Multidimensionally constrained relativistic Hartree-Bogoliubov study of spontaneous nuclear fission

Background: Recent microscopic studies, based on the theoretical framework of nuclear energy density functionals, have analyzed dynamic (least action) and static (minimum energy) fission paths, and it has been shown that in addition to the important role played by nonaxial and/or octupole collective degrees of freedom, fission paths crucially depend on the approximations adopted in calculating the collective inertia.Purpose: To analyze effects of triaxial and octupole deformations, as well as approximations to the collective inertia, on the symmetric and asymmetric spontaneous fission dynamics, and compare with results of recent studies based on the self-consistent Hartree-Fock-Bogoliubov (HFB) method.Methods: Deformation energy surfaces, collective potentials, and perturbative and nonperturbative cranking collective inertia tensors are calculated using the multidimensionally-constrained relativistic Hartree-Bogoliubov (MDC-RHB) model, with the energy density functionals PC-PK1 and DD-PC1. Pairing correlations are treated in the Bogoliubov approximation using a separable pairing force of finite range. The least-action principle is employed to determine dynamic spontaneous fission paths.Results: The dynamics of spontaneous fission of Fm264 and Fm250 is explored. The fission paths, action integrals, and the corresponding half-lives predicted by the functionals PC-PK1 and DD-PC1 are compared and, in the case of Fm264, discussed in relation with recent results obtained using the HFB model based on the Skyrme functional SkM∗ and a density dependent mixed pairing interaction.Conclusions: The inclusion of nonaxial quadrupole and octupole shape degrees of freedom is essential for a quantitative analysis of fission dynamics. The action integrals and, consequently, the half-lives crucially depend on the approximation used to calculate the effective collective inertia along the fission path. The perturbative cranking approach underestimates the effects of structural changes at the level crossings and the resulting collective inertia varies relatively smoothly in the (β20,β22) and (β20,β30) planes. In contrast, the nonperturbative collective mass is characterized by the occurrence of sharp peaks on the surface of collective coordinates, that can be related to single-particle level crossings near the Fermi surface. This enhances the effective inertia, increases the values of the action integral, and results in longer fission half-lives