On the $Q$-dependence of the lowest-order QED corrections and other properties of the ground $1^1S-$states in the two-electron ions

TL;DR

This paper derives formulas for lowest-order QED and recoil corrections in two-electron ions, calculates key properties with high precision, and provides interpolation formulas for bound state properties as a function of nuclear charge Q.

Contribution

It introduces new formulas and high-accuracy calculations for QED and recoil corrections, along with interpolation formulas for properties across different nuclear charges.

Findings

Derived formulas for QED corrections in two-electron ions.

Calculated expectation values of key operators with high accuracy.

Provided interpolation formulas for properties as a function of nuclear charge Q.

Abstract

Formulas and expectation values which are need to determine the lowest-order QED corrections ($\sim \alpha^3$) and corresponding recoil (or finite mass) corrections in the two-electron helium-like ions are presented. Other important properties of the two-electron ions are also determined to high accuracy, including the expectation values of the qausi-singular Vinti operator and $\langle r^{-2}_{eN} \rangle$ and $\langle r^{-2}_{ee} \rangle$ expectation values. Elastic scattering of fast electrons by the two-electron ions in the Born approximation is considered. Interpolation formulas are derived for the bound state properties of the two-electron ions as the function of the nuclear electric charge $Q$.