Relativistic, QED, and finite nuclear mass corrections for low-lying states of Li and Be$^+$

TL;DR

This paper provides highly accurate calculations of energy levels and corrections for low-lying states of lithium and beryllium ions, enabling precise determination of nuclear charge radii through comparison with experimental isotope shifts.

Contribution

It introduces a computational approach using Hylleraas basis sets to accurately compute relativistic, QED, and finite nuclear mass corrections for specific atomic states of Li and Be$^+$.

Findings

Calculated nuclear charge radii for Li and Be isotopes.

Achieved high-precision energy and correction values for selected states.

Enabled extraction of nuclear properties from isotope shift comparisons.

Abstract

Accurate results for nonrelativistic energy, relativistic, QED, and finite nuclear mass corrections are obtained for $2^1S_{1/2}$, $3^1S_{1/2}$ and $2^1P_{1/2}$ states of the Li atom and Be$^+$ ion. Our computational approach uses the Hylleraas basis set with the analytic integration and recursion relations. From comparison of experimental results for the isotope shifts to theoretical predictions including nuclear polarizabilities, we obtain nuclear charge radii for Li and Be isotopes.