Nuclear Polarization Corrections to theμHe+4Lamb Shift

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 μ(4)He(+) leading to an energy correction in the 2S-2P transitions of δ(pol)(A)=-2.47 meV ±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 be instrumental to the μ(4)He(+) experiment planned for 2013.

Update on nuclear structure effects in light muonic atoms

“…The details of the calculation and formula for each of these terms are illustrated in Ref. [3]. Some of the terms that contribute to the NS corrections have been updated in Ref.…”

“…[3,4], where the various terms contributing to δ A pol are obtained in a multipole expansion formalism…”

“…[3,4,5,6] we have provided values for the various terms in δ TPE for the hydrogen-like muonic systems with 2 ≤ A ≤ 4, based on ab initio calculations with various state-of-the-art models for the nuclear Hamiltonian and newly developed methods [7]. This has enabled us to provide improved precision and uncertainty estimates compared to previous results.…”

Understanding the proton radius puzzle: Nuclear structure effects in light muonic atoms

“…We calculated the nuclear structure effects to the Lamb shift in μ 4 He + , including the inelastic part of δ TPE due to nuclear excitations (δ nucl pol ) [20] and the elastic part due to nuclear charge distributions (δ Zem ) [21]. We have recently improved the treatment of nucleon size effects and we show in Table 1 updated results of δ nucl pol for μD and μ 4 He + .…”

“…Combining the modern inter-nucleon potentials with few-body methods, i.e., effective interaction hyperspherical harmonics expansion (EIHH) [18] and Lanczos sum rules (LSR) [19], we also calculated δ TPE in μ 4 He + [20,21], μ 3 He + and μ 3 H [22]. By comparing the results using different potential models, we show that the uncertainty in δ TPE is dominated by nuclear physics.…”