Calculation of the nonrelativistic Bethe logarithm in the velocity gauge

TL;DR

This paper presents a new general method for calculating the Bethe logarithm in nonrelativistic quantum systems, achieving highly accurate results for helium and H₂⁺ molecular ion that surpass previous benchmarks.

Contribution

The authors develop a general procedure to evaluate the Bethe logarithm for few-body systems, improving accuracy over existing methods.

Findings

Calculated Bethe logarithm for helium: 4.37016022306(2)

Calculated Bethe logarithm for H₂⁺: 3.012230335(1)

Results significantly improve previous values.

Abstract

We consider a general procedure to evaluate the Bethe logarithm for a general few-body atomic or molecular system. As benchmarks we use calculation for the ground states of a helium atom and H_2^+ molecular ion. The obtained values are: \beta_He=4.37016022306(2) for the helium atom and \beta_{H_2^+} = 3.012230335(1) for the H_2^+. Both results substantially improve the best known values for these quantities.