Double beta decay of some medium-mass nuclei

Abstract

This study examines the double beta decay of Zn-70, Se-80, Ru-104 and Cd-114. These nuclei are even, middle mass nuclei with open major shells. Their structure calls for the pairing interaction between like nucleons. In this study this is achieved by using the nuclear Bardeen-Cooper-Schrieffer (BCS) model. In the BCS model, the valence nucleons are treated as a sort of condensate that has spread across the valence energy levels. In the BCS model, interacting particles are replaced by non-interacting quasiparticles.

Double beta decay is a rare process, with only a handful of nuclei being predicted to experience them. The decay process involves accounting for the intermediate states between the initial and final nuclei. This is done by summing over the various possible levels, and weighing them by the occupation amplitudes of the level in question and dividing by the average energy between the initial and final states. An alternative proposal, the single-state-dominance hypothesis (SSDH), replaces this sum by assuming that only the ground state is relevant. This study uses the SSDH in its main results. The BCS double beta decay matrix elements were determined to be: Zn:0.91 Se:0.48 Ru:1.61 and Cd:0.95

The BCS results for the single beta decays of the intermediate nucleus are not wholly in agreement with the experimental $\log{ft}$ values. There are various possible error sources, the major one being that the basic BCS model assumes that the quasiparticles do not interact. There are extensions that allow correcting such things. As an alternative, I tested a model where the ground state of the intermediate nucleus was replaced by a linear combination of $1^+$ states that could experience beta decay. The coefficients for these combinations were determined by requiring that one of the single beta decay $\log{ft}$ values is correct.

The aforementioned linear combinations were also used to calculate the double beta decay matrix element for each of the processes in this study. To evaluate these results, I also calculated the double beta decay matrix element using the single decay matrix elements that produced the experimental $\log{ft}$ values for the intermediate nucleus. This could have been achieved by calculating backwards from the $\log{ft}$ equation, but even more trivial was to take one linear combination that had been fitted to the corresponding process. These results were: Zn:0.045 Se:0.027 Ru:0.116 and Cd:0.076.