Microscopic description of fission in uranium isotopes with the Gogny energy density functional

Abstract

The most recent parametrizations D1S, D1N, and D1M of the Gogny energy density functional are used to describe fission in the isotopes ${}^{232--280}U$. Fission paths, collective masses, and zero-point quantum corrections, obtained within the constrained Hartree-Fock-Bogoliubov approximation, are used to compute the systematics of the spontaneous fission half-lives ${t}_{\mathrm{SF}}$, the masses and charges of the fission fragments, and their intrinsic shapes. The Gogny-D1M parametrization has been benchmarked against available experimental data on inner and second barrier heights, excitation energies of the fission isomers, and half-lives in a selected set of Pu, Cm, Cf, Fm, No, Rf, Sg, Hs, and Fl nuclei. It is concluded that D1M represents a reasonable starting point to describe fission in heavy and superheavy nuclei. Special attention is also paid to understand the uncertainties in the predicted ${t}_{\mathrm{SF}}$ values arising from the different building blocks entering the standard semiclassical Wentzel-Kramers-Brillouin formula. Although the uncertainties are large, the trend with mass or neutron numbers are well reproduced and therefore the theory still has predictive power. In this respect, it is also shown that modifications of a few percent in the pairing strength can have a significant impact on the collective masses leading to uncertainties in the ${t}_{\mathrm{SF}}$ values of several orders of magnitude.