Relativistic quantum defect calculations on the copper isoelectronic sequence

Abstract

The quantum defect orbital (am) method and its relativistic (RQDO) counterpart have been employed in this work to compute oscillator strengths for several fine-structure transitions in members of the copper isoelectronic sequence up to Z = 92. The RQDO results are found to be in quite good agreement with the best estimates derived from other sources, whenever the comparison is possible.

Relativistic oscillator strengths for transitions in the principal spectral series of the silver isoelectronic sequence

“…In the Na isoelectronic sequence [7] this rise in the 1/2 ~ 3/2 resonance f-value did not appear until the 43rd. ion of the sequence, and in the Cu sequence [8] it appeared at the 31st. ion.…”

“…The correct trend for the fine-structure f-values in the resonance transition is known [7,8,16] to be the appearance of a small maximum at the low-Z end of the sequence for both to then the 1/2 ~ 1/2 f-value decreases gradually, up to very high Z, and a gradual decrease of the 1/2 -~ 3/2 f-value up to a given Z, to rise again after reaching a minimum value. In the Na isoelectronic sequence [7] this rise in the 1/2 ~ 3/2 resonance f-value did not appear until the 43rd.…”

“…The quantum defect orbital (QDO) method [9][10][11][12] and its relativistic (RQDO) generalisation [13] belong to simple and reliable methods for estimating oscillator strengths [e.g., 1,7,8,12,14], and very recently have proven to perform well in the diffuse and sharp spectral series of the AgI sequence [1]. In principle, one would expect that, given the fact that the silver-like systems only possess a single electron out side a filled 4d subshelt, their behaviour become alkali-like at some high charge stage.…”

“…In addition, the latter techniques can be quite accurate, and have revealed empirical regularities among members of isoelectronic and homologous sequences, as well as Rydberg series, that are not so well predicted by ab initio techniques [5]. These regularities, which were indicated as early as 1964 by Edl~n [6], have been amply verified, and their validity has been confirmed up to very heavy and highly ionised systems [7,8]. These methods can be used with confidence to make precise interpolative and extrapolative predictions.…”

“…Deviations from the Coulomb potential, often phenomenologically classified as "penetration" and "polarisation" (depending on the degree of overlap between the active and passive electrons, in the context of electronic transitions), may, at least to a reasonable extent, be accounted for by a model Hamiltonian that contains a parameter related to the quantum defect. More specifically, the two above effects seem to be adequately described in the Quantum Defect Orbital method, which was originally proposed [9] and has been applied for years [10][11][12] in a non-relativistic (QDO) approach, and recently reformulated in the context of the second-order Dirac equation (RQDO) [13] and amply used to successfully calculate atomic transition probabilities [e.g., 1,7,8,14, and references therein] Regularities along isoelectronic sequences and homologous series have also been studied in these works. In most of our more recent studies, the need for explicitly introducing corepolarisation through an appropriately modified form of the dipole-length transition operator, has been discussed.…”