Relativistic random-phase approximation calculation with negative energy states of nuclear polarization in muonic atoms

Abstract

We study the muonic nuclear-polarization corrections, which provide level shifts due to the two-photon exchange process between a bound muon and a nucleus. We choose $^{16}\mathrm{O}$ as a nucleus for the demonstration of the amount and the property of the nuclear polarization in the muonic atoms. The nuclear states of $^{16}\mathrm{O}$ are constructed in the random-phase approximation including the negative-energy states based on the relativistic mean field model. The spatial components of the transition current have large couplings between positive- and negative-energy states. As a result, the contribution from the negative-energy states of nucleus to the nuclear-polarization correction is found to be significant and also essential to achieve gauge invariance. The nuclear-polarization effect in muonic $^{16}\mathrm{O}$ is also calculated using the collective model. We find that the nonrelativistic nuclear model with the effective mass provides similar results as the relativistic one.