Spectroscopic quadrupole moments from muonic atoms: Nuclear polarizability correction

Abstract

In extracting spectroscopic quadrupole moments from the quadrupole hyperfine structure of intermediate orbits of muonic atoms nuclear polarizability is an important theoretical correction. Whilst the electric quadrupole polarizability is fairly well understood, this is not so for the electric dipole polarizability. We show that the latter yields a center-of-gravity shift δ 0 of the quadrupole multiplet and a shift δA 2 of the quadrupole hyperfine constant. The quantity δ 0 is evaluated using nuclear sum rules and is found to be in good agreement with existing numerical studies. The shift δA 2 is very small due to strong cancellations in the nuclear matrix elements. This cancellation is studied and proven in a number of nuclear models.