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Predicting the properties of neutron-rich nuclei far from the valley ofstability is one of the major challenges of modern nuclear theory. In heavy andsuperheavy nuclei, a difference of only a few neutrons is sufficient to changethe dominant fission mode. A theoretical approach capable of predicting suchrapid transitions for neutron-rich systems would be a valuable tool to betterunderstand r-process nucleosynthesis or the decay of super-heavy elements. Inthis work, we investigate for the first time the transition from asymmetric tosymmetric fission through the calculation of primary fission yields with thetime-dependent generator coordinate method (TDGCM). We choose here thetransition in neutron-rich Fermium isotopes, which was the first to be observedexperimentally in the late seventies and is often used as a benchmark fortheoretical studies. We compute the primary fission fragment mass and chargeyields for 254 Fm, 256 Fm and 258 Fm from the TDGCM under the Gaussian overlapapproximation. The static part of the calculation (generation of a potentialenergy surface) consists in a series of constrained Hartree-Fock-Bogoliubovcalculations based on the D1S, D1M or D1N parameterizations of the Gognyeffective interaction in a two-center harmonic oscillator basis. The2-dimensional dynamics in the collective space spanned by the quadrupole andoctupole moments is then computed with the finite element solver FELIX-2.0. Theavailable experimental data and the TDGCM post-dictions are consistent andagree especially on the position in the Fermium isotopic chain at which thetransition occurs. The main limitation of the method lies in the presence ofdiscontinuities in the 2-dimensional manifold of generator states.

From Asymmetric to Symmetric Fission in the Fermium Isotopes within the Time-Dependent GCM Formalism