The energies of a large number of low-lying levels in the atoms and ions of the Magnesium isoelectronic sequence from Mg I to Mn XIV have been calculated in a configuration interaction calculation. The orbitals are determined as eigenfunctions of the one-particle Schrödinger equation for a central potential that is variationally optimized. A relativistic calculation using the Breit approximation is carried out in the potentials calculated non-relativistically. The results are generally in good agreement with experiment, but a number of possible reassignments are suggested. Singlet-triplet separations important for forbidden transition rates, and fine-structure intervals are also tabulated.
Oscillator strength calculations for the transition elements are complicated by the occurrence of many strongly coupled terms from a single configuration. For example, there are nine 2Fo terms in the 3d44p configuration of the vanadium sequence. Using the specific example of the transition 3d44s 4H to 3d44p 4Go in Cr II, it is shown that calculations having poor energy separations for the four 3d44p terms are very unreliable but, if corrected for energy spacing, a calculation using reasonable but rather simple wavefunctions is as good as one using considerably more elaborate forms.
Configuration interaction calculations have been carried out to obtain rates for electric dipole transitions and lifetimes for the 1s22s22p63s2 3p63d44d and 5s6D and 4d6F levels in Cr II. Up to 40 configurations have been included so correlation effects should be well accounted for. Relativistic interactions are included through the use of the Breit-Pauli hamiltonian to obtain the level wave functions and energies. Strong mixing of the 4d levels occurs and this leads to substantial departures from earlier nonrelativistic calculations that assume LS coupling for these states. Results include the actual compositions of both even and odd parity levels where significant mixing occurs and the rates for all transitions that are allowed to lower levels from these 4d and 5s levels.
Transition rates have been calculated for all electric dipole allowed decays for Cr II of the 3d44p levels arising from the closely spaced 6Po, 6Do and 4Po terms, to all lower levels that arise from the 6S, 6D, 4P, and 4D terms of the 3d5 and 3d44s configurations. We have applied a previously developed method of selecting a 'natural' basis for the algebraic expansion of the spectroscopic states that results in a very substantial reduction in the size of the problem, and hence contributes significantly towards rendering the problem at all tractable. To our knowledge, no previous ab initio calculations exist that explore these decays involving the even quartets with a serious consideration of both configuration interaction and relativistic effects. Our calculations include corrections to give the correct observed splittings for closely spaced levels in each J P subspace, and corrections for the difference between calculated and observed transition energies have also been applied. Based on the calculated transition rates, we have further determined the lifetimes of the 4P 6,4PJo and 4P 6DJo levels of the Cr II ion, and compared them with available observed values. The agreement with the recent experiments of Schade et al. (1990) is reasonably satisfactory, whereas comparison with some of the older work shows larger discrepancies.
Rates for electric-dipole transitions in V II from all levels of the 4p z 5 G o ,z 3 D o , z 5 F o ,z 5 D o ,z 3 G o and z 3 F o terms to the levels of the 4s a 5 F and a 3 F terms have been calculated in a configuration-interaction model. All the lower (even-parity) levels and certain upper (odd) levels are essentially unmixed by spin-orbit and other relativistic effects, while other odd levels are moderately to very strongly mixed. The calculated transition rates are compared with those obtained elsewhere in semiempirical calculations and in recent observations. Good agreement is obtained with observations in the case of the relatively unmixed levels, while for some of the strongly mixed levels the agreement is poorer. We comment on possible sources of disagreement.
Lifetimes for the spin forbidden decay of the 3s3p3 5s20 level in the ions with nuclear charge 15 ⩽ Z ⩽ 30 of the Si isoelectronic sequence are calculated in the multiconfiguration optimized potential model and compared with other calculations and observations. When the Hamiltonian is corrected so that the 5S20–3P20 energy splittings equal the observed values, excellent agreement with the few available observed lifetimes is obtained.
The method of carrying out configuration interaction calculations using orbitals that are derived from a variationally optimized potential [K. Aashamar, T. M. Luke, J. D. Talman, J. Phys. B: Atom. Molec. Phys. 12, 3455 (1979), 14, 803 (1981)] is studied by applying it to the ground state and a considerable number of excited states of the nitrogen atom. The results of applying the method, using several correlation configurations, to the ground state multiplet are only slightly less satisfactory than the corresponding multiconfiguration Hartree-Fock results. It is shown furthermore that it is possible to obtain a unified description of a large number of excited states within the model using quite restricted configuration sets which are chosen in a reasonable way. Wavelengths and oscillator strengths for a large number of transitions are calculated and compared with experiment.
A multiconfiguration close-coupling calculation of the photoionisation of the ground state and low-lying 1Se excited states of neon has been made using a Ne+ target based on orbitals from the optimised potential model. The final-state energies considered extend from threshold into the region of the lowest autoionisation state resonances whose shapes were calculated and found to compare well with experiment where comparison is possible. The largest of the calculated resonances, originating from an excited state, peaks at over 5*101-15 cm2 which is about three orders of magnitude higher than when excited from the ground state. Oscillator strengths for certain bound-bound transitions, and near-threshold cross sections exhibiting d-channel minima for photoionisation of the excited states are also given. Finally, further development of the complex-amplitude analysis of the photoionisation at the resonances is described.
Cross sections for the process in which photoionization of an atom is accompanied by excitation of an electron from an occupied orbital to an unoccupied orbital are calculated in lowest order in perturbation theory. The calculation is carried out in a local-effective-potential model for the atom that permits the summation over the intermediate states by using the Green's function for ordinary differential equations. It is assumed that the coupling scheme for the final ionic state is that the two holes couple to a state of definite ${L}_{12}$ and ${S}_{12}$ that then combines with the particle state to give a state of definite L and S. Expressions for the total cross section and asymmetry parameter are given for closed-shell atoms. Calculated results for Ne photoionization are compared with experimental results.
