Numerical evaluations of the isotopic shifts and lowest-order QED corrections for the ground $1^1S-$states of the ${}^{3}$He and ${}^{4}$He atoms

TL;DR

This paper provides high-precision calculations of isotopic shifts and QED corrections for the ground states of helium-3 and helium-4 atoms, including recoil effects using a new corrected formula applicable to any nuclear charge.

Contribution

It introduces a new corrected formula for recoil correction to the lowest-order QED correction applicable to atoms with any nuclear charge Q ≥ 1.

Findings

High-accuracy isotopic shift values for ${}^{3}$He and ${}^{4}$He.

Evaluation of lowest-order QED and recoil corrections.

Implementation of a new recoil correction formula.

Abstract

The both mass-dependent and field shift components of the isotopic shifts and the lowest order QED corrections for the ground (singlet) $1^1S(L = 0)-$states of the ${}^{3}$He and ${}^{4}$He atoms are determined to high accuracy. For the same states we also evaluated the lowest-order QED corrections and the corresponding recoil (or finite mass) corrections. In our calculations we have used the new (corrected) formula for the recoil correction to the lowest-order QED correction which can be applied to atoms/ions with arbitrary nuclear charge $Q \ge 1$.