Abstract
The non-perturbative method to compute Adiabatic Time Dependent Hartree Fock Bogoliubov (ATDHFB) collective inertias is extended to the Generator Coordinate Method (GCM) in the Gaussian overlap approximation (GOA) including the case of density dependent forces. The two inertias schemes are computed along the fission path of the 234U and compared with the perturbative results. We find that the non-perturbative schemes predict very similar collective inertias with a much richer structure than the one predicted by perturbative calculations. Moreover, the non-perturbative inertias show an extraordinary similitude with the exact GCM inertias computed numerically from the energy overlap. These results indicate that the non-perturbative inertias provide the right structure as a function of the collective variable and only a phenomenological factor is required to mock up the exact GCM inertia, bringing new soundness to the microscopic description of fission.
Highlights
Despite its discovery dates back almost 80 years, fission still remains a major challenge for nuclear theory [1]
Within this approximation the fission probability is obtained as the probability of the nucleus to tunnel under the fission barrier, which is driven by the potential energy surface (PES) and the collective inertias felt by the nucleus in its way to scission [4,5]
This comparison confirms the results found in the non-perturbative study and indicating the inadequacy of multiplying the perturbative inertias by a phenomenological factor to grasp the structure of the exact Generator Coordinate Method (GCM)–Gaussian overlap approximation (GOA) collective inertia [26]
Summary
Despite its discovery dates back almost 80 years, fission still remains a major challenge for nuclear theory [1]. The starting point in any traditional energy density functional calculation is the original assumption that fission can be described using a reduced set of collective variables [2,3]. Within this approximation the fission probability is obtained as the probability of the nucleus to tunnel under the fission barrier, which is driven by the potential energy surface (PES) and the collective inertias felt by the nucleus in its way to scission [4,5]. Together with the collective ground-state energy, enter in the collective action integral allowing for the calculation of the spontaneous fission lifetime by means of the semiclassical Wentzel–Kramers–Brillouin (WKB) approach.
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