QED nuclear recoil effect in helium isotope shift

TL;DR

This paper refines the calculation of the QED nuclear recoil effect in helium isotope shifts by including second-order finite-mass corrections, leading to more precise nuclear charge-radius difference measurements.

Contribution

It derives formulas for the $m\alpha^5$ QED correction up to second order in $m/M$ and applies them to helium isotopes, improving previous theoretical models.

Findings

Enhanced accuracy in helium isotope shift calculations.

More precise determination of nuclear charge-radius differences.

Validation of second-order finite-mass correction formulas.

Abstract

We present a detailed investigation of the leading-order $m\alpha^5$ QED correction with inclusion of the finite-nuclear-mass effects. Previously, this correction had been calculated within an expansion in the electron-nucleus mass ratio $m/M$ up to the first order. In this work, we derive formulas for the $m\alpha^5$ QED contribution that are valid up to the second order in $m/M$, and perform its calculation for the $^3$He$-$$^4$He isotope shift, leading to an improved determination of the nuclear charge-radius difference.