QED Theory of the Nuclear Recoil with Finite Size

We investigate the modification of the transverse electromagnetic interaction between two pointlike 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.

Figure 1

Finite-size nuclear recoil correction for the $1s$ state of H-like ions, in terms of function $\delta P=E_{\text{recfns}}/[(m^2/M)(Z\alpha {)}^5/\pi ]$.