Selfconsistent calculation of phonon gyromagnetic ratios in $^{208}$Pb

Within the Theory of Finite Fermi systems the gyromagnetic ratios $g_L^{ph}$ of all low-lying phonons in $^{208}$Pb are calculated. The input data, i.e. single-particle energies, single-particle wave functions, and the $ph$-interaction are derived from the Energy Density Functional by Fayans et al. For the $3^-_1$ phonon which is the most collective state, the $g_L^{ph}$ value is close to the prediction of the collective Bohr–Mottelson (BM) model. Gyromagnetic ratios of other phonons that are included in our calculations, two $5^-$ states and six positive parity phonons, differ significantly from the BM model prediction.