Nuclear Polarization in Muonic Atoms of Deformed Nuclei

The analysis of muonic x-ray spectra in deformed nuclei was carried out in the past by diagonalizing the electric quadrupole interaction between the spin doublets ($2p_{\frac{3}{2}}, 2p_{\frac{1}{2}}$), ($3d_{\frac{5}{2}}, 3d_{\frac{3}{2}}$) and the lowest rotational band of the nucleus. With the present experimental accuracy, this procedure is no longer adequate. To take into account the muonic and nuclear states not included in the diagonalization, we renormalize the electric quadrupole interaction by virtual excitations into those states. We find that the renormalization correction amounts to a few percent of the quadrupole matrix elements. This explains the systematic tendency for the intrinsic quadrupole moments obtained from the traditional analysis to be a few percent larger than the values deduced from Coulomb excitation experiments. We also find that the inclusion of the renormalization corrections has a very significant effect on the parameters of the charge distribution and the intensity ratios of the hyperfine multiplets.