Upload
taha-sochi
View
99
Download
0
Embed Size (px)
Citation preview
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.
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
• 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 3PJ levels
Table 1: The configurations used to define the scattering target. The 1s2 core is suppressed fromall 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
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 theenergies with no two-body fine-structure terms and Eth2 include them
Index Level Eexp Eth1 Eth21 2s2 2p2 3Pe
00.00 0.00 0.00
2 2s2 2p2 3Pe1
113.18 115.00 113.00
3 2s2 2p2 3Pe2
306.17 339.00 308.00
4 2s2 2p2 1De2
20273.27 21489.00 21471.00
5 2s2 2p2 1Se0
43185.74 45900.00 45882.00
6 2s 2p3 5So2
60324.79 59600.00 59582.00
7 2s 2p3 3Do3
120058.20 121800.00 121775.00
8 2s 2p3 3Do2
120053.40 121804.00 121799.00
9 2s 2p3 3Do1
120025.20 121812.00 121805.00
10 2s 2p3 3Po2
142393.50 145316.00 145307.00
11 2s 2p3 3Po1
142381.80 145321.00 145307.00
12 2s 2p3 3Po0
142381.00 145331.00 145319.00
13 2s 2p3 1Do2
187054.00 191025.00 191006.00
14 2s 2p3 3So1
197087.70 200423.00 200405.00
15 2s 2p3 1Po1
210461.80 215609.00 215591.00
16 2p4 3Pe2
283759.70 288653.00 288629.00
17 2p4 3Pe1
283977.40 288863.00 288854.00
18 2p4 3Pe0
284071.90 288965.00 288951.00
Table 3: LS gf values within the n=2 complex in the length and velocity formulations
(gf)L (gf)V3Pe - 3Do 1.01 0.99
3Po 1.28 1.313So 1.70 1.61
1De - 1Do 1.57 1.611Po 1.18 1.22
1Se - 1Po 0.27 0.27
The scattering calculations
• ICFT and BP calculations with 9CC, 10CC, 20CC and 72CC.
• 9CC includes all terms of 2s22p2 and 2s2p3
• 10CC also includes 2p4 3P
• 20CC includes 2p4 3P, 1D and 1S 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 2s22p3d
• Maximum 2J=19 in N+1 problem
• 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?
• Collision strength vs final electron energy (Ryd)
• BP calculations with 9CC, 10CC, 20CC, 72CC
• Shows very good convergence
• Comparing 9CC ICFT with 9CC BP
• ICFT with Gailitis averaging (stgicfdamp) generated clearly incorrect results and
a bug was corrected
• 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
• Comparing ICFT results with and without N+1 state correction
•
•
•
Table 4: Comparison of effective collision strengths, Υ, between Lennon & Burke (LB, IP II) andthe current work. The first row of each temperature is from Table (3) of LB, the second and thirdrows 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 0.42410.5352 0.2390 1.1540 2.1829 0.2577 0.9770 0.40440.5199 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 0.42680.5279 0.2419 1.1715 2.1364 0.2557 0.9677 0.41050.5154 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 0.43570.5236 0.2435 1.1823 2.0794 0.2526 0.9702 0.42950.5132 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 0.46520.5246 0.2467 1.1991 2.0559 0.2527 1.0208 0.48190.5158 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 0.52320.5334 0.2533 1.2304 2.1202 0.2635 1.1215 0.56050.5260 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 0.58150.5483 0.2639 1.2762 2.2629 0.2841 1.2172 0.61930.5421 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 0.61000.5610 0.2769 1.3228 2.4204 0.3066 1.2731 0.63350.5551 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 0.60900.5669 0.2909 1.3619 2.5446 0.3230 1.2792 0.61480.5609 0.2835 1.3378 2.5184 0.3339 1.2380 0.6022
Table 5: Comparison of effective collision strengths, Υ, between Palay et al (PA) and the currentwork as a function of temperature. The first row of each transition is from Table (1) of PA while thesecond and third rows are from the current BP calculation using the 20-term and 72-term targetsrespectively.
T /K 100 500 1000 5000 10000 20000 30000
3P0-3P1 0.5814 0.5005 0.4866 0.5240 0.5648 0.6007 0.61160.6606 0.5628 0.5352 0.5279 0.5483 0.5646 0.56810.6350 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 0.32640.2361 0.2339 0.2390 0.2495 0.2639 0.2838 0.29640.2259 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 1.49901.1562 1.1320 1.1540 1.2125 1.2762 1.3432 1.37581.1121 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 0.32560.2363 0.2433 0.2425 0.2306 0.2514 0.2766 0.28610.2318 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 0.98020.7114 0.7321 0.7300 0.6945 0.7574 0.8328 0.86150.6975 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 1.64501.1943 1.2289 1.2254 1.1676 1.2735 1.3992 1.44641.1702 1.2057 1.1965 1.1474 1.2620 1.3850 1.4310
Table 6: Comparison of effective collision strengths, Υ, between Palay et al (PA) and the currentwork as a function of temperature. The first row of each transition is from Table (1) of PA while thesecond 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 0.62190.3977 0.4005 0.4044 0.5201 0.6193 0.6271 0.60170.3827 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 0.04420.0289 0.0288 0.0286 0.0285 0.0316 0.0351 0.03620.0299 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 0.13320.0870 0.0867 0.0862 0.0859 0.0951 0.1059 0.10910.0900 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 0.22350.1460 0.1455 0.1447 0.1443 0.1601 0.1782 0.18360.1512 0.1506 0.1497 0.1496 0.1657 0.1839 0.1902
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, 3d74s) 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