Relation between the $0νββ$ and $2νββ$ nuclear matrix elements revisited

Details Relation between the $0νββ$ and $2νββ$ nuclear matrix elements revisited Relation between the $0νββ$ and $2νββ$ nuclear matrix elements revisited

2010-12-02

arxiv.org/abs/1012.0512v1

Phys.Rev.C83:015502,2011

Physics

Nuclear Physics

Nuclear Theory

Scientific paper

10.1103/PhysRevC.83.015502

We show that the dominant Gamow-Teller part, $M^{0\nu}_{GT}$, of the nuclear matrix element governing the neutrinoless $\beta\beta$ decay is related to the matrix element $M^{2\nu}_{cl}$ governing the allowed two-neutrino $\beta\beta$ decay. That relation is revealed when these matrix elements are expressed as functions of the relative distance $r$ between the pair of neutrons that are transformed into a pair of protons in the $\beta\beta$ decay. Analyzing this relation allows us to understand the contrasting behavior of these matrix elements when $A$ and $Z$ is changed; while $M^{0\nu}_{GT}$ changes slowly and smoothly, $M^{2\nu}$ has pronounced shell effects. We also discuss the possibility of phenomenological determination of the $M^{2\nu}_{cl}$ and from them of the $M^{0\nu}_{GT}$ values from the experimental study of the $\beta^{\pm}$ strength functions.

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