Analysis of Muonic-Atom Isomer Shifts inBi209andPb207

The observed muonic-atom isomer shifts in ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ and ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ are analyzed in terms of a single particle or hole coupled to collective vibrations of the nuclear core by means of the weak-coupling Hamiltonian of Bohr. The isomer shift is a delicate effect which is sensitive to certain details of nuclear structure. Although the data for these two nuclei are limited, they strongly suggest two conclusions: (1) that vibrational excitation is not strictly volume conserving, but results in a slight increase of nuclear volume; and (2) that the proton core reacts significantly to changes in state of the valence particle, in a way which is not accounted for by the present model. This reaction is found to be stronger in the case of a valence neutron than in the case of a valence proton. In addition, the Ford-Wills radial-moment analysis is found to be adequate for the analysis of isomer shifts, though the refined method of Barrett is superior. As a byproduct of this work, nuclear wave functions are obtained which may be useful for other applications.