QED theory of the nuclear recoil with finite size

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.

arXiv comment5 pages, 1 figure, corrected description of $(Z\alpha {)}^5$ correction

References in corpus (16)

• Improved Measurement of the Hydrogen 1S - 2S Transition Frequency
• Probing new light force-mediators by isotope shift spectroscopy
• Relativistic nuclear recoil corrections to the energy levels of hydrogen-like and high $Z$ lithium like atoms in all orders in $\alpha Z$
• QED theory of the nuclear recoil effect in atoms
• Isotope shift, non-linearity of King plots and the search for new particles
• Recoil correction to the ground state energy of hydrogenlike atoms
• Direct Bound-Electron $g$ factor Difference Measurement with Coupled Ions
• Nuclear recoil corrections to the $2p_{\frac{3}{2}}$ state energy of hydrogen-like and high $Z$ lithium like atoms in all orders in $\alpha Z$
• Three-photon exchange nuclear structure correction in hydrogenic systems
• Nuclear recoil effect in the Lamb shift of light hydrogen-like atoms
• Theory of the Lamb shift and Fine Structure in muonic ${}^4\mathrm{He}$ ions and the muonic ${}^3\mathrm{He}{-}^4\mathrm{He}$ Isotope Shift
• Theory of the n=2 levels in muonic helium-3 ions
• Dispersive evaluation of the Lamb shift in muonic deuterium from chiral effective field theory
• Nuclear recoil corrections to the Lamb shift of hydrogen and light hydrogen-like ions
• Finite nuclear size corrections to the recoil effect in hydrogenlike ions
• Forming Molecular States with Hadronic Rescattering

Cited by in corpus (5)

• Comprehensive theory of the Lamb shift in light muonic atoms
• Ab initio calculations of the $2p_{3/2}\to 2s$ transition in He-, Li-, and Be-like uranium
• QED calculations of the nuclear recoil effect in muonic atoms
• Two-body $P$-state energies at ${\alpha }^6$ order
• QED calculations of the $2p$-$2s$ transition energies in Li-like ions