Phase space factors and half-life predictions for Majoron emitting $\beta^-\beta^-$ decay

TL;DR

This paper provides detailed calculations of phase space factors for Majoron-emitting neutrinoless double beta decay, enabling improved half-life predictions and constraints on Majoron-neutrino coupling constants.

Contribution

It offers a comprehensive calculation of phase space factors using exact Dirac wave functions, including nuclear effects, for Majoron-emitting decay modes, which was not previously available.

Findings

Calculated phase space factors with finite nuclear size and screening effects.

Predicted half-lives for Majoron-emitting decay modes.

Set limits on Majoron-neutrino coupling constants based on experimental data.

Abstract

A complete calculation of phase space factors (PSF) for Majoron emitting $0\nu\beta^-\beta^-$ decay modes is presented. The calculation makes use of exact Dirac wave functions with finite nuclear size and electron screening and includes life-times, single electron spectra, summed electron spectra, and angular electron correlations. Combining these results with recent interacting boson nuclear matrix elements (NME) we make half-life predictions for the the ordinary Majoron decay (spectral index $n$=1). Furthermore, comparing theoretical predictions with the obtained experimental lower bounds for this decay mode we are able to set limits on the effective Majoron-neutrino coupling constant $\langle g_{ee}^M\rangle$.