Partially resolved transition array model for atomic spectra

Abstract

The unresolved transition array (UTA) model of atomic spectra describes the lines in a configuration-to-configuration transition array with a single feature that conserves the total strength as well as the energy first and second strength-weighted moments. A new model is proposed that uses a relatively small detailed line calculation together with the extant variance formula to generate a series of Gaussians to describe the transition array. This partially resolved transition array (PRTA) model conserves the known array properties, yields improved higher moments, and systematically accounts for initial level populations. Numerical examples show that the PRTA model provides excellent fidelity to line-by-line methods using only a small fraction of the computational effort for the full calculations.

Statistical line-by-line model for atomic spectra in intermediate coupling

“…rather than comparing € σ K 2 to the total array variance [9]. This reflects that spin-orbit splitting contributes to the total array variance, but not to the individual relativistic sub-array variance [3].…”

“…Recently an extension of the UTA approach to complement DLA calculations in JJ coupling was developed [9]. The partially resolved transition array (PRTA) model replaces the single feature of the UTA by a number of Gaussians that conserve the known arrays properties, provides improved higher moments, and accounts for initial level populations.…”

“…The PRTA method computes the contribution to the line spectrum by splitting the open subshells into two groups: main and secondary [9]. An explicit DLA calculation of the main group that is by design small compared to the full DLA calculation is performed.…”

“…An explicit DLA calculation of the main group that is by design small compared to the full DLA calculation is performed. This smallscale DLA calculation generates In local thermal equilibrium (assumed throughout the work), the PRTA spectrum for the transition array is described by a sum of Gaussians [9],…”

“…The idea is to include in the main group the subshells that most strongly couple with the active electrons treating the remaining subshells statistically. Although presently this separation is intuitive and not rigorous, it is reasonable to assume those subshells with the largest contribution to the variance couple most strongly with the active electrons [9].…”