Efficient method for computing the Thouless-Valatin inertia parameters

Starting from the adiabatic time-dependent Hartree-Fock approximation (ATDHF), we propose an efficient method to calculate the Thouless-Valatin moments of inertia for the nuclear system. The method is based on the rapid convergence of the expansion of the inertia matrix. The accuracy of the proposed method is verified in the rotational case by comparing the results with the exact Thouless-Valatin moments of inertia calculated using the self-consistent cranking model. The proposed method is computationally much more efficient than the full ATDHF calculation, yet it retains a high accuracy of the order of $1\%$.

Figure 1

The moment of inertia ${\mathcal{I}}_x$ of ${}^{154}$Sm computed using the cranking RMF framework. The various curves correspond to calculations that successively include the following terms of the residual interaction: the time-even part (Inglis-Belyaev formula denoted by IB), the linear (VL), nonlinear (VNL), and derivative (VD) time-odd terms in the isoscalar-vector channel.

Figure 2

The moment of inertia ${\mathcal{I}}_x$ of ${}^{154}$Sm computed at the zeroth-, first-, and second-order in the expansion Eq. (23) based on the PC-F1 density functional, and compared with the values obtained at the corresponding iteration steps in the cranking RMF based on the same density functional.

Figure 3

The moments of inertia ${\mathcal{I}}_x$ of ${}^{152-164}$Sm. The values computed at the zeroth-, first-, and second-order in the expansion Eq. (23) are compared with the exact Thouless-Valatin moment of inertia calculated using the RMF cranking model (upper panel). For the same nuclei the ratio of the Thouless-Valatin and Inglis-Belyaev moments of inertia (lower panel).