Cranking inertia of odd nuclei from time-dependent pairing equations: Application to Th cold fission

Abstract

A new formalism for the nonadiabatic collective inertia from time-dependent pairing equations for odd numbers of nucleons is described in detail. The effective masses and the moments of inertia result from the occurrence of matrix elements of the time derivatives and of the angular couplings, respectively, between states of different seniority configurations. For low collective velocities, the formulas for the inertia reduce to the known cranking expressions available for quasitationary states. The effective mass and the perpendicular moment of inertia are evaluated for the $^{230--232}\mathrm{Th}$ parent nuclei along the fission path. The inertia for the even-odd system is larger than those of the even-even ones and exhibits fluctuations due to the intrinsic nuclear structure. The ground state theoretical value of the moment of inertia for $^{231}\mathrm{Th}$ agrees well with the evaluated experimental data if the blocking effect is neglected.