Instanton-motivated study of spontaneous fission of odd-A nuclei

TL;DR

This paper develops a method based on instanton theory to calculate spontaneous fission rates in odd-A nuclei, addressing limitations of previous approximations and improving predictions of fission hindrance factors.

Contribution

It introduces a hybrid model combining instanton actions for unpaired nucleons with cranking actions for even-even cores, enhancing the understanding of fission hindrance in odd-A nuclei.

Findings

Instanton-like actions improve fission hindrance estimates.

Freezing Kπ configurations overestimates hindrance factors.

Adiabatic configurations underestimate fission hindrance.

Abstract

Using the idea of the instanton approach to quantum tunneling we try to obtain a method of calculating spontaneous fission rates for nuclei with the odd number of neutrons or protons. This problem has its origin in the failure of the adiabatic cranking approximation which serves as the basis in calculations of fission probabilities. Selfconsistent instanton equations, with and without pairing, are reviewed and then simplified to non-selfconsistent versions with phenomenological single-particle potential and seniority pairing interaction. Solutions of instanton-like equations without pairing and actions they produce are studied for the Woods-Saxon potential along realistic fission trajectories. Actions for unpaired particles are combined with cranking actions for even-even cores and fission hindrance for odd-A nuclei is studied in such a hybrid model. With the assumed equal mass parameters for neighbouring odd-A and even-even nuclei, the model shows that freezing the K {\pi} configuration leads to a large overestimate of the fission hindrance factors. Actions with adiabatic configurations mostly show not enough hindrance; instanton-like actions for blocked nucleons correct this, but not sufficiently.