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2. The calculation

Collision strengths are calculated using the Breit-Pauli version of the R-matrix method (Scott & Taylor 1982), following a similar procedure to that of Berrington (1988), who studied atomic oxygen.

The target wavefunctions are constructed from 1s, 2s, 2p, 3s, 3p, 3d, 4s, tex2html_wrap_inline1049 and tex2html_wrap_inline1051 orbitals; The 1s through 4s radial orbitals are from Clementi & Roetti (1974), optimised on the tex2html_wrap_inline1053 ground state. The tex2html_wrap_inline1055 correlation orbital is optimised on the tex2html_wrap_inline1057 states using Hibbert's (1975) program CIV3, in order to account for the different radial distribution of the d-orbital in the ground and excited states. This improved the term energy splitting of the states.

Long-range polarization effects are included by introducing the pseudostates (tex2html_wrap_inline1059, tex2html_wrap_inline1061, tex2html_wrap_inline1063, tex2html_wrap_inline1065), each of which involves a tex2html_wrap_inline1067 pseudo-orbital. The first three pseudostates are chosen to represent the dipole polarizability of the tex2html_wrap_inline1069 ground state; that is, the tex2html_wrap_inline1071 orbital and the pseudostate eigenvectors are optimised on the polarizability using program CIVPOL (Hibbert et al. 1977). The fourth pseudostate, tex2html_wrap_inline1073, is inserted to include as much as possible of the dipole polarizability of the tex2html_wrap_inline1075 metastable state. With these pseudostates, the calculated dipole polarizability of the tex2html_wrap_inline1077 ground state is 92.58 au, and of the tex2html_wrap_inline1079 state is 61.42 au.

To estimate the true polarizability, two previous R-matrix photoionization calculations were used, namely the tex2html_wrap_inline1081 targets of Sawey & Berrington (1992) and of Bautista (1996). The static dipole polarizability (calculated using the R-matrix programs: Berrington et al. 1996) of the tex2html_wrap_inline1083 ground state was found to be 104.36 and 103.83 au respectively which shows excellent agreement between both calculations. This means that 89% of the ground state polarizability is accounted for in the Fe I target.

The tex2html_wrap_inline1085 and tex2html_wrap_inline1087 orbitals generated and used for this calculation are tabulated in Table 1 (click here). The configurations used in each target state are in Table 2 (click here). There are of course many more configurations allowable in LS coupling for each symmetry, but only those making a significant contribution are retained.

These four pseudostates, together with the three physical states (tex2html_wrap_inline1089, tex2html_wrap_inline1091, tex2html_wrap_inline1093) give rise to 31 fine-structure levels, which are explicitly included in the R-matrix calculation (see Table 3 (click here)). Configuration-interaction wavefunctions are used for the target states; considerable effort is needed to handle the resulting open d-shell atomic system in the collision calculation. In particular, (N+1)-electron configurations are restricted to certain d-shell couplings, such as tex2html_wrap_inline1097.

The collision strengths were calculated using the FARM packaged developed by Burke & Noble (1995).

 table266
Table 1: tex2html_wrap_inline1099 and tex2html_wrap_inline1101 radial orbitals used in the Fe R-matrix calculation (the remaining target orbitals are from Clementi & Roetti 1975). Each orbital is in the form tex2html_wrap_inline1103  

 table285
Table 2: Configurations used in the Fe I target term expansions. (All tex2html_wrap_inline1123 combinations are assumed unless otherwise stated)  

 table348
Table 3: Fine-structure energy levels of the states of Fe I included in the R-matrix calculation, in Rydberg units. Observed energies are from Reader & Sugar (1975)  


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