Multidimensionally-constrained relativistic mean-field study of spontaneous fission: coupling between shape and pairing degrees of freedom

TL;DR

This study investigates how the coupling between shape and pairing degrees of freedom affects spontaneous fission dynamics, using a multidimensional relativistic mean-field model to compute fission paths, actions, and half-lives.

Contribution

It introduces a multidimensionally-constrained relativistic mean-field approach that includes pairing fluctuations as collective variables for more accurate fission modeling.

Findings

Pairing correlations favor axially symmetric shapes during fission.

Including pairing fluctuations reduces the action integral and shortens half-lives.

Results align with recent HFB model findings for $^{264}$Fm.

Abstract

Studies of fission dynamics, based on nuclear energy density functionals, have shown that the coupling between shape and pairing degrees of freedom has a pronounced effect on the nonperturbative collective inertia and, therefore, on dynamic (least-action) spontaneous fission paths and half-lives. Collective potentials and nonperturbative cranking collective inertia tensors are calculated using the multidimensionally-constrained relativistic mean-field (MDC-RMF) model. Pairing correlations are treated in the BCS approximation using a separable pairing force of finite range. Pairing fluctuations are included as a collective variable using a constraint on particle-number dispersion. Fission paths are determined with the dynamic programming method by minimizing the action in multidimensional collective spaces. The dynamics of spontaneous fission of $^{264}$Fm and $^{250}$Fm are explored. Fission paths, action integrals and corresponding half-lives computed in the three-dimensional collective space of shape and pairing coordinates, using the relativistic functional DD-PC1 and a separable pairing force of finite range, are compared with results obtained without pairing fluctuations. Results for $^{264}$Fm are also discussed in relation with those recently obtained using the HFB model. The inclusion of pairing correlations in the space of collective coordinates favors axially symmetric shapes along the dynamic path of the fissioning system, amplifies pairing as the path traverses the fission barriers, significantly reduces the action integral and shortens the corresponding SF half-life.