![Collision strengths for O2+
+ e−
Pete Storey and Taha Sochi
• The planetary nebula NGC7009, showing the [O iii] (green) and [N ii]+Hα
(red) emission.](https://image.slidesharecdn.com/storeysochipresentation-151117085815-lva1-app6892/85/Collisions-strengths-for-O2-e-1-320.jpg)
![Introduction
• The forbidden lines of [O iii] are probably the most important features in the
spectra of photoionized nebulae (H ii regions and Planetary Nebulae)
• The strongest lines are very bright and are used to determine oxygen abundances
and physical conditions in our and other galaxies out to cosmological distances
(z = 3 at least)
• It has been recently suggested that the abundance/temperature anomalies seen
in PNe might be resolved by using non-Maxwell Boltzmann distributions for the
free electrons
• If electron distributions are generally non-Maxwellian in nebulae it would affect
the analysis of [O iii] lines significantly
• Hence a need for reliable collision strength data to compute Upsilons and
Downsilons
• Surely the collision strengths are well known by now?
• There have been many calculations, the most recent a BP calculation by Palay,
Nahar, Pradhan and Eissner, which shows some significant differences from
careful earlier work (Lennon and Burke, IP ii)
• Checking/confirmation was considered appropriate
• There followed many adventures in stgicf/TCC land - a program bug and
ignorance have slowed progress](https://image.slidesharecdn.com/storeysochipresentation-151117085815-lva1-app6892/85/Collisions-strengths-for-O2-e-2-320.jpg)
Collisions strengths for O2+ + e-
- 1. Collision strengths for O2+ + e− Pete Storey and Taha Sochi • The planetary nebula NGC7009, showing the [O iii] (green) and [N ii]+Hα (red) emission.
- 2. Introduction • The forbidden lines of [O iii] are probably the most important features in the spectra of photoionized nebulae (H ii regions and Planetary Nebulae) • The strongest lines are very bright and are used to determine oxygen abundances and physical conditions in our and other galaxies out to cosmological distances (z = 3 at least) • It has been recently suggested that the abundance/temperature anomalies seen in PNe might be resolved by using non-Maxwell Boltzmann distributions for the free electrons • If electron distributions are generally non-Maxwellian in nebulae it would affect the analysis of [O iii] lines significantly • Hence a need for reliable collision strength data to compute Upsilons and Downsilons • Surely the collision strengths are well known by now? • There have been many calculations, the most recent a BP calculation by Palay, Nahar, Pradhan and Eissner, which shows some significant differences from careful earlier work (Lennon and Burke, IP ii) • Checking/confirmation was considered appropriate • There followed many adventures in stgicf/TCC land - a program bug and ignorance have slowed progress
- 3. • Only interested in forbidden transitions among the 5 lowest levels for temperatures up to 20000K • Maximum 2J=15 for N+1 problem is ample for convergence • Energies up to 5kT at 20000K means ≈ 0.6Ryd above threshold is sufficient • Very low temperatures might be of importance (T≈100K) when kT ≈ 0.001Ryd • Target comprises n=2 physical orbitals + 3l and 4f correlation orbitals • Made several calculations with increasing numbers of target states, both with BP and ICFT method • Use option in LS RM code to correct for effects of spurious N+1 states causing non-physical resonances • Try to put realistic error bars on collision strengths/Upsilons based on – Convergence as target size is increased – Effect of correcting for N+1 resonances – Inclusion of (pseudo) states to represent dipole polarisability of the important target states – Effect of Gailitis averaging of Rydberg series of resonances between the ground 3 PJ levels
- 4. Table 1: The configurations used to define the scattering target. The 1s2 core is suppressed from all configurations. 2s2 2p2 , 2s 2p3 , 2p4 2s2 2p 3l, l=0,1,2; 4f 2s2p2 3l, l=0,1,2; 4f 2p3 3l, l=0,1,2; 4f 2s2 3l 3l’, l,l’=0,1,2; 4f2 2s2p 3l 3l’, l,l’=0,1,2; 4f2 2p2 3l 3l’, l,l’=0,1,2; 4f2
- 5. Table 2: The 18 lowest energy levels of O2+ and their experimental (Eexp) and theoretical (Eth1 and Eth2) energies in wavenumbers (cm−1 ). Eexp are from the NIST database, Eth1 are the energies with no two-body fine-structure terms and Eth2 include them Index Level Eexp Eth1 Eth2 1 2s2 2p2 3Pe 0 0.00 0.00 0.00 2 2s2 2p2 3Pe 1 113.18 115.00 113.00 3 2s2 2p2 3Pe 2 306.17 339.00 308.00 4 2s2 2p2 1De 2 20273.27 21489.00 21471.00 5 2s2 2p2 1Se 0 43185.74 45900.00 45882.00 6 2s 2p3 5So 2 60324.79 59600.00 59582.00 7 2s 2p3 3Do 3 120058.20 121800.00 121775.00 8 2s 2p3 3Do 2 120053.40 121804.00 121799.00 9 2s 2p3 3Do 1 120025.20 121812.00 121805.00 10 2s 2p3 3Po 2 142393.50 145316.00 145307.00 11 2s 2p3 3Po 1 142381.80 145321.00 145307.00 12 2s 2p3 3Po 0 142381.00 145331.00 145319.00 13 2s 2p3 1Do 2 187054.00 191025.00 191006.00 14 2s 2p3 3So 1 197087.70 200423.00 200405.00 15 2s 2p3 1Po 1 210461.80 215609.00 215591.00 16 2p4 3Pe 2 283759.70 288653.00 288629.00 17 2p4 3Pe 1 283977.40 288863.00 288854.00 18 2p4 3Pe 0 284071.90 288965.00 288951.00
- 6. Table 3: LS gf values within the n=2 complex in the length and velocity formulations (gf)L (gf)V 3 Pe - 3 Do 1.01 0.99 3 Po 1.28 1.31 3 So 1.70 1.61 1 De - 1 Do 1.57 1.61 1 Po 1.18 1.22 1 Se - 1 Po 0.27 0.27
- 7. The scattering calculations • ICFT and BP calculations with 9CC, 10CC, 20CC and 72CC. • 9CC includes all terms of 2s2 2p2 and 2s2p3 • 10CC also includes 2p4 3 P • 20CC includes 2p4 3 P, 1 D and 1 S plus several non-physical terms • 72CC also includes all further odd parity terms that contribute significantly to the polarisability of the three lowest even parity terms. Mainly from 2s2 2p3d • Maximum 2J=19 in N+1 problem
- 8. • Collision strength vs final electron energy (Ryd) • ICFT calculations with 9CC, 10CC, 20CC, 0.05Ryd equiv to ≈ 8000K • The 9CC results are so different to earlier work and BP that considerable time was spent trying to understand the reason - insufficient target states? bug in stgicf?
- 9. • Collision strength vs final electron energy (Ryd) • BP calculations with 9CC, 10CC, 20CC, 72CC • Shows very good convergence
- 10. • Comparing 9CC ICFT with 9CC BP • ICFT with Gailitis averaging (stgicfdamp) generated clearly incorrect results and a bug was corrected
- 11. • Since the results for the 9CC BP calculation are in agreement with earlier work we concluded (incorrectly) that the 9-state target was not the problem and looked for a bug in stgicf (which was not found) • The difference between the 9CC BP and ICFT calculations is that in the BP run, the entire N+1 LS Hamiltonian is passed to stgjk where the SLJ H is computed. • All the channels arising from states that interact with the 9 target states are included • This is not the case with a pure LS calculation where the channels are dropped in stg2 • Hence we need to ensure that when specifying NAST in stg2, that all terms that interact by CI with the terms of interest are included • Sounds obvious now
- 12. • Comparing ICFT results with and without N+1 state correction
- 13. •
- 14. •
- 15. •
- 16. Table 4: Comparison of effective collision strengths, Υ, between Lennon & Burke (LB, IP II) and the current work. The first row of each temperature is from Table (3) of LB, the second and third rows are current work using the 20-term and 72-term targets respectively. log(T /K) 3P0-3P1 3P0-3P2 3P1-3P2 3P-1D2 3P-1S0 3P-5S2 1D2-1S0 3.0 0.4975 0.2455 1.1730 2.2233 0.2754 0.9760 0.4241 0.5352 0.2390 1.1540 2.1829 0.2577 0.9770 0.4044 0.5199 0.2313 1.1218 2.1331 0.2667 0.9110 0.3897 3.2 0.5066 0.2493 1.1930 2.1888 0.2738 0.9673 0.4268 0.5279 0.2419 1.1715 2.1364 0.2557 0.9677 0.4105 0.5154 0.2349 1.1430 2.0811 0.2643 0.9044 0.3968 3.4 0.5115 0.2509 1.2030 2.1416 0.2713 0.9712 0.4357 0.5236 0.2435 1.1823 2.0794 0.2526 0.9702 0.4295 0.5132 0.2367 1.1558 2.0237 0.2610 0.9126 0.4200 3.6 0.5180 0.2541 1.2180 2.1117 0.2693 1.0224 0.4652 0.5246 0.2467 1.1991 2.0559 0.2527 1.0208 0.4819 0.5158 0.2398 1.1736 2.0107 0.2616 0.9732 0.4799 3.8 0.5296 0.2609 1.2480 2.1578 0.2747 1.1196 0.5232 0.5334 0.2533 1.2304 2.1202 0.2635 1.1215 0.5605 0.5260 0.2462 1.2057 2.0913 0.2732 1.0814 0.5621 4.0 0.5454 0.2713 1.2910 2.2892 0.2925 1.2074 0.5815 0.5483 0.2639 1.2762 2.2629 0.2841 1.2172 0.6193 0.5421 0.2568 1.2526 2.2425 0.2941 1.1769 0.6174 4.2 0.5590 0.2832 1.3350 2.4497 0.3174 1.2574 0.6100 0.5610 0.2769 1.3228 2.4204 0.3066 1.2731 0.6335 0.5551 0.2698 1.2994 2.3987 0.3165 1.2295 0.6254 4.4 0.5678 0.2955 1.3730 2.5851 0.3405 1.2720 0.6090 0.5669 0.2909 1.3619 2.5446 0.3230 1.2792 0.6148 0.5609 0.2835 1.3378 2.5184 0.3339 1.2380 0.6022
- 17. Table 5: Comparison of effective collision strengths, Υ, between Palay et al (PA) and the current work as a function of temperature. The first row of each transition is from Table (1) of PA while the second and third rows are from the current BP calculation using the 20-term and 72-term targets respectively. T /K 100 500 1000 5000 10000 20000 30000 3P0-3P1 0.5814 0.5005 0.4866 0.5240 0.5648 0.6007 0.6116 0.6606 0.5628 0.5352 0.5279 0.5483 0.5646 0.5681 0.6350 0.5430 0.5199 0.5199 0.5421 0.5587 0.5623 3P0-3P2 0.2142 0.2153 0.2234 0.2469 0.2766 0.3106 0.3264 0.2361 0.2339 0.2390 0.2495 0.2639 0.2838 0.2964 0.2259 0.2247 0.2313 0.2424 0.2568 0.2766 0.2890 3P1-3P2 1.0360 1.0320 1.0720 1.2100 1.3300 1.4510 1.4990 1.1562 1.1320 1.1540 1.2125 1.2762 1.3432 1.3758 1.1121 1.0928 1.1218 1.1873 1.2526 1.3194 1.3518 3P0-1D2 0.1959 0.2088 0.2154 0.2347 0.2693 0.3094 0.3256 0.2363 0.2433 0.2425 0.2306 0.2514 0.2766 0.2861 0.2318 0.2389 0.2370 0.2265 0.2492 0.2739 0.2832 3P1-1D2 0.5903 0.6285 0.6483 0.7067 0.8108 0.9313 0.9802 0.7114 0.7321 0.7300 0.6945 0.7574 0.8328 0.8615 0.6975 0.7187 0.7132 0.6823 0.7506 0.8247 0.8527 3P2-1D2 0.9934 1.0560 1.0890 1.1880 1.3630 1.5640 1.6450 1.1943 1.2289 1.2254 1.1676 1.2735 1.3992 1.4464 1.1702 1.2057 1.1965 1.1474 1.2620 1.3850 1.4310
- 18. Table 6: Comparison of effective collision strengths, Υ, between Palay et al (PA) and the current work as a function of temperature. The first row of each transition is from Table (1) of PA while the second and third rows are from the current work using the 20-term and 72-term targets respectively. T /K 100 500 1000 5000 10000 20000 30000 1D2-1S0 0.3900 0.3899 0.3899 0.4544 0.5661 0.6230 0.6219 0.3977 0.4005 0.4044 0.5201 0.6193 0.6271 0.6017 0.3827 0.3856 0.3897 0.5208 0.6174 0.6163 0.5886 3P0-1S0 0.0597 0.0535 0.0496 0.0409 0.0407 0.0430 0.0442 0.0289 0.0288 0.0286 0.0285 0.0316 0.0351 0.0362 0.0299 0.0298 0.0296 0.0295 0.0327 0.0363 0.0375 3P1-1S0 0.1765 0.1590 0.1477 0.1228 0.1223 0.1294 0.1332 0.0870 0.0867 0.0862 0.0859 0.0951 0.1059 0.1091 0.0900 0.0897 0.0892 0.0890 0.0985 0.1093 0.1131 3P2-1S0 0.2850 0.2587 0.2421 0.2045 0.2046 0.2170 0.2235 0.1460 0.1455 0.1447 0.1443 0.1601 0.1782 0.1836 0.1512 0.1506 0.1497 0.1496 0.1657 0.1839 0.1902
- 19. Conclusions • For this kind of calculation, concentrating on a few low levels with a lot of correlation, BP is much safer (although also much slower) than ICFT • The ICFT requires that all significant CI is included in the CC expansion in stg2 • This can be very difficult to judge - for example in Co ii - where there is strong interaction between spectroscopically interesting configurations (3d8 , 3d7 4s) and those including 4d • Also for lowly ionized systems resonances can have very low principal quantum number - ie channels are deeply closed which can cause problems for MQDT. This difficulty evaporates as Z increases due to Z-scaling • On O iii our summed collision strength results agree well with the earlier LS calculation by Lennon & Burke in IP ii • We do not agree with Palay et al for some transitions and the differences are spectroscopically significant