Nuclear polarization corrections in the mu-4He+ Lamb shift

TL;DR

This paper provides an ab-initio calculation of nuclear polarization corrections in mu-4He+ to improve the precision of Lamb shift measurements, aiding in accurate determination of the helium nucleus charge radius.

Contribution

It introduces a new, detailed ab-initio approach using advanced nuclear Hamiltonians and few-body methods to accurately estimate nuclear polarization effects in muonic helium.

Findings

Calculated polarization correction: -2.47 meV with 6% uncertainty.

Reduced the nuclear polarization uncertainty compared to previous estimates.

Predictions support upcoming mu-4He+ Lamb shift experiments.

Abstract

Stimulated by the proton radius conundrum, measurements of the Lamb shift in various light muonic atoms are planned at PSI. The aim is to extract the rms charge radius with high precision, limited by the uncertainty in the nuclear polarization corrections. We present an ab-initio calculation of the nuclear polarization for mu-4He+ leading to an energy correction in the 2S-2P transitions of $\delta_{pol}=-2.47$ meV $\pm$ 6%. We use two different state-of-the-art nuclear Hamiltonians and utilize the Lorentz integral transform with hyperspherical harmonics expansion as few-body methods. We take into account the leading multipole contributions, plus Coulomb, relativistic and finite-nucleon-size corrections. Our main source of uncertainty is the nuclear Hamiltonian, which currently limits the attainable accuracy. Our predictions considerably reduce the uncertainty with respect to previous estimates and should timely serve the mu-4He+ experiment planned for 2013.