Stimulated by the the proton radius conundrum [1] a measurement of the 2S-2P transition frequencies in muonic ⁴He⁺ and ³He⁺ are planned in PSI. The aim of these measurements is to determine the nuclear rms charge radius with relative accuracy of 3x10^-4 limited by the uncertainty in the nuclear polarization contribution. In fact, to shed light on the radius puzzle the nuclear polarizability should be known with an accuracy better then 5% [2].

In order to achieve this accuracy, we present in this work the first ab-initio calculation of the nuclear polarizability contribution to the Lamb shift in μ⁴He⁺. We have used the EIHH [3] and the LIT [4] methods to obtain the ⁴He response functions for the state of the art nuclear potential models, taking into account the leading multipoles and relativistic corrections. The systematic accuracy of our analysis is estimated to be comparable with the desired 5% goal.

[1] R. Pohl et al., The size of the proton, Nature 466, 213 (2010).
[2] A. Antognini et al., Illuminating the proton radius conundrum: the μHe⁺ Lamb shift, Can. J. Phys. 89, 47 (2011).
[3] N. Barnea, W. Leidemann, and G. Orlandini, State dependent effective interaction for the hyperspherical formalism, Phys. Rev. C 61, 054001 (2000).
[4] V.D. Efros, W. Leidemann, and G. Orlandini, Response functions from integral transforms with a Lorentz kernel, Phys. Lett. B 338, 130 (1994).