Phase Space Factors for Double-Beta Decays

Double-beta decay is presently a very studied process both theoretically and experimentally3 due to its potential to provide valuable information about important, but still unknown issues rela-4 ted to the neutrino properties and conservation of some symmetries. In the theoretical study of5 the double-beta decay two key quantities entering the half-life formulas are important, namely6 the phase space factors embedding the influence of the Coulomb field of the daughter nucleus7 on the emitted electrons/positrons, and the nuclearmatrix elements embedding the nuclearstru-8 cture effects of the nuclei participating in the decay. Accurate calculation of both of them are9 needed for good predictions of the double-beta decay half-lives and transitions still unmeasured,10 and for constraining various beyond Standard Model parameters associated with mechanisms11 that may contribute to the neutrinoless double-beta decay modes. During time much attention12 has been paid to the nuclear matrix elements that were considered to bring the largest uncer-13 tainties in the computation of the double-beta decay half-lives, while the phase space factors14 were considered until the recent past to be computed with enough precision. However, newer15 computation of the phase space factors performed with more precise methods revealed relevant16 deviations from their values reported previously, especially for heavier nuclei and for positron17 emitting and electron capture decay modes. In this paper we review the progress made in the18 computation of the phase space factors for double beta decay. We begin with the non-relativistic19 approaches, continue with the relativistic approaches which use approximate electron/positron20 wave functions, and end up with recent, more precise, computations of the phase space factors21 where exact electron wave functions are obtained from the resolution of a Dirac equation in a22 Coulomb-type potential and with inclusion of finite nuclear size and screening effects. We report23 an up-dated and complete list of the phase space factors (PSF) for the following DBD modes:24 β−β−, β+β+, ECβ+ and ECEC and for transitions to final ground and first excited 2+ and 0+25 statesofthedaughternuclei. Wealsomakeacomparisonbetweendifferentvaluesofthephase26 space factors found in literature and discuss the differences between these results.