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

A complete calculation of phase space factors (PSF) for Majoron emitting $0νβ^-β^-$ 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 $\langle g_{ee}^M\rangle$.

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