Correlation potential and ladder diagrams

TL;DR

This paper extends the all-order correlation potential method for atomic structure calculations by including ladder diagrams, significantly improving accuracy for cesium and thallium energy levels.

Contribution

The authors incorporate ladder diagrams into the correlation potential method, enhancing its accuracy for atoms with one external electron.

Findings

Inclusion of ladder diagrams reduces energy calculation discrepancies to below 1%.

The method achieves high accuracy for cesium and thallium atomic states.

The approach broadens the applicability of correlation potential calculations.

Abstract

The all-order correlation potential method of accurate atomic structure calculations for atoms with one external electron is extended to include one more class of correlation diagrams to all orders. These are the so-called ladder diagrams which describe residual Coulomb interaction between an external electron and atomic core. This is in addition to the screening of Coulomb interaction by core electrons and the hole-particle interaction in the core polarization operator which are also included in all orders. Calculations of the energies of the lowest $s$, $p$ and $d$ states of cesium and thallium show that inclusion of the ladder diagrams leads to significant improvement of the accuracy of the calculations. The discrepancy between theoretical and experimental energies is reduced to a small fraction of a per cent in all cases. This widens the range of atoms and atomic states for which the correlation potential method can produce very accurate results.