From asymmetric to symmetric fission in the fermium isotopes within the time-dependent generator-coordinate-method formalism
Background: Predicting the properties of neutron-rich nuclei far from the valley of stability is one of the major challenges of modern nuclear theory. In heavy and superheavy nuclei, a difference of only a few neutrons is sufficient to change the dominant fission mode. A theoretical approach capable of predicting such rapid transitions for neutron-rich systems would be a valuable tool to better understand $r$-process nucleosynthesis or the decay of superheavy elements. Purpose: In this work, we investigate for the first time the transition from asymmetric to symmetric fission through the calculation of primary fission yields with the time-dependent generator coordinate method (TDGCM). We choose here the transition in neutron-rich fermium isotopes, which was the first to be observed experimentally in the late 1970s and is often used as a benchmark for theoretical studies. Methods: We compute the primary fission fragment mass and charge yields for 254 Fm, 256 Fm, and 258 Fm from the TDGCM under the Gaussian overlap approximation. The static part of the calculation (generation of a potential energy surface) consists of a series of constrained Hartree-Fock-Bogoliubov calculations based on the D1S, D1M, or D1N parametrization of the Gogny effective interaction in a two-center harmonic oscillator basis. The two-dimensional dynamics in the collective space spanned by the quadrupole and octupole moments ( $\hat{Q}_{20}$, $\hat{Q}_{30}$) is then computed with the finite element solver Felix-2.0. Results: The available experimental data and the TDGCM post-dictions are consistent and agree especially on the position in the fermium isotopic chain at which the transition occurs. In addition, the TDGCM predicts two distinct asymmetric modes for the fission of 254 Fm. Conclusions: Thanks to its intrinsic accounting of shell effects and to its ability to describe the dynamics of the system up to configurations close to scission, the TDGCM is able to describe qualitatively the fission yield transition in the neutron-rich fermium isotopes. This makes it a promising tool to study the evolution of the fission yields far from the valley of stability. The main limitation of the method lies in the presence of discontinuities in the two-dimensional manifold of generator states.