QED theory of the nuclear recoil with finite size

TL;DR

This paper derives a quantum electrodynamics (QED) formula for the nuclear recoil effect considering finite nuclear size, revealing higher-order contributions that dominate over lower-order terms across various atomic numbers.

Contribution

It provides the first complete QED derivation for finite-size nuclear recoil, surpassing the Breit approximation and including significant higher-order effects.

Findings

The QED formula is exact in the coupling strength parameter Zα.

Numerical results show the (Zα)^6 term dominates over the (Zα)^5 term.

The (Zα)^6 contribution is linear in nuclear radius.

Abstract

We investigate the modification of the transverse electromagnetic interaction between two point-like particles when one particle acquires a finite size. It is shown that the correct treatment of such interaction cannot be accomplished within the Breit approximation but should be addressed within the QED. The complete QED formula is derived for the finite-size nuclear recoil, exact in the coupling strength parameter $Z\,\alpha$. Numerical calculations are carried out for a wide range of $Z$ and verified against the $(Z\,\alpha)^5$ contribution. The comparison with the $Z\,\alpha$ expansion identifies the contribution of order $(Z\,\alpha)^6$, which is linear in the nuclear radius and numerically dominates over the lower-order $(Z\,\alpha)^5$ term.