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High partial waves contribution in calculations of the polyvalent atoms

M. G. Kozlov

Abstract

High accuracy calculations of atomic properties require using long basis sets. In particular, it is necessary to include large number of partial waves and estimate truncation corrections. The convergence in partial waves is known to be rather slow, so calculations become very costly. We use valence perturbation theory [PRA \textbf{105}, 052805 (2022)] to calculate contribution of the high partial waves and estimate truncation corrections. These estimates may be useful to make assessment of theoretical error in atomic calculations more reliable.

High partial waves contribution in calculations of the polyvalent atoms

Abstract

High accuracy calculations of atomic properties require using long basis sets. In particular, it is necessary to include large number of partial waves and estimate truncation corrections. The convergence in partial waves is known to be rather slow, so calculations become very costly. We use valence perturbation theory [PRA \textbf{105}, 052805 (2022)] to calculate contribution of the high partial waves and estimate truncation corrections. These estimates may be useful to make assessment of theoretical error in atomic calculations more reliable.
Paper Structure (6 sections, 6 equations, 2 figures, 7 tables)

This paper contains 6 sections, 6 equations, 2 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Results
  4. Scaling of corrections with $l$ and estimates of truncation errors
  5. Summary
  6. Acknowledgments

Figures (2)

  • Figure 1: Corrections to the binding energies of Sc I for the ground state multiplet $^2D_\mathrm{gs}$ and multiplets ${}^2D$ and ${}^4D^o$ from S and D excitations to the partial wave $l$ and respective fits with functions ${A}/{L^q}$.
  • Figure 2: Function $R(L)\,{L^q}$ from Eq. \ref{['eq:Ratio']} (red circles) and the fit with function \ref{['eq:Ratio_fit']}.