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2. Target expansion

In the close coupling (CC) approximation the total wave function of the electron-ion system is represented as
equation220
where tex2html_wrap_inline1174 is the target ion wave function in a specific state Si Li, tex2html_wrap_inline1180 is the wave function for the free electron, and tex2html_wrap_inline1182 are short range correlation functions for the bound (e + ion) system. Accurate CC calculations of atomic processes require, first of all, a good representation of the target ion. For complex ions an accurate representation must include a large number of correlation configurations. However, in order for the computations to be computationally tractable, the configuration expansion must be carefully and economically chosen.

The CC expansion for this calculation includes 31 LS terms of the target ion Fe V. The atomic structure code SUPERSTRUCTURE (Eissner etal. 1974; Eissner 1991) was used to compute eigenfunctions for the 31 states of the Fe V target ion dominated by tex2html_wrap_inline1184, tex2html_wrap_inline1186, and tex2html_wrap_inline1188. Table 1 (click here) presents the complete list of configurations included in the target, as well as a comparison between the calculated target term energies and the observed energies, averaged over the fine structure, taken from Sugar & Corliss (1985). The agreement between the energies is very good; in all but six cases the agreement with the experimental values is within tex2html_wrap_inline11722%. The overall agreement is better than 4%. Another indicator of the accuracy of the target representation is the good agreement between the length and the velocity oscillator strengths (f-values), which for the present case is typically about 10% (for a complicated atomic system such as Fe IV it is to difficult to achieve higher accuracy for LS f-values).

 

Level tex2html_wrap_inline1200 tex2html_wrap_inline1202 Level tex2html_wrap_inline1200 tex2html_wrap_inline1202
1 tex2html_wrap_inline1184tex2html_wrap_inline1210 0.000000 0.00000 17 tex2html_wrap_inline1212tex2html_wrap_inline1214 2.12336 2.161109
2 tex2html_wrap_inline1184tex2html_wrap_inline1218 0.227038 0.232252 18 tex2html_wrap_inline1220tex2html_wrap_inline1222 2.33251 2.355847
3 tex2html_wrap_inline1184tex2html_wrap_inline1226 0.223059 0.259441 19 tex2html_wrap_inline1220tex2html_wrap_inline1230 2.35148 2.386004
4 tex2html_wrap_inline1184tex2html_wrap_inline1214 0.237769 0.261593 20 tex2html_wrap_inline1236tex2html_wrap_inline1238 2.34905 2.419861
5 tex2html_wrap_inline1184tex2html_wrap_inline1242 0.267818 0.309157 21 tex2html_wrap_inline1220tex2html_wrap_inline1246 2.36577 2.391652
6 tex2html_wrap_inline1184tex2html_wrap_inline1238 0.327553 0.379240 22 tex2html_wrap_inline1220tex2html_wrap_inline1254 2.36838 2.397309
7 tex2html_wrap_inline1184tex2html_wrap_inline1218 0.561290 0.618696 23 tex2html_wrap_inline1220tex2html_wrap_inline1262 2.40378 2.440669
8 tex2html_wrap_inline1184tex2html_wrap_inline1214 0.560546 0.618706 24 tex2html_wrap_inline1220tex2html_wrap_inline1270 2.42943 2.469158
9 tex2html_wrap_inline1272tex2html_wrap_inline1274 1.70206 1.695583 25 tex2html_wrap_inline1276tex2html_wrap_inline1278 2.49342 2.534489
10 tex2html_wrap_inline1272tex2html_wrap_inline1214 1.78024 1.782194 26 tex2html_wrap_inline1276tex2html_wrap_inline1230 2.51746 2.556067
11 tex2html_wrap_inline1288tex2html_wrap_inline1290 1.86264 1.874768 27 tex2html_wrap_inline1276tex2html_wrap_inline1294 2.50752 2.551853
12 tex2html_wrap_inline1296tex2html_wrap_inline1242 1.89927 1.910388 28 tex2html_wrap_inline1300tex2html_wrap_inline1302 2.52243 2.558687
13 tex2html_wrap_inline1288tex2html_wrap_inline1218 1.93610 1.963195 29 tex2html_wrap_inline1300tex2html_wrap_inline1262 2.54016 2.585237
14 tex2html_wrap_inline1312tex2html_wrap_inline1218 1.94802 1.975859 30 tex2html_wrap_inline1300tex2html_wrap_inline1270 2.54951 2.597140
15 tex2html_wrap_inline1320tex2html_wrap_inline1238 1.96486 1.984966 31 tex2html_wrap_inline1324tex2html_wrap_inline1294 2.60523 2.623293
16 tex2html_wrap_inline1328tex2html_wrap_inline1226 1.96974 1.985141
Table 1: Calculated and observed term energies (Rydbergs) for Fe V relative to the tex2html_wrap_inline1196 ground state. The spectroscopic and correlation configurations for Fe V, and the values of the scaling parameters tex2html_wrap_inline1198 for each orbital in the Thomas-Fermi-Dirac potential used in Superstructure, are also given

Fe V configurations.

Spectroscopic: tex2html_wrap_inline1332, tex2html_wrap_inline1334, tex2html_wrap_inline1336.

Correlation: tex2html_wrap_inline1338 , tex2html_wrap_inline1340 , tex2html_wrap_inline1342, tex2html_wrap_inline1344, tex2html_wrap_inline1346, tex2html_wrap_inline1348, tex2html_wrap_inline1350, tex2html_wrap_inline1352, tex2html_wrap_inline1354, tex2html_wrap_inline1356.

tex2html_wrap_inline1198: 0.92092(1s), 1.12967(2s), 1.30081(2p), 1.30177(3s), 1.10895(3p), 1.08238(3d), 1.08360(4s), 1.08238(4p), 1.19316(4d).  


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