CH= CH2)
Barium fluoride (BaF2) 92.1 146 1.303 9.91 2.05
Bismuth germanate (BOO) (Bi4
GePI2) 97.4 156 1.251 7.98 1.12
Cesium iodide (CsI)
1.243
Lithium fluoride (LiF) 62.00 88.24 1.614 39.25 14.91
Sodium fluoride (NaF) 66.78 97.57 1.69 29.87 11.68
Sodium iodide (NaI) 94.8 152 1.305 9.49 2.59
Silica Aerogel 65.5 95.7 1.83 29.85 = 150
NEMA GI0 plate 62.6 90.2 1.87 33.0 19.4
Note: Table revised June 1994. Gases are evaluated at 20°C, 1 atm (in parentheses), or at STP [square bracketsJ.
Source: From Ref 1.1.
Density Refractive
(glcm3) index n
() is for gas () is (n-I) X 106
(gle) for gas
(1.205) [1.29J (273) [293J
1.00 1.33
[1.977J [41OJ
2.5
2.23 1.474
2.32 1.458
0.423 [0.717J [444J
0.509 (1 .356) (1.038)
(1.879)
[2.67J [1900J
0.703
0.93
1.14
1.200
1.39
0.92-D.95
1.420
1.16-1.20 = 1.49
1.032 1.581
2.20
1.032
4.89 1.56
7.1 2.15
4.51
2.632 1.392
2.558 1.336
3.67 1.775
0.1-D.3 1.0+0.25p
1.7

1.4 Coupling constants
What about the characteristic strength of the forces between particles? These
are defined by dimensionless coupling constants whose size gives us a measure
of the strength of the interaction. For electromagnetism we have the familiar
fine-structure constant, 0', which has the strength of roughly 11137, Table 1.1.
The strong interactions have a coupling constant O's which is larger because the
forces are stronger. Why is 0' dimensionless? The dimension of U = e2
lr, indi-
cated by brackets, is energy so [e2
] = [energy· length]. The dimension of nis
[energy· time] and of ne is [energy· length]. Thus 0' = e2
/ne is indeed dimen-
sionless.
0' = e2/ne ~ 11137
O's = .fslne ~ (1/10 - 1) (Table 1.1)
(1.2)
The electromagnetic force is very familiar in everyday life. The existence of a
strong force may be inferred by the observation that nuclei are bound systems
containing one or more protons. Coulomb repulsion of the protons must then
be overcome by another, stronger force. The strong interaction is responsible
for binding the hadronic, or strongly interacting, particles like the proton
together. Nuclei are then bound together by means of a residual 'strong inter-
action' in analogy to the van der Waals molecular binding of neutral atoms.
Our treatment of the strong interactions will be completely phenomenological
and contained only in the last two chapters. We will not discuss the weak
interaction which is responsible for radioactive decay nor the gravitational
interaction. Detectors using non-destructive methods usually use only the
electromagnetic interaction of a particle with the detecting medium.
1.5 Atomic energy scales
Let us now turn towards a description of the energy scales of systems, begin-
ning with the atomic energy scale. The atom is held together by the electro-
magnetic attraction between the nucleus and the 'orbiting' electrons. Since the
proton is so much heavier than the electron, m/mp - 112000 (Table 1.1), it is
essentially at rest and there is only one dynamic mass scale in the problem
which is the electron mass, as illustrated in Fig. 1.1. The bound state lowest
Bohr energy level is Eo.
Eo= - me20'2/2 (Table 1.1, Rydberg)
(1.3)

1.5 Atomic energy scales 13
(3c
Fig. 1.1. Definition of orbital radius and velocity of the electron.
We know experimentally from spectroscopy that the energy levels of bound
systems are quantized. The hydrogen atom is characterized by a quantum
number n defining an energy En = Ein2. An example of data for atomic hydro-
gen is shown in Fig. 1.2 where the discrete atomic spectrum of the emitted light
is obvious and the 1In2
behavior of the lines is evident. Let us compute the Her
wavelength to give us confidence. This line is due to a transition from n = 3 to
n = 2 which causes emission of a photon with energy CEq. 1.3) of 1.89 eY. Using
the Planck constant to convert energy to frequency, A= 2'TTClic)/1.89 eV =
6645 Aas seen in Fig. 1.2. The ionization continuum where the atom is broken
apart and the electron is freed is also seen in Fig. 1.2.
It is easy to 'derive' the Bohr energies by appealing to the minimization of
the total system energy in the ground, or lowest energy, state. The kinetic, T,
plus the potential energy, U, is the total system energy, E, which is a conserved
constant. There is a balance between the negative attractive potential, whose
magnitude increases as the radius of the system, a, decreases and the positive
kinetic energy which also increases as the radius decreases. Since T goes as 11a2
,
while Ugoes as 1Ia, there is a stable minimum. The minimum occurs at the first
Bohr radius, ao' which defines the atomic size scale, 0.54 A, Table l.l. The
Heisenberg uncertainty principle for position and momentum uncertainties
!lp, !lx, !lp !lx ~ Ii supplies the crucial element of this 'derivation'. Throughout
this text p represents particle momentum, and we assume that the uncertainty
in p, !lp, is of order p while the uncertainty in position, !lx, is of order a.

+--A
-< -<
8 0
0
0 Approximate range of 0
,... "'f
14 visible wavelengths --I
-<
<I)
CO':!
L()
"': --~
N (0 ci
- ci ai .,;
(j)
~
0 ,... :g (')
L() II)
-
(j) "'f '<t ~ '? ~
I I
f.-j-'
, ,
1
I' .
' ..
jI:
t..,.
. .<.~ . . .
I I I I I
H" H. H, H
. H, H. H7 H~
"'f
.,; (j)
CO) "'f
~ <0
CO)
I I
H7 H ~ Continuum
(b)
Fig. 1.2. Discrete emission spectrum for atomic hydrogen. (From Ref. 1.7, with per-
mission.)
(/lp)2 11,2
- - + U=E= ---e2/a
2m 2ma2
(1.4)
JE/Ja=O at a=ao
The other characteristic length scale is the Compton wavelength of the elec-
tron, X= hime, which is much smaller than ao
(see Table 1.1). The characteristic
size of the hydrogen atom is the Compton wavelength divided by 0'.
a = X/a=O.54A E=E = -e2
/2a
o ' 0 0
X=hime=O.004A (Table 1.1) (1.5)
{3=O', {3=v/c
For example, if the coupling, 0', went to zero the characteristic size for the
system would become infinite, which means that the system is unbound. A

larger value of a would mean tighter binding or a smaller bound state radius.
Plugging the Bohr radius back into the expression for E we can show that the
electron velocity with respect to that of light, {3, is in fact equal to the fine-struc-
ture constant. Therefore, the atom is fairly loosely bound and its motion is non-
relativistic, {3 ~1.
Perhaps this should not be surprising because we know that, for example,
batteries are driven by processes with atomic (or chemical) energy scales. Hence
we expect them to produce of the order of 1 volt and they do. As another
example, since the atomic energy scales are electron volts, we expect the light
which is emitted in making transitions between those energy levels to be a few
thousand angstroms which is indeed the wavelength of visible light, Eq. 1.1.
Thus, if we knew only that human beings see at the thousand angstrom scale
of wavelength, we could infer that they live in a world with atomic energy levels
that were of the order of electron volts.
1.6 Atomic size
The structure of multielectron atoms is determined by the Fermi exclusion
principle which states that one and only one electron can occupy a quantum
state. Recall that the energy levels in the hydrogen atom are Ell = EJn2, n = 1,
2 ... Higher level atomic states, with larger n, have more momentum, and are
thus less deeply bound. As n increases the electrons are less tightly bound, all =
aon2 (see Appendix B). Therefore in atoms lower n values are filled by electrons
first.
The angular momentum, L, is quantized in units of h, L2=f(f+ 1)h2, f <n
and the number of projections of angular momentum along an arbitrary axis
is Lz = mh, - f < m < f or (2f +1) projections. The electron spin, Sz = shl2 can
be s= +1 or or s= - 1. Thus there are 2(2f +1) electron states for a given f.
These are called 'shells'. Since the centrifugal force pushes us away from the
origin, the effective potential is positive (repulsive) and lower f states lie lower
in energy and hence are filled first (see also Appendix B). The fact that lower n
fill first and that within a given n lower f fill first is sufficient to understand
much of the periodic table of the elements.
The atomic size, a, and ionization potential I (the energy needed to free a
single electron from the element) of the first, Z ~ 36, elements are shown in Fig.
1.3. Note that the atomic 'shell structure' (labeled in the figure) is clearly mir-
rored in the behavior of I, which rises until the shell is filled at the location of
a noble gas. That is n= 1, f =0,2 states (1s). For n=2, f=O, 2 states (2s) plus
f = 1 or 6 states (2p). For n = 3, f = 0,2 states (3s), plus f = lor 6 states (3p). At

(Is) He
(2p)
(3p)
(4p)
J(eV)
(3d)
10 z
a(A) 2.0
1.0
Fig. 1.3. Ionization potential and atomic size for atoms with Z:5 36. The scales are
-10 eV for Iand-l A for tI.
that point n = 4 e= 0, 2 states (4s) intervenes prior to n = 3, e= 2 or 10 states
(3d).
The behavior of the size is to decrease with the filling of the shell. The largest
atoms therefore correspond to metals with a single electron loosely bound
outside a closed (noble gas) shell. The variation of a and I is less than a factor
of about 4 for Z < 36. Thus, to lowest approximation, all atoms have the same
size because as Z increases the force on the electrons becomes stronger but the
Pauli exclusion principle forces the occupation of higher quantum states, n,
which are more loosely bound. The inner closed shells of electrons are tightly

1.8 Cross section and mean free path 17
bound and largely chemically inert and only the outer or valence electrons are
chemically active.
The small size of atoms means that we perceive macroscopic bodies as
continuous. For example, for atoms of loA size, a 1m X 1m X 1m object has
1 billion X 1 billion 'pixels'. Compared to a computer screen of high resolution
this number is enormous. A dust speck 0.1 mm on a side, just visible to us, con-
tains 100000 X 100000 atomic 'pixels'.
1.7 Atomic spin effects
In what follows we will essentially ignore spin effects. The reason we can do this
is that the energy of an electron magnetic moment, f,L=ehl2me' in a magnetic
field, B, is, EB- "",B. Numerically "",-6 X 10-6 eV/kG, Table 1.1. For B = 20 kG,
EB
- 1.2 X 10-4 eV Hence, the spin energies are normally tiny with respect to Eo
which allows us to ignore them for the purposes of describing detectors.
1.8 Cross section and mean free path
Let us now consider the cross section, IT, which describes the probability of
collision. It gets its name from the fact that in some cases it is related to the geo-
metric cross sectional area of the system which is scattered from. The kinematic
definitions of circular frequency, w, wavelength, A, and wave number, k, for an
incident wave packet scattering off an extended object of radius a are shown in
Fig. 1.4. The linear frequency is / and w= 2'TrJ Assuming the velocity of
propagation is c, then/A =c. The wave number k is related to was, k= w/c, k=
1I2'TrA.
The geometric cross section of the scattering centers is classically simply the
cross sectional area of a sphere of characteristic size a.
(he? = 0.4GeV2mb
(1.6)
1mb = 10-27 cm2, 1b= 1O-24 cm2
The geometric cross section for atoms is expected to be hundreds of millions
of barns, while the cross section for nucleons is expected to be on the order of
tens of millibarns. That ratio of 1010
is simply the square of the ratios of the
characteristic sizes of the systems. For reference, the dimensionless quantity
(he)2is 0.4 (GeV? mb which means that a system bound with typical energies

w .. k
Fig. 1.4. Kinematic quantities for wave packet scattering off an extended object of
size ~ a.
of GeV has a geometric cross section of order millibarns. The cross section will
be a fundamental concept in what follows because it quantifies the probability
of a particle to interact with the detecting medium.
It is useful to define a quantity related to uwhich is called the mean free path,
(L). The quantity(L) is defined to be the average distance between scatterings.
The scatterings are distributed in distance x of material traversed as
exp(- NoPxu/A), where u is the cross section to scatter off a nucleus, No is
Avogadro's number, (see Table 1.1), p is the mass density of scattering centers
and A is the atomic weight. Thus Nop/A is the number of nuclei per unit volume
of the medium having density p.
This equation can be easily visualized. Suppose we throw N objects at a slab
of material of thickness dx. We cannot aim at the nuclei, so the chance to
scatter is probabilistic. The number of nuclei per unit area transverse to the
incident x direction is (NoPdx/A). Therefore, if each nucleus has an effective
transverse area of u, the probability to scatter is dN= - N(Nopu/A)dx which
has the solution
N(x)=N(O)exp( - Nopxu/A)
The mean free path(L) is then
(L)- I = Napu/A cm- I
(Lp)- I = Nau/A (glcm2)- 1
(1.7)
(1.8)
We define the mean free path in centimeters or in grams per centimeter squared
by using the mass density p. The latter definition is more compact in that differ-
ent systems will typically have mean free paths which are fairly constant in
g/cm2 units. See, for example, the column of entries in Table 1.2 for AT which
varies by only a factor of about 2 over the full periodic table. As defined, dN/N
= - dx/(L), so that (x )= (L) where the bracket notation denotes an average over
some statistical distribution. For example, taking uatom
from Eq. 1.6, assuming
a gas with p= 10- 3 glcm3 (Table 1.2) and A = 10 we find an atomic mean free

1.9 Partial waves and differential cross section 19
10.15 Argon
N
E
u
b
1 10
£ (eV)
Fig. 1.5. Atomic cross section offargon as a function of projectile energy. (From Ref.
B.l, with permission.)
path of (L)atom ~ 5X 10-5
em = 0.5 (..Lm. In contrast, using anue' we find (L)nue~
5.5 xl 05
em in the gas, or~ 550 em in a solid of density equal to 1 g/cm3• Thus
the atomic mean free path in a gas is of order (..Lm, which we refer to in Chapter
8, while the nuclear mean free path in a solid is of order meters. Clearly detec-
tors of atoms can be rather compact.
The atomic cross section for scattering on argon as a function of projectile
energy is shown in Fig. 1.5.1t should be noted that, although there is an energy
dependent structure, the estimate given in Eq. 1.6 is certainly a reasonable
representation of the typical size of the atomic cross section. The two decades
shown span the region from 107 to 109 barns.
1.9 Partial waves and differential cross section
In order to motivate the geometric cross section given in Eq. 1.6 let us very
briefly review the quantum mechanical theory of scattering [6]. Some addi-
tional detail is given in Appendix B.
The wave function of a scattering state, P, consists of an incoming plane
wave and an outgoing spherical wave with a scattering amplitude, A, which can
be decomposed into individual partial waves since central forces conserve
angular momentum. The wave number is k which is related to the momentum
pas p == hk. In the spinless case the conservation of angular momentum means
that the quantum number eis conserved. The elastic differential cross section,
or the distribution function for the scattering angle, da!dn, is related to the

square of the scattering amplitude. The solid angle is the spherical area element
dD = d(cos (J) de/>. Note that A((J) is dimensionless and that the dimensions of u
are inverse momentum squared, or length squared, as expected.
In the case of purely elastic scattering the amplitude is
1[1' -7 eikz +A((J)(eikrlkr)
A((J) = ~ 2:(2e + 1)(eiSl - 1)P,(cos (J)
2l e
du = IA((J)121k2
dD
(1.9)
The phase shift De is caused by the scattering interaction; De -7 0 means A((J) -7
O. Pe(cos (J) is the Legendre polynomial of index f. The total scattering cross
section, u, integrated over all scattering angles can also be decomposed as a
sum over partial waves.
u= :: 2:(2f +1)sin2oe
e (1.10)
471"
= k2 [Im(A(O»]
The optical theorem relates the imaginary part of the forward scattering ampli-
tude, Im(A(O», to the total cross section, u. We can relate the total cross section
to the index of refraction in order to make the connection to optics. As we will
see in Chapter 3, a wave propagating in a medium is characterized by an index
of refraction n. Since the phase factor of the associated field is i(k .x - wt) and
wlk = c/n, the attenuation of the wave is exp[- (lmk)x]. Since the probability
goes as the square of the wave function, the mean free path is (L) = 112 Imk=
C/[2wIm(n)]. (See Chapter 3.)
Unitarity is another incarnation of the conservation of probability. Each
partial wave, labeled by f, has a unitary upper limit which, as can be seen from
Eq. 1.10, occurs when the sine of the phase shift 8eis a maximum. The center
of mass (CM) wave number is k, while the CM energy is Vs. (See Appendix
A.)
471"
ue< k2 (2f+ 1)
k=p*=Vs/2, p=nk, n= 1
s=(CM energy)2
(1.11)
If there are absorptive processes then the phase shift becomes complex, and we
must distinguish between elastic scattering, uEL
' inelastic scattering, ul' and the

1.9 Partial waves and differential cross section 21
1.0
/I
Fig. 1.6. Ratio of elastic to inelastic cross section for proton scattering off nuclei of
different atomic weight A. A 'transparent' nucleus has rrEL/rrl~O while a 'black'
nucleus has rrEL/rrl~ 1.
total cross section, CTT" In the absence of absorption CTEL = CTT , CTr= O. A classi-
cal example with non-zero inelastic cross section is scattering off a completely
absorbing body. In that case CTEL =CTp CTT == CTEL +CTr =2CTEL. The intermediate
case of partial absorption is discussed in the references given at the end of this
chapter, e.g. Ref. 6, and in Appendix B.
The ratio of CTEL/CT
r is shown in Fig. 1.6 for proton scattering off nuclei (see
Table 1.2). As A ~ 0, CTEL/CTr ~ 0 indicating little absorption, while heavy nuclei
look like 'black' fully absorbing objects, since as A ~ 00, CTEL/CT! ~ 1. These facts
will be applied in our description of calorimetry in Chapter 12.
A geometric interpretation of the cross section is possible if the incoming
wave suffers no scattering when it is outside an absorbing object of radius a but
is totally absorbed when it is inside radius a. In that case there is an absorption
of all angular momenta, L, up to some maximum which is proportional to the
radius.
emax
~ka(L==rXp, L~he, p=hk)
emax 4'IT (ka)
CTT~ ~ CTe= k2 ~(2e+ 1)
o 0
(1.12)
~4'ITa2

Indeed, the cross section is proportional to the geometric cross section of the
object. The fact that the cross section exceeds the physical area is due to the
quantum mechanical wave nature of the scattering. Basically in the presence of
absorption there must be elastic 'shadow' scattering. At high energies the
absorptive diffraction pattern is confined to an angle ()~ 1 where ()~!1p-lP~
Ala~liJap~ lIt'rnax' since the uncertainty principle implies that there is an irre-
ducible momentum impulse !1PT given to the wave in scattering off an object of
size a, !1pT~liJa.
1.10 Nuclear scales of energy and size
We now turn to the cross section and size scale characteristic of the atomic
nucleus. Basically we think of a nucleus as containing Z protons plus (A - Z)
neutrons or A 'nucleons' in total. If we consider them to be spherical objects
with a size of order the Compton wavelength of a proton, Xp
' packed together
in a nucleus of volume V, it is clear that the size of the nucleus, aN' scales as the
atomic weight, A, to the 113 power.
4'TT 4'TT
V= - a3 =A- X3
- 3 N 3 p
a ~X A1I3
N p
(1.13)
Notice that the Compton wavelength of a proton, Xp
' is about 0.2 fermi.
Referring to Eq. 1.4, a= XIa, and knowing that the strong coupling constant as
is large, we expect a proton size of about Xp. Using the derived geometrical
interpretation of the total cross ection, we expect scaling of the nuclear cross
section, (TN' as the 2/3 power of the atomic weight, and the scaling of the mean
free path, (L) as the 1/3 power of the atomic weight. In Table 1.2 (L) is given,
in g/cm2
units, as the column labeled "T
(Eq. 1.8)
(1.14)
~(35 g/cm2)AI/3
For example, a detection device which absorbed all the energy in an incident
proton might take roughly 10,11 since the secondary debris may itself interact.
Thus, a steel device (hadron calorimeter - Chapter 12) could be expected to be
roughly 1.6 m 'deep'. This device is less compact than a detector of atoms.

1.11 Nuclear cross section 23
100
total
-----------
.. .
10
100
J3
E
b
pp
10 elastic
II
-----I
.--,-
•
5 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
0.1 10 100 1000 104
105
106
107
Pbeam (GeV/c)
I I I I II IIII I I I I I III I I I II I III
1.9 2 3 4 5 7 10 20 30 50 100 200 500 1000
Ecm (GeV)
Fig. 1.7. Proton/antiproton cross section on proton as a function of projectile energy.
(From Ref. 1.1.)
1.11 Nuclear cross section
In Fig. 1.7 are shown the proton-protron and antiproton-proton scattering
cross section as a function of energy. The geometric cross section is about 30
millibarns which is comfortably within an order of magnitude of the observed
total cross section over a substantial range of energy.

10
A
100
Fig. 1.8. Proton cross sections on nuclei, as a function of atomic weight, A. The
straight line has A2/3 functionality.
The nuclear cross section, atomic number Z, and atomic weight A are given
in Table 1.2 along with several other properties of materials. For different
materials the total cross section, O"T' the inelastic cross section, 0"1' the inelastic
mean free path, AI' and other quantities which will be discussed later (the ion-
ization, the ionization per unit length and the radiation length) are all given in
Table 1.2. This table serves as the source of data for many of the numerical
calculations given in later chapters of the text. For example, using Table 1.2 we
find that aIm long liquid hydrogen target has a 14% (NopLO"/A =0.14) prob-
ability that an incident proton will interact in traversing it.
In order to display the expected functional dependence of the inelastic cross
section, that quantity is plotted as a function of the atomic weight in Fig. 1.8.
It is clear that the expected power law dependence of the cross section going as
A2/
3 describes the data well.

0.8
~0.6
.n
E
b
0.4
0.2
+
+
1P total
---- . ....... - ..
O ~--~-J~~~~~--~~~~~~----~~~~~~--~
0.1
I
2
1.1
I I I ' I
10
Pbeam (GeV/c)
3 4
I I I II
4 5 6
Ecm (GeV)
5 6 7 8 910
I I I I I I
I I I I
7 8 910 15
100 200
15
I
I I
20 25
25
-yp
-yd
Fig. 1.9. Photon cross section on nucleons as a function of photon energy. (From Ref.
1.1.)
In the case of photons scattering off protons, a compilation of the energy
dependence of the total cross section is shown in Fig. 1.9. Note that the scale
is about 0.2 millibarns which, compared to the nucleon scattering case, is
reduced by a factor of about 100. As shown in Eq. 1.2, this is roughly the ratio
of the strong to the electromagnetic coupling constant. The factor of a can be
thought of as the probability that a photon will virtually disassociate into a
strongly interacting particle.
The energy dependence of the cross section after some low energy structure
at Vs~2-3 GeV is reasonably constant over several decades in energy. In
analogy to the transition from nucleon- nucleon to nucleon-nucleus cross sec-
tions, in Fig. 1.10 we show the cross sections of photons on nuclei.
The high energy behavior is fairly straightforward. The energy dependence
above about 1 GeV is very slight. However, the low energy behavior of the
photon- nucleus cross section is rather complicated. At energy scales of a few
keY the photoelectric effect, which will be discussed in Chapter 2, is the dom-
inant process. In the intermediate range, at energy scales of order 1 MeV, the
Compton cross section, discussed in Chapter 10, becomes the dominant

!
1
1Mb
..c
~:r 1 kb
~
~
'"
~
1b
10mb
'r
O~~
Carbon (Z = 6)
0- experimental 0tot
~
<IS
-...
Ul
j
1Mb
§ lkb
~
q)
Ul
Ul
Ul
e
C)
1b
".,
'..
'0
.V~
,...... 0
°p.e.
°coherent
0. h '
lnco , , -'
,
,
,
i
,
Lead (Z = 82)
o - experimental 0tot
KN
10 mb ' Ii' r, "
L'~__L
' _
· __~~~____~!~~~~~d~~-L__~~__~__~
lOeV lkeV 1 MeV
Photon Energy
1 GeV 100 GeV 10 eV 10keV 1 MeV
Photon Energy
1 GeV 100 GeV
Fig. 1.10. Photon cross sections on carbon and lead as a function of photon energy. (From Ref 1.1.)

Exercises 27
process. At high energies radiative processes such as pair production, which are
constant in energy, dominate. We will discuss all of these processes in sub-
sequent chapters. The cross section for photons on nuclei above a few MeV is
of order 100b which is intermediate between atomic (Fig. 1.5) and nuclear (Fig.
1.8) cross sections.
Some interaction rates are remarkably small. For example, we are all bathed
in a sea of photons of temperature 2.3 K with a blackbody frequency spec-
trum which are a relic of the 'big bang' creation of the universe. The number
density of these photons is about 400 photons/cm3 which implies a flux of
roughly 1.2 X 1013
photons/(cm2 s). However, since these photons are below the
energy threshold to excite any bound atoms (photon energy~kT= 1140 eV at
T = 300 or kT~ 114000 eV, k = Boltzmann constant, see Table 1.1), our atoms
are transparent to the photons. Therefore, we do not directly experience them;
they only appear in sensitive detectors. For example, they can be seen as the
'snow' on our personal photon detectors - our TV sets. If you tune to a blank
channel, some of the speckles you see are relic photons from the birth of the
umverse.
Exercises
1. How far does light travel in a time interval of 1 nanosecond (ns) = 10-9 s?
2. How many electrons cross the plane of a wire carrying a current of 1
ampere in 1 s? In 1 ns?
3. What is the size of the dimensionless quantity ka for the Ha line shown in
Fig. 1.2? The assumption that the wavelength of the light is much greater
than the size of the atom is often made. Is it valid in this case?
4. Fill in the steps to calculate a at the energy minimum for the hydrogen
atom. Show that at a = ao' U= - mc2
a2/2 and T= - u/2. Thus show that T
= mv2/2 =p2/2m = mc2f32/2 or f3 = a.
5. Compute the number of quantum states for n = 1, 2 and 3. Identify where
they appear in Fig. 1.3. Identify the 'metal' which has a single loosely
bound electron outside a shell at Z = 1, 3, 11, 19.
6. What are the radius and binding energy of an innermost electron com-
pared to aoand Eo for an element with atomic number Z? Ignore the effect
of the other electrons. Modify the derivation of Eq. 1.4.
7. Show that (IiC)2 is equal to 4x 1014 (eV2b).
8. Show that for a nuclear cross section of 0.23 b on carbon the mean free
path is about 38 cm using the data given in Table 1.2.
9. Consider the collision of an electron with 100 eV energy with an atom of
radius 10 angstroms. Show that the maximum partial wave excited has

1- 50 and that the diffraction pattern is confined to forward angles of
about 1 degree.
10. Suppose an electron is bound by 1eV in an atom of silicon. Consider a
cube 1em on a side. Estimate how many electrons are thermally ionized in
this sample at room temperature using Boltzmann statistics.
References
[1] Review of particle properties, Phys. Rev D. PC
lI'licles alld Field 50 (1994).
[2] Twentieth Century Physics, ]' Norwood Jr. Prenlice-Hall, Inc. (1 976).
[3] Elementary Modem Physics, A.P. Arya Addi on-We ley (1974).
[4] Principles of Modern Physics R.B. Leighton McG raw-Hill Book Company Inc.
(1959).
[5] Atomic Physics M. Born Hafnor PubJi bing C mpany (1935).
[6] Quantum Mechanics, L.r. Schiff McGraw-J-Ij(( Book ompany (1955).
[7] An Introduction to Quantum Physics, A.P. French and Edwin F. Taylor w.w.
Norton & Company Inc. (1978).

Part II
Non-destructive measurements
The particles emitted in a collision, Fig. 1.1, have position, momentum, charge,
and other properties (e.g. lifetime) which we wish to measure. If the interaction
with a detecting medium transfers but little energy to that medium, the
measurement is called non-destructive. Within this category we distinguish
between measurements of time and velocity (Chapters 2-4) and measurements
using ionization (Chapter 6) but limited by scattering (Chapter 5) of the tra-
jectory of the particles in the detecting medium (Chapters 7-9).
In the first case physical processes which depend on velocity are used, while
in the latter the trajectory in electric and magnetic fields is used (Chapters 7-9)
to infer the position, momentum, and charge of a particle.
Part IIA
Time and velocity
In Chapter 2, we examine the photoelectric effect whereby light is converted to
an electrical signal. Devices using this effect are commonplace; for example
photocells which are used to control the doors of elevators. By utilizing photo-
multiplier tubes and scintillating materials, precise time measurements can be
made. These 'clocks' are then used to measure velocity as the time to go to a
fixed distance. In Chapter 3 we turn to the Cerenkov radiation which is emitted
at a velocity dependent angle when a charged particle moves with a velocity
which exceeds the velocity of light in a medium. The emitted light can be con-
verted to an electrical signal using the techniques of Chapter 2. Chapter 4 con-
cerns x-ray radiation emitted by a charged particle in a medium with index
of refraction < 1. This 'sub-threshold' Cerenkov photon emission is used to
measure particles moving at velocities very near to the speed of light.
29

2
The photoelectric effect, photomultipliers,
scintillators
There is a crack in everything, that's how the light gets in.
Leonard Cohen
Time is nature's way of keeping everything from happening at once.
Anon
Of the physical scattering processes introduced in Chapter 1, the photoelectric
effect is our starting point. The effect is due to the absorption of a photon by
an atom with subsequent electron emission. We first derive the photoelectric
cross section and examine the regime (low photon energy) where it dominates.
This chapter then takes up our first extended discussion of a detector, the pho-
tomultiplier tube. Applications of the device include time of flight measure-
ments with fast scintillators, and coincidence logic. A discussion of light
collection in scintillation counters explores both classical 'light pipes' and
'wavelength shifting' techniques. Other devices also require a knowledge of the
photoelectric effect. For example see Chapter 4 where the transition radiation
detector performance depends critically on photoelectric absorption of the
emitted x-rays.
2.1 Interaction Hamiltonian
As we saw from the data shown in Chapter l, the low energy interaction of a
photon is dominated by the photoelectric effect. This effect was first explained
quantitatively by Einstein, using the new quantum theory and treating the
photon as a particle. A schematic of the process in which there is an incident
plane wave with wave number k, wavelength A, and frequency w, is shown in
Fig. 2.1. Also indicated is the energy level diagram appropriate to the kine-
matics. The atom is initially in a bound state with negative energy - e and is
described by a wave function uo(r). The final state for the electron has momen-
tum p and exists in the ionization continuum as a free particle.
The free particle Hamiltonian H o' is modified in the presence of an electro-
magnetic field by an interaction term arising from a replacement of the
momentum, p ~ p- ieA where A is the vector potential of the electromagnetic
field. This replacement is valid in both classical mechanics and quantum
31

32 2 The photoelectric effect, photomultipliers, scintillators
....
I---____~ k
w
Fig. 2.1. Energy level diagram for the kinematics of the photoelectric effect.
mechanics. It leads to an interaction term in the Hamiltonian, HI' which is pro-
portional to the vector potential, A, of the photon and the momentum p of the
electron.
Ho=p2/2m
p-7p-ieA
HI-Ce~A)
The kinematics for classical energy and momentum conservation are
-e+hw=p2/2m
l!.e+hk=p
(2.1)
(2.2)
Ignoring the small energy of the recoil atom, the final state energy is simply the
kinetic energy of the ionized electron. The wave vector k refers to the initial
photon state, while p refers to the final state free electron. The initial electron
momentum Pe is not observed. Therefore this free variable is 'integrated over'
in the sense that the initial state wave function, uo(r), contains the probability
to obtain different initial electron momenta.
2.2 Transition amplitude and cross section
In non-relativistic perturbation theory the lowest order transition amplitude is
the matrix element, A, of the interaction potential between the unperturbed
initial and final states.
- - e (A·p)u (r)dr
e fip'rlh
m 0
(2.3)

2.2 Transition amplitude and cross section 33
Details of the calculation are given in Appendix C. Here we simply sketch the
steps.
We need an expression for the bound state wave function of the inner shell
electrons in the lowest angular momentum state. Recall that the square of the
wave function is the probability density. Since the characteristic size for the
state is the Bohr radius, a, the wave function is contained in a volume < 'Ira3
or
luo(r)12~ Ihra3
• Referring to Appendices Band C, the bound state wave func-
tion is:
I
u (r) ~-- e-rla
o ~
(2.4)
ao=Xia, a~aiZ
The inner electrons in an atom 'see' the full charge, Z, of the nucleus
unscreened by the other electrons and thus are bound tightly. Therefore, their
radius is reduced with respect to the hydrogenic Bohr radius by a factor liZ.
The matrix element A is proportional to (ADia)4 where ADB is the outgoing
electron de Broglie wavelength ADB =.h/p. The smallness of the amplitude is due
to the poor overlap integral for A since a ~ ADB• Basically, it is very unlikely to
find a high momentum in the initial state. Thus the photoelectric cross section,
(TPE' scales in a complicated way with photon energy. The main physics contri-
bution is the (ADia)8 = (hlpa)8 behavior coming from the square of the matrix
element. As before, X is the Compton wavelength of the electron.
(TPE ~aJ2[~~J[ADBla]5
(2.5)
hw~p2/2m (Eq.2.2)
The cross section falls rapidly with incident photon energy; in this approxima-
tion as lIw7l2. Therefore the photoelectric effect is only important at low
photon energies as is, indeed, clear looking back at Chapter 1.
If the photon has an energy which is equal to the energy of one of the inner
electrons, an enhanced absorption will occur. The simple approximate gener-
alization of the Bohr result for different principle quantum numbers, n, and for
inner electrons bound to atoms with atomic number Z is given below. The effect
for En is taken care of by the replacement U= e21r ~ U= (Ze)(e)/r or a ~ Za.
[
me
2
J
En=- 2 (Za)2 In2
(2.6)
=-13.6eV [z2ln2]

10
w
8
~
.~ 6
Q)
C
4
2
0.5
Kp Ka
t t
CI CI
~ ~
o 0
~ ~
0.7
A (A)
0.9
Fig. 2.2. Data on the intensity of emitted x-rays as a function of wavelength in
various heavy elements. The 'quantized' lines corresponding to the binding energies of
the inner electrons are very evident. (From Ref 1.7, with permission.)
Some representative data on the intensity of the emitted x-ray for the inverse
process in various heavy elements is shown in Fig. 2.2. In this inverse process,
e+A ~ 'Y +A*, elements under electron bombardment emit x-ray photons.
The photon emission occurs when the atom, A*, de-excites by an inner elec-
tron transition accompanied by the emission of an x-ray with a quantized wave
length. The scale for Ais A, or keY energies, as expected from Eq. 2.6.
Data on the relationship between the square root of the emitted frequency
and the atomic number is shown in Fig. 2.3. As expected from Eq. 2.6, the
bound state energies, and therefore the emitted x-ray frequencies are propor-
tional to z2, which is called Moseley's law. The mechanism of x-ray emission
by electron bombardment is the basis of medical and dental radiology and is
now a commonplace.
The inverse mean free path, in (glcm2)-I, as a function of the photon energy
incident on lead is shown in Fig. 2.4. We calculate the inner electron binding
energy for lead for the first two principle quantum numbers. The computed
energies from Eq. 2.6 are 91 and 23 keY respectively. As seen in Fig. 2.4, there
is pronounced structure at an incident photon energy corresponding to these

24 -
22 -
20
Q)
:§ 18
•
l<
- 16
0
4
2
2.2 Transition amplitude and cross section
.Iv - (Z-1)
10 15 20 30
Atomic Number Z
35
Fig. 2.3. Data on the relationship between the x-ray wavelength and the atomic
number. The hw=E-ZJ behavior expected from Eq. 2.6 is observed. (From Ref. 1.7,
with permission.)
two energies. We compare the photoelectric cross section to the Thomson cross
section, O'p for photon elastic scattering off free electrons given in Table 1.1
and derived later in Chapter 10. Assuming that Thomson scattering is inco-
herent, the sum over Z electrons is simply Z times the cross section off a single
electron.
32'TT ( m )7/2
O'PE ~-3- y'2(Za)4Z nw (a.i:)2
8'TT
O'T~3Z(aX)2
O'pE/O'T~ 4y'2(Za)4(mec2/nw)112
(2.7)
Therefore, for heavy atoms where Za ~ 1, we expect the photoelectric effect to
dominate over Thomson scattering for energies, nw<mc2 ~O.51 MeV. Indeed,
this is the observed behavior and the approximate energy region where the two
cross sections are comparable. For example, in lead, a photon with 10 keY

100
10
1.0
C'I
.......
~
N
E Compton

u
---
0.1 -....
.... ........
,~
a.
-
::t . ....
. ....
Photo
.... ,
0,01
....
0.001 L-_ _----.Jl -_ _--'-'-_ _~_-2~---l
0.01 0.1 1.0 10 100
Ey(MeV)
Fig. 2.4. The inverse mean free palh, 1/(L)p, for photons incident on lead. The d
tinct physical mechanism of photoelectric effect Compton scattering and pair pr
duction are evident, along with the resonant' behavior near the bound state energ
indicated by Eq. 2.6. (From Ref. B.I, with permission.)
energy has (TPE/(TT~6.8 X 105
or (TpE~0.46 Mb. This estimate from Eq. 2.7
reasonably close to the value which can be read off from Fig. l.10.
At photon energies below about 1MeV in lead the photoelectric effect dom
inates. Above 1MeV the Compton effect (relativistic elastic photon scattering
see Chapter 10, then dominates briefly before pair production rises rapidly
be the major physical effect at high energy. At low energies a power law beha
ior is observed, as expected from Eq. 2.5 which gives a straight line on t
log-log plot of Fig. 2.5. The mean free path, (L)p, for photon attenuation
shown, as a function of photon energy, in different materials in Fig. 2.5 f
energies from 1keV to 100 GeV. At high energies the constant value of the pa
production cross section is evident as is strong dependence on the atom
number, (L) ~ Xo~ liZ, where Xo is the radiation length, to be defined later.
At intermediate energies the incoherent nature of the elastic Compton sc
tering implies that (L) is independent of Z, as is seen for photons of 1 to
MeV energy.

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When he reached Mont-Mer, the testimony continued, he had given
a fictitious name, gained the sympathy and credence of the doctor
and undertaker, and finally, by a clever ruse, escaped from town as
custodian of the body of the very man whom he had planned to kill.
Knowing that Marstan was dead, he felt himself completely secure
and foot-free to carry out his designs. The only person upon whom
he did not reckon, because he didn't know of his existence, was
Richard Glover.
The one missing link in the story was supplied by evidence which,
although circumstantial, seemed undeniably convincing to the jury.
The woman who had notified the coroner must also have been an
inmate of Rest Hollow, the mistress of Marstan, who had lived in
ease and luxury, unknown to the physician's employer or any one
else. She knew that her reputation lay in Kenwick's hands. She was
tired of Marstan and was eager but afraid to escape. The criminal
had supplied her with the means at small cost. The time of the
disclosure of the crime had been skilfully worked out between them.
And it had been executed with a masterly skill. Depot authorities had
reported later that a woman traveling alone had bought a ticket on
the late train for San Francisco that evening. The station-agent
remembered the incident perfectly. By good luck Kenwick had caught
the same train. They had traveled to the city together.
Glover, who had been recalled to the stand and was giving this
testimony, stated that upon dismissing the detective from his employ
he had followed the case himself and was certain that Kenwick and
his accomplice had lived together intermittently in San Francisco,
and that he had been supplying her with funds.
It was at this point that Roger Kenwick, who had been sitting like a
man frozen to his chair, suddenly electrified the court-room by
springing to his feet. He had forgotten his surroundings, was
contemptuous of the formalities, oblivious to everything save the
insolent assurance in Richard Glover's eyes, and the steady gaze
with which Marcreta Morgan's brother was regarding him. His
sensitive nostrils quivered like those of a highly strung race-horse.

His hands, those hands so impatient of delay, were clenched till the
knuckles showed through the drawn skin like knobs of ivory. He
struggled to speak but no words came. Then he became aware of
the fact that the sheriff was forcing him back into his seat. Dayton
leaned over and whispered sharply to him. "Sit down, man. You'll kill
your case. What do you want them to think of you?"
The words recalled him to his surroundings. From sheer physical
weakness he sank back into his chair. Another moment intervened
while the auditors relaxed from the moment of tension. Then out of
the deathly silence came Dayton's voice again, calm and with no
trace of excitement.
"You say that when you first discovered the prisoner in San Francisco
you employed a detective to help you on his case, Mr. Glover. Look
around the court-room. Is that man present?"
"He is." There was a shade of reluctance in the reply.
"What is his name?"
"Granville Jarvis."
The next moment Glover had stepped down from the stand and
resumed his place at the far end of the long table. Dayton leaned
across to his client. "Jarvis?" he inquired, his pencil poised above his
pad. "Granville Jarvis; is that the name?"
The light had gone out of Kenwick's eyes and the fire out of his
voice. He had crumpled down in his chair like a man suddenly
overcome with a spinal disease. He looked at Dayton with dead
eyes.
"The name," he said bitterly, "is Judas Iscariot!"

CHAPTER XVIII
It was two o'clock before court, which had been dismissed for lunch
after Richard Glover's testimony, convened again. During the noon
hour a tray containing the only tempting food which the prisoner had
seen since his incarceration was brought up to his cell. It had
become apparent to the jailer that he had friends, and perhaps he
was moved thereby to a tardy compassion. But Kenwick, despite
Dayton's admonition to "Brace up and eat a good meal," waved it
indifferently aside.
"I'm done for," he said simply. "I don't see how any twelve men
could hear the evidence that was presented this morning and find
me innocent. And by the time Jarvis gets through telling anything he
likes, and proving it——Well, it appears that every person who has
been connected in any way with me since this trouble fell upon me
has taken advantage of my misfortune to enrich himself. I don't care
much now what they do with me. When you lose your faith in
humanity it's time to die. I'm no religious fanatic, Dayton, but for
these last two months I've thanked God on my knees every night of
my life for having brought me back into the light. Now I wish that I
had died instead."
Dayton made no further effort to rouse him from his despair. For
although not of a sensitive or particularly intuitive temperament
himself, he had come to realize the utter impossibility of finding this
other man in his trouble. "You don't seem to have much faith in me,"
was all he said as he made some notes on the back of an envelope.
But he finally induced his client to eat some of the food upon his tray
and after the first few mouthfuls Kenwick was surprised to find that
he was ravenously hungry.

"That's something like," the lawyer approved, as they made their
way back through the court-house grounds. "Now you're good for
another three hours."
It hadn't seemed possible to Kenwick that he was, that his nerves
could stand the strain of hours and hours more of this, and there
was no assurance that the ordeal would end to-day or to-morrow.
But Dayton's easy assurance gave him a new grip upon himself.
They found the audience waiting and eager. None of them seemed
to have moved since they had been dismissed for recess two hours
before. Only the jury were absent, but five minutes after Kenwick's
arrival they filed in and took their places. The district attorney
appeared to have lost interest in the case. He sat staring out of the
window with a sort of wistful impatience as though he were
visualizing a potential game of golf. Dayton glanced at some notes
on the table at his elbow and issued his first command. "Call
Madeleine Marstan."
In response to this summons one of the veiled women in the rear of
the room rose and came forward. She was quietly dressed in a gown
of clinging black silk and a black turban with a touch of amethyst.
Every eye in the court-room was fixed upon her, but she took the
oath with the unembarrassed self-possession of one long
accustomed to the public gaze. Kenwick, turned toward her, detected
a faint odor of heliotrope.
"Where do you live, Mrs. Marstan?" Dayton inquired.
She gave a street and number in San Francisco.
"What is your occupation?"
"I am an actress."
"Do you know the prisoner?"
Without glancing at him she replied, with her unruffled composure,
"I do."

"How long have you known him?"
"About two months."
"Describe the occasion on which he was first brought to your
notice."
She settled back slightly in her chair, like a traveler making herself
comfortable for what promised to be a long journey. "It was on the
afternoon of November 19 that my husband, a physician, came into
our apartment in San Francisco and announced to me that he had
just secured a remunerative position with a wealthy man down at
Mont-Mer. He said that the work would begin immediately and we
must be ready to leave the following day. I asked him for more
details and he told me that the position was a secretaryship which
would involve little labor and afford us a luxurious home with
excellent salary. He had never been a success in his profession,
owing chiefly to the fact that he was dissipated, and I had seriously
considered leaving him and going back to the stage. But I had
decided to give him another chance, and since he appeared to find
my questions concerning this new work annoying, I agreed to go
and allow him to explain more fully when we should arrive.
"We went down in our own car and arrived at Rest Hollow in mid-
afternoon. My husband showed me over the house and grounds and
I thought I had never seen such a beautiful place. There was no one
about when we came, and after he had given me every opportunity
to be favorably impressed with the new home, we went to an
upstairs sitting-room in the left wing, and he told me, while he
smoked one of the expensive-looking cigars that he found there,
further details concerning his employer. I learned that he was an
invalid, a young man by the name of Roger Kenwick, who was
recuperating from too strenuous service overseas. We discussed the
matter for only a few minutes before my husband announced that it
was time for him to go to the depot and meet his charge, who was
being brought up from Los Angeles by the previous companion, who
had taken him there to be outfitted with winter clothes.

"This development in the case rather startled me, and as we walked
along the upper hall and over into the right wing, which he said had
been recently cleaned but was not to be used, I demanded more
specific details concerning the arrangement. I wanted particularly to
know why there was to be a change of 'secretaries' and whether the
young man himself was willing to accept the companionship of
people whom he had never seen.
"My husband had been drinking. I think he must have found a well-
stocked wine-closet at Rest Hollow. And he finally grew furious at my
insistence. The more angry he became the more he betrayed to me
the fact that there was something to conceal. He had never told me
the name of the man who had offered him this position, but I knew
that there must be an intermediary. While I continued to question
him he opened the door of one of the rooms in the right wing,
hoping, I suppose, to distract my attention. We went on with our
discussion there. And at last I refused pointblank to have anything to
do with the affair, and told him that I was going to leave him and go
back to the profession that would afford me an honest living. This
infuriated him. He lost all self-control and confessed then, what I
had already begun to suspect, that young Kenwick was a mental
patient and had been in no way consulted in the arrangement. This
disclosure terrified me, for I knew that my husband was not a
competent person for such a responsibility. Hot words followed
between us, and ended in his knocking me senseless on the floor.
When I recovered consciousness, perhaps an hour later, I found
myself locked into the room with no possible means of escape. The
blow had dislodged a vertebra and I was in horrible pain. For a long
time I lay on the bed massaging the injured place and trying to get
comfortable.
"Early in the evening I heard some one being dragged into the
house from the rear. I was unable to see anything, of course, but I
could distinctly hear footsteps and the subsequent running around of
an attendant. I concluded that my husband had returned drunk, and
I was relieved to know that he had evidently not brought the patient

with him. I knew that I had no recourse but to wait until the stupor
had worn off and my husband came to release me. I spent a wakeful
and wretched night. In the morning——"
Here a vivid and convincing description of her first encounter with
the patient ensued. She drew a clear-cut picture of her own horror in
hearing footsteps outside her door and of having the name "Roger
Kenwick" called in through the closed portal; of her terror at finding
herself unaccountably alone with a man whom she believed to be a
violent maniac.
Here Dayton held up the narrative. "What evidence did he give to
convince you of his insanity?'
"None at first. He seemed to talk quite rationally, and fearing that I
might make him angry if I kept silence, I made evasive answers to
his questions. He prepared food and sent it up to me at what I know
now must have been immense physical cost to himself. I had come
to the conclusion that he, like myself, was the victim of some foul
conspiracy and had decided to risk confiding in him when all at once
his manner changed. He began to talk wildly of finding a loaded
revolver and of shooting any one who came near the place. A few
minutes later, for no apparent reason, I heard him smash a window
in the room just under mine. My terror increased a hundredfold, for I
know absolutely nothing about the proper care of the insane. Late
that same night I heard him crawl out through the broken window,
and he called up to me that he was either going to get help or
commit suicide.
"Almost insane myself now with terror, I waited until I heard his
footsteps grow faint in the distance, then worked at the lock of my
door, and at last succeeded in picking it with a pen-knife. Then I
rushed downstairs, turned on the lights, and tried to make my
escape. I had several of my own personal keys in my possession,
and with one of these I opened the front door, which had been
securely locked, I suppose by the gardener. My one frantic object
was to get away and find my husband.

"But just as I got the door open I heard a shot fired from the side of
the house. I hurried around there, and when I reached the spot
from which the sound had come, I found just what I feared—a man
lying dead under the window. I thought, of course, that it was the
patient who had killed himself in a mania, as he had threatened to
do. Filled with horror at the idea of leaving him there alone and
uncovered in the storm, I ran back to the living-room, picked up the
first thing at hand (an Indian blanket), and threw it over him. Then I
hurried to the nearest house, about a mile away, and gave the
alarm.
"Believing that it was my husband's neglect that had caused the
tragedy, my purpose was to find him and get his version of the story
before I betrayed him. So I furnished no further information to the
authorities in town save that Roger Kenwick, the inmate of Rest
Hollow, had committed suicide. I really knew nothing else about it
but that bare fact.
"But that night I discovered, when I reached Mont-Mer, that my
husband had been killed in an auto accident while coming out from
the depot. I went to the morgue and identified his body, ordered the
remains to be shipped north for interment, and left, unknown to any
one, on the late northbound train. The undertaker told me that there
had been no other victim of the tragedy, so I reasoned that the story
which Mr. Kenwick had told me about a sprained leg was true, after
all, that he had been injured in the catastrophe and had, by a
curious freak of chance, found his way back alone to the very place
that was awaiting him and in which he had been living for the
preceding ten months."
Dayton declared himself satisfied with the testimony and turned the
witness over to the prosecution. The district attorney had recovered
his interest. "Mrs. Marstan," he said, groping for his glasses, "can
you produce a certificate of marriage to Dr. Marstan?"
"I cannot. Important papers, including that, were among the few
things that I took to Rest Hollow in November, and you have been

informed that the place is completely destroyed."
"That will do."
She stepped down from the stand, and for the first time her eyes
rested upon the prisoner. In them was an expression that would
have given him new courage had he seen it, but Roger Kenwick sat
motionless as a statue, his gaze fixed immutably upon the floor. It
was only when the name of the next witness was called that he
came back to a sense of his surroundings. "Call Granville Jarvis."
Dayton surveyed the Southerner sharply before he put his first
question. "You are the detective whom Richard Glover employed in
San Francisco to shadow the prisoner?"
"I am."
"How long were you in Mr. Glover's employ?"
"About two weeks."
"Two weeks? Why did you give up the case then?"
"Because at the end of that time I was convinced that Roger
Kenwick was neither mentally unbalanced nor guilty of any crime. I
communicated this opinion to Mr. Glover and resigned from further
service."
"But you still continued to shadow the prisoner?"
"I still continued to cultivate his acquaintance. I considered him one
of the most interesting men I had ever met."
"And your connections with him since then have been of a purely
friendly character? Not in any way professional, Mr. Jarvis?"
"No, I can't say that. For a few weeks after I had resigned from Mr.
Glover's service I was asked to take up the case again from a
different angle; employed, I may say, by some one else."

"By whom?"
For just an instant the witness hesitated. Then, "By Mr. Clinton
Morgan."
"Describe that incident, please."
Jarvis clasped his hands behind his head and stared off into space.
"It was near the end of December that Professor Morgan came to
my rooms one evening and asked my assistance on the case of
Richard Glover."
For the first time since the beginning of the trial, the chief witness
for the prosecution betrayed an unguarded emotion. The narrow slit
of amber, showing between his drooping lids, widened.
"My caller," Jarvis went on, "explained to me that he and his sister,
who were friends of Roger Kenwick, had stumbled upon a clue the
previous day that had made them suspect that there was foul play
about his death; that perhaps he might even be alive after all, and a
base advantage taken of his helplessness."
Here Dayton interjected a question. "Was there any special reason
why Professor Morgan should have chanced upon you as the
detective for this investigation? Had you had any previous
connection with him?"
"Only an academic connection. He knew, through university
affiliations, that I was out here on the coast doing some research
work for Columbia in my chosen profession—criminal psychology."
"Then you are not a detective?"
"Not in the strict sense of the word. The finding out of a criminal is
only the introductory part of my interest."
"Proceed with your story, Mr. Jarvis."
"Well, Professor Morgan and I had lunched together several times
over at the Faculty Club on the campus, so I was not greatly

surprised to receive a call from him. Furthermore, having heard the
other side of this case, I was much interested in the opportunity to
study it from a new angle. For while I was in Mr. Glover's employ, I
had, unsuspected by Kenwick himself, subjected him to a variety of
exacting psychological tests. Under the pretext of making some
photographic experiments in which I was at that time interested, I
had enlisted his aid on several occasions and in this way had made a
rather thorough examination of his five senses, his power of
association, his memory (both for retentiveness and recall), and had
tried him out, by means of various athletic games, for muscular
coördination, endurance, poise, and many other essentials of
normality. In only one of these did I find him defective. And that one
was memory.
"My research was made the more interesting by the fact that shortly
after I undertook the work for Mr. Glover the subject gave me,
voluntarily and quite unsuspectingly, the complete story of his
strange adventure at Rest Hollow, an adventure for which he frankly
confessed that he could not account. It coincided exactly with the
hypothesis which I had established for him; that he had at one
period of his life been mentally unbalanced, and that he had in some
way re-gained his sanity but not completely his memory. When I
knew that there was likely to be a crime attributed to him (for Mr.
Glover had hinted as much) my interest doubled. For Mr. Kenwick
had on various occasions shown himself possessed of the highest
ideals and a fineness of caliber which I have not often encountered.
And so, in the employ of Professor Morgan, I shifted the focal point
and turned the search-light of science upon the accuser. It has
resulted in the most startling revelations."
There was an inarticulate stir in the crowded room. From the rear
seats men and women strained forward to catch every word as it
fell, clear-cut and decisive, from the scientist's lips. Jarvis sat with
one hand thrust into his pocket, and his keen eyes fixed upon the
group of lawyers below. A casual observer of the scene might easily

have mistaken his position and assigned to him the role of
prosecuting attorney.
"There was an insurmountable barrier, of course," he continued, "to
my making any personal examination of Mr. Glover, as I had done
with the former subject. One man was innocent and unsuspecting;
the other, I felt certain, would be on his guard. And he was. Since I
left his service, Richard Glover has avoided me. So a more indirect
means of accomplishing my task had to be devised. After some
consideration I decided to enlist the aid of an ally whom I knew to
be both clever and discreet."
A long-drawn sigh swept the court-room. It was that sigh, a mixture
of eagerness and satisfaction by means of which an audience at a
theater indicates to the actors that the performance is living up to its
advertisements.
"Mr. Kenwick himself," the witness went on in his calm, even voice,
"had called my attention to a certain Madame Rosalie, a spiritualistic
medium, who was taking the city by storm. He had interviewed her
for his paper, and from his description I imagined that she might be
able and willing to assist me. So I went to see her, and at the first
mention of Mr. Kenwick's name she became intensely interested."
Here Dayton's voice, sounding a curious little note of exultation,
broke in again. "You have referred to this medium as 'Madame
Rosalie.' Was that her professional or her real name?"
"Her professional name. Her real name, as she disclosed it to me on
the occasion of my first call, was Madeleine Marstan."
Another moment of silence and then the witness proceeded. "Having
told me her real name, she went on to describe her unexpected
encounter, a few days previously, with Roger Kenwick, who she had
thought was dead. It seemed that when Kenwick had come to her
for a sitting, his name had been accidentally revealed to her by
another client, and it had struck her with the force of a blow. For it
recalled to her mind a horrible adventure at Mont-Mer, which she

narrated for me then in detail. At first she had surmised that this
must be some relative of the unfortunate young man, and she had
done all she could, she said, to start him upon the track of the
tragedy. When she discovered that it was the man himself, she was
glad to place all her powers at my disposal. For she had returned to
the city in November with two dominating purposes; first to find
some employment which would bring in quick money and so pay her
husband's debts and clear his name, and second to discover, if
possible, the identity of the man who had led them both into the
miserable Mont-Mer trap, which resulted so disastrously for every
one concerned in it. She had not been able to make a stage
contract, she said, for the season was too far advanced, and so she
had turned to the occult, in which she had always felt a deep
interest, and for which she knew herself to have an unaccountable
talent. Fortunately her strange psychic ability had caught the
attention of one of the university faculty and she had been given just
the publicity which she needed.
"And so we deliberately plotted between us the scientific testing of
Richard Glover. I prepared a list of apparently random words in
which were mingled what I call 'dangerous terms'; that is, words
which were connected with the adventure at Rest Hollow. When
these and the other tests were ready, I induced Glover, by means of
a casual suggestion from a mutual acquaintance, to seek the aid of
'Madame Rosalie.' I felt certain that if he were not intimately
connected with the tragedy he would scorn this idea, and that if he
were, it was exactly the time that he would turn to the supernatural
for aid. And I was not mistaken. For almost immediately he called
upon the clairvoyant. And his response to the tests for association
was amazing even to me. If I may quote from the list of words——"
He drew a folded paper from his pocket. "Among many perfectly
irrelevant terms I had smuggled in such words as 'blanket' and
'window' and 'oleander.' Madame Rosalie reported that his gaze
always returned to such suggestive words (despite her admonition to
look at something else) before she could change the card. The
subconscious response to evil association was almost perfect. There

were many other tests, of course, and by the time he had completed
them he had shown an intimate knowledge of the crime at Rest
Hollow and an uneasiness from which any skilful psychologist could
take his starting-point. And then, as a culminating incident, he
supplied to the medium, quite of his own accord, the name 'Rest
Hollow,' and put to her the unexpected question, 'Where is Ralph
Regan?'
"Having been thus convinced that he was the man we sought, Mrs.
Marstan and I continued our investigations together. She went out
with him, upon several occasions, and once, by pre-arrangement,
accompanied him to the theater. On the same evening I invited
Kenwick, and, all at once, called his attention to Glover. The
response was like match to powder. The visual image of his former
warden restored, in large degree, his memory. He was eager to
reëstablish the connection. Mrs. Marstan had been careful to point
out Kenwick to her escort, and the result was just what we had
foreseen. It was he who evaded the encounter, supplying a pretext
upon which he and Mrs. Marstan immediately left the theater.
"But Glover now suspected that he was entrapped. He had already, I
knew, put another detective upon Kenwick's track. When news was
published of Mrs. Fanwell's arrival in Mont-Mer, and the subsequent
demand to have the disappearance of her brother investigated, he
decided that his only course was to act at once. Mrs. Marstan, aided
by her unmistakable psychic ability, had advised him to follow his
third plan, and this plan was to have Kenwick convicted of murder."
"And this was the report that you turned over to Professor Morgan at
the end of your investigation?" Dayton inquired.
"This was the report. I was working on it with him up in San
Francisco until late last night. We almost missed the train trying to fit
together the final details. But I think the story, as I have given it to
you, is now complete."

"Now, one other thing, Mr. Jarvis. In the first part of your testimony
you said that Mr. Morgan told you that he had stumbled upon a clue
that had made him suspicious of Glover. Did he disclose to you the
nature of that clue?"
"Not at first. I told him that I preferred to work upon some theories
of my own, unprejudiced by any evidence that he might have to
offer."
"And how many times have you seen Mr. Morgan since then?"
"Only once. We came down from San Francisco together last night."
"Then you made no reports to him before?"
For the first time, the witness hesitated. Then his reply came with
the customary clearness. "Not to him. I have reported to Miss
Morgan on several occasions."
"Then you have been really working with her upon this case?"
"Yes, almost entirely with her."
There was a very obvious reluctance in his voice now, but Dayton
went on imperturbably. "When you came down from San Francisco
last night, Mr. Jarvis, was Professor Morgan's sister in your party?"
"Yes."
Dayton swept a glance over the rows of faces before him. "Is Miss
Morgan in the court-room now?"
"She has just come in." The promptness with which the witness had
given his earlier testimony served to make his present reluctance the
more apparent.
Dayton brought his eyes back to the witness-stand. "That will do."
Jarvis stepped down. The voice of the auditors, beginning in a
subdued murmur, rose in marked crescendo. No word in it could be

distinguished from another. Yet upon Roger Kenwick's sensitive
nerves this message from the outer world registered. It was
unmistakably applause.
For the first time since the trial began, he felt his mask of graven
indifference slipping from him. He was trembling in every fiber, and
with one unsteady hand he made a pathetic effort to quiet the other.
And then there fell upon his ears like the crash of thunder Dayton's
curt command, "Call Miss Morgan."

CHAPTER XIX
As the men standing in the far aisle made way for the new witness,
Kenwick sat with averted eyes. Through the open window he stared
out at the court-house palms which grew to gigantic size and then
diminished under his blistering gaze. It was a monstrous thing, he
told himself, for Clinton Morgan to allow this; to permit his sister to
subject herself to such a strain. What could he be thinking about?
But underneath his miserable apprehension for her there was
something else; something else that sent the fiery blood rioting
through his veins. For she must have been willing. Over and over he
repeated to himself this assurance. She must have been willing to
come to his defense, for had she not been, they could have found a
way to avoid it.
Marcreta Morgan, in long fur-trimmed motor-coat and dark veil, took
the place which Granville Jarvis had vacated. She had none of
Madeleine Marstan's calm self-assurance, but although she gave her
testimony in a low voice, it was distinctly audible throughout the
court-room. She sat with one gloved hand clasping the arm of the
chair and her eyes resting upon Dayton. Only once, at the very end
of the examination, did she raise them to meet the argus-eyed
spectators. Dayton put his questions in an easy conversational tone
as though he and the witness were alone in the room.
"Miss Morgan, how long have you known the prisoner?"
"About two years."
"Describe the occasion of your first meeting."
She did so in words that sounded carefully rehearsed.

"And after he left San Francisco to go East and visit his brother did
you ever hear from him?"
"Yes. He wrote frequently, telling me about his brother's recovery
from illness and other affairs, and then later that he had decided to
enlist in the army."
"At that time, Miss Morgan, had you ever known the State's witness
here, Richard Glover?"
"It was about that time that I first met him."
"Describe your first encounter with him."
Again the carefully prepared report. But she was gaining in self-
possession now, and the veil seemed to annoy her. With steady
fingers she reached up and removed it. Clinton Morgan, watching
her from the front row of seats, with a hawklike vigilance, was
suddenly reminded of that Sunday night in the old library when she
had first broken her long silence concerning Roger Kenwick, and had
seemed all at once to come into a belated heritage.
The jurymen were leaning slightly forward in their seats, their eyes
fixed upon the regal, fur-coated figure with delicately flushed profile
showing clear-cut as a cameo against the frosted window-pane.
Dayton thought that he caught an elusive fragrance that reminded
him of something growing in his mother's garden.
"And how many times," he proceeded, "how many times have you
seen Richard Glover during the past year?"
"I can't say exactly. For several months after our first meeting I
didn't see him at all. But during the last three months his calls have
been more and more frequent."
"Has your brother known of these visits?"
"My brother was in government service in Washington until about
two months ago. He didn't know of them until he returned."

"And has he approved of them?"
"No, I can't say that he has."
"Did he ever give any reason for his opposition?"
"He told me that he suspected Mr. Glover of being an adventurer
who was in need of——"
Here the district attorney interrupted. "We object. The suspicions of
another person are irrelevant, incompetent, and have nothing to do
with the case."
"Sustained," the judge decreed. "Stick to the facts, Mr. Dayton."
"During those three months, Miss Morgan, has Richard Glover made
an effort to induce you to marry him?"
Her reply was given in a very low voice, but Dayton was sure that
the jury caught it and he did not ask her to repeat. It was evident
that the audience heard it, too, for another murmur rose and trailed
off into silence before the lawyer went on. "Is it true that you were
the one who discovered the clue which led you and your brother to
seek the services of Mr. Jarvis on this case?"
She acknowledged it with a single word.
"And what was that clue?"
The gloved fingers closed a little closer over the arm of the chair.
And then followed a story which caused Roger Kenwick to tear his
gaze away from the fantastic palm-trees and fix it upon Richard
Glover's face. There was no resentment in his eyes, but only the
dawning of a great light. Granville Jarvis, watching him as a
physician might watch beside the bedside of an unconscious patient,
knew by the leaping flame in those somber eyes that the last lap of
the long journey had been covered, and that Roger Kenwick's
memory had come home to him. But if that knowledge brought him
a scientist's satisfaction, he gave no sign of it. After that one intent

moment, his eyes returned to the witness-stand and fixed
themselves upon Marcreta Morgan's face. Dayton was proceeding
relentlessly.
"If you knew from the first that Richard Glover had stolen this story
which he read to you as his own, why didn't you relate the
circumstance to Mr. Kenwick when you saw him on the night that he
was arrested for murder?"
The reply came haltingly, as though the witness were feeling her
way over uneven ground. "My brother and I had consulted Mr. Jarvis
about that and he had advised against it. He didn't wish to arouse
any suspicions in—in the prisoner's mind just then. And—well, you
see, Mr. Kenwick and I had not seen each other since his—illness
and during that first meeting we both avoided everything connected
with—with the tragedy as much as possible. Of course if we had
known that this charge of—of crime was to be preferred against him,
I suppose we would have acted differently."
This was no carefully rehearsed response, but nothing that she could
have said would have disclosed more clearly the inside workings of
the opposition's conspiracy. The web that had been woven around
the prisoner had enmeshed with him every one who had ever been
intimately associated with his past.
And now that romance had entered upon the sordid scene the whole
aspect of the case was changed. The air became charged all at once
with an electric current of sympathy. To every man and woman in
the room Richard Glover now appeared in the guise of a baffled
adventurer, and Roger Kenwick as a man who had loved, and
because of cruel circumstance had lost. But had he really lost? The
crux of public interest shifted with the abruptness of a weathercock,
from mystery to romance.
"You assert, Miss Morgan, that you knew this story, 'A Brother of
Bluebeard,' to be the one which the prisoner had read to you before

he left for the East almost two years ago. What proof could you
furnish of this?"
"At the time that Mr. Glover read the story to me I had in my
possession the sequel to it, which Mr. Kenwick had sent me in
manuscript for my criticism, just before he left for training-camp. It
used many of the same characters and was rooted in the same plot."
"Could you produce that manuscript?"
"Mr. Jarvis can produce it. I turned it over to him."
The former witness leaned forward and laid a heap of pencil-written
manuscript upon the table. But Dayton scarcely glanced at it. With
one hand he pushed it aside, and then shifted the current of his
interest into another channel. "When, and by what means, Miss
Morgan, did you discover that Roger Kenwick had returned from
France mentally disabled?"
Her reply to this question came in a voice that was struggling
against heavy odds for composure. "It was exactly one year ago to-
day that I received that news. Several letters of mine to—the
prisoner were returned to me unopened. And with them came a
communication from Mr. Everett Kenwick telling me that—that it had
become necessary for them to send his brother to a private asylum."
"Did you know where that asylum was?"
"Not then. He told me that he was debating over several different
places but that he had almost decided upon a friend's home in
southern California. He didn't tell me where this home was. I think
he realized that—that I would rather not know."
"And when did you discover that that place was Mont-Mer?"
"On the night that Mr. Kenwick was reported dead."
A murmur that was distinctly a wave of sympathy filled the chamber.
But eagerness to catch the next question quieted it.

"After that first letter telling you about the prisoner's misfortune, did
you ever hear from Mr. Everett Kenwick again?"
"Only once. Just a week before he died, he wrote again. He had just
lost his wife and he seemed to have a premonition that he was not
going to live very long."
She was feeling for her handkerchief in the pocket of the fur-
trimmed coat. Some of the men in the court-room averted their
eyes. The face of more than one woman softened. Clinton Morgan
sat regarding his sister with a curious composure. In his eyes was
that mixture of compassion and awe that he had worn on the night
when the gold and ivory book had betrayed to him her secret.
"Yes?" Dayton went on gently, but with the same relentless
persistence. "He wrote to you again? And what did he say?"
"He said that he wanted me to have something that had belonged—
to his brother. He told me that he felt that Roger Kenwick would
have wished me to have it. And with the letter there came a box in
which I found——"
She had finished her search in the pocket of the motor-coat, and
now she held something between her gloved fingers. "Mr. Everett
Kenwick himself had only received it a short time before. There had
been some delay and confusion about it, owing I suppose to his
brother having been sent home—in just the way that he was. He
himself never knew that he had won it. But it was such a wonderful
display of courage——And the French officer whose life he had
saved sent a letter, too, saying that France was grateful and wanted
to express her appreciation in some way so——"
And then she held it up before them; before the lawyers and the
jury and the crowd of spectators—a bit of metal on its patch of
ribbon. Holding it out before them, she sat there like a sovereign
waiting to confer a peerage. And not the judge's gavel nor the
commanding voice of the district attorney could still the tumult that
rose and swelled into tumultuous applause.

On the day following the notorious Kenwick murder trial, the Mont-
Mer papers carried little other news. A special representative from
the "San Francisco Clarion" and several Los Angeles journalists fed
their copy over the wires and had extras out in both cities by eight
o'clock.
"Kenwick Acquitted" was the head-line which his own paper ran,
with his picture and one of Richard Glover sharing prominence upon
the front page. And because of Kenwick's previous connection with
this daily and the fact that the two star witnesses for the defense
were well known in the Bay region, the "Clarion's" story was the
most comprehensive and colorful.
It opened with a report of Dayton's speech which, it appeared, had
electrified every one in the court-room, including the prisoner
himself. But it had been unnecessary for the attorney to make a plea
for his client, after the quietly dramatic testimony of the last witness
for the defense. In thrilling terms the "Clarion" described Kenwick's
final service at the front, when he had made his way alone across
No-Man's-Land and saved for France one of her most gallant
officers, and had given in exchange that thing which is more
precious than life itself. Only through an accident, which had killed
the man who had meant to batten upon his misery, had he been
released from a pitiable bondage.
Having thus sketched in his "human interest," the reporter
proceeded to tell the story which had proved so overwhelmingly
convincing to the jury and audience. How, in his skilfully planned
narrative, Richard Glover had transposed the identities of the two
dead men. How, upon receiving his commission from Everett
Kenwick, he had first turned over his charge to Ralph Regan,
admitted by his own sister to be an addict to drugs and a ne'er-do-
well whom she was helping, in a surreptitious way, to support. How
the accounts, forwarded from the Kenwick lawyer in New York,
showed that Regan must have received out of the arrangement only

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The Physics Of Particle Detectors Dan Green

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