On highly accurate calculations of the excited $n^1S(L = 0)-$states in helium atoms

TL;DR

This paper achieves highly accurate calculations of excited $n^1S$ states in helium atoms, including energies, properties, and QED corrections, advancing precision in two-electron atomic systems.

Contribution

It introduces highly precise computational methods for excited states in helium, including convergence analysis and QED correction estimates, extending to higher principal quantum numbers.

Findings

High-accuracy energies and properties for $2^1S$ states in helium.

Convergence analysis of expectation and cusp values.

Estimation of isotope shift and QED corrections for helium states.

Abstract

The total energies and various bound state properties of the excited $2^1S(L = 0)-$states in two-electron helium atoms, including the ${}^{\infty}$He, ${}^4$He and ${}^3$He atoms, are determined to very high numerical accuracy. The convergence of the results obtained for some electron-nuclear and electron-electron expectation values and, in particular, for the electron-nuclear and electron-electron cusp values, is discussed. The field component of the isotope shift and lowest order QED correction are estimated for the $2^1S(L = 0)-$states in the ${}^4$He and ${}^3$He atoms. We also apply our highly accurate methods to numerical computations of the excited $n^1S-$states (for $n$ = 3 and 4) in two-electron atomic systems.