T M Luke

Oscillator Strengths in the Aluminum Sequence

The structures of the 3s23p 2P0 ground state and of a number of excited states for aluminum and ions along the isoelectronic sequence up to Ca VIII have been calculated in the Multiconfiguration Optimized Potential Model. The excited states include the following: 3s23d 2D, 3s24s 2S, 3s3p2 2D, 2S, as well as 3s24p, 3p3 and 3s3p(3P0)3d 2P0. There is strong configuration mixing in the spectroscopic terms but on the basis of our calculations we recommend a different designation from that currently adopted for the 3p3 and 3s3p(3P0)3d 2P0 terms. Oscillator strengths for transitions among these terms have been calculated in the length and velocity formulation with particular emphasis on accurate description in the vicinity of term crossings. Comparison is made with other theory and with experiment where results are available. At present, the experimental data are inadequate to verify the many calculated structures in the isoelectronic gf dependence.

Calculation of spin forbidden decay rates of the 3s3p3 5S02 level in the Si isoelectronic sequence for 15≤Z≤30

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.

A multi-configuration optimised central potential method for atomic structure calculations: application to carbon

A multi-configuration optimised central potential model for atomic structure is described. In this model, the expectation value for the Hamiltonian is minimised by varying the central potentials in which are calculated the orbitals of the multi-configuration atomic state. Each potential satisfies a linear integral equation which is solved numerically. Results for the energies of some low-lying even- and odd-parity states of carbon are given and compared with experiment as well as with multi-configuration Hartree-Fock and close-coupling calculations. As in the case of the single-configuration optimised potential model, whose generalisation is presented here, the results compare favourably with those from other rather more complicated methods.

Energy Levels in the Magnesium Sequence, Mg I-Mn XIV, Calculated in the Multiconfiguration Optimized Potential Model

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 Schrodinger 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.

A correction method for fine-structure calculations. II. Application to neon 3s and 3p excited levels

For pt.I see ibid., vol.18, no.4, p.589 (1985). The transition rates for transitions among the 3s and 3p excited fine-structure levels of neutral neon are calculated and compared with experimental observations. The method of calculation involves accurate non-relativistic calculation of the wavefunctions in LS coupling followed by diagonalisation of the Breit-Pauli Hamiltonian to yield the fine structure. Particularly in the case of the 3p levels, very slight errors in the non-relativistic energies can lead to very significant errors in the relativistic level-mixing coefficients with consequently large errors in the transition rates. A method for correcting energy levels, based on inverting the eigenvalue problem using the eigenvalues (the observed level energies) as known input, allows accurate determination of level-mixing coefficients, and hence transition rates, in a test case involving levels that are strong mixtures of three terms. The paper extends earlier work by demonstrating that the method remains effective for obtaining corrected mixing coefficients in a somewhat more complicated situation involving levels with significant mixtures of four non-relativistic terms as well as in cases where only two terms are mixed. The resulting transition rates compare well with observation and some discussion of the errors implicit in the method indicates that the method is stable and accurate in the context of such transition rate calculations.

Oscillator strengths for transitions from 3s4s and 3s4p levels calculated in the magnesium sequence, MgI-MnXIV using the multiconfiguration optimized potential model

Oscillator strengths for downward transitions from the 3s4p and 3s4s levels in the Magnesium isoelectronic sequence are reported. These, as well as lifetimes for these levels, have been calculated for MgI to MnXIV using the Multiconfiguration Optimized Potential Model (MCOPM) with inclusion of relativistic corrections. Generally, the level splittings are reasonably accurate but at certain level crossings - occurring near Sv and C1VI - considerable energy level accuracy is required to ensure accurate relativistic mixing coefficients and transition rates. Corrections have been applied to the energies in these cases.

Calculation of doubly excited resonances in neon

Close coupling calculations of doubly excited autoionization states of three low-lying 1P0 series in neutral neon are reported and compared with the results of photoionization experiments. Certain anomalies appearing in both the experiments and the calculations are discussed.

Autoionisation states in neon: photoionisation from ground and excited states

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.

A correction method for fine-structure calculations: application to neon 3p J=2 levels

This work is concerned with the question of calculating transition oscillator strengths for atomic fine-structure levels that are described by strongly mixed superpositions of terms. Rather accurate non-relativistic calculations of wavefunctions followed by perturbation treatment of relativistic interactions can lead to very poor term mixing, hence poor oscillator strengths, in situations where there is near degeneracy of the non-relativistic energy eigenvalues. It is shown in a three-term mixing case how a corrected Hamiltonian can be constructed using observed level energies as known input. The example, involving the three J=2 levels of the 2p53p configuration of neutral neon, shows a dramatic improvement for transition probabilities and Lande factors when the correction is made and the results compared with recent observations.

Allowed and forbidden transitions in singly ionized vanadium

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.