Phase Space Factors for Double-Beta Decays

Double-beta decay is presently a very studied process both theoretically and experimentally due to its potential to provide valuable information about important, but still unknown issues related to the neutrino properties and conservation of some symmetries. In the theoretical study of the double-beta decay two key quantities entering the half-life formulas are important, namely the phase space factors embedding the influence of the Coulomb field of the daughter nucleus on the emitted electrons/positrons, and the nuclear matrix elements embedding the nuclear structure effects of the nuclei participating in the decay. Accurate calculation of both of them are needed for good predictions of the double-beta decay half-lives and transitions still unmeasured, and for constraining various beyond Standard Model parameters associated with mechanisms that may contribute to the neutrinoless double-beta decay modes. During time much attention has been paid to the nuclear matrix elements that were considered to bring the largest uncertainties in the computation of the double-beta decay half-lives, while the phase space factors were considered until the recent past to be computed with enough precision. However, newer computation of the phase space factors performed with more precise methods revealed relevant deviations from their values reported previously, especially for heavier nuclei and for positron emitting and electron capture decay modes. In this paper we review the progress made in the computation of the phase space factors for double beta decay. We begin with the non-relativistic approaches, continue with the relativistic approaches which use approximate electron/positron wave functions, and end up with recent, more precise, computations of the phase space factors where exact electron wave functions are obtained from the resolution of a Dirac equation in a Coulomb-type potential and with inclusion of finite nuclear size and screening effects. We report an up-dated and complete list of the phase space factors (PSF) for the following DBD modes: β−β−, β+β+, ECβ+, and ECEC and for transitions to final ground and first excited 2+ and 0+ states of the daughter nuclei. We also make a comparison between different values of the phase space factors found in literature and discuss the differences between these results

Present status and future programs of the n_TOF experiment

CNR*11 – Third International Workshop on Compound Nuclear Reactions and Related TopicsThe neutron time-of-flight facility n_TOF at CERN, Switzerland, operational since 2001, delivers neutrons using the Proton Synchrotron (PS) 20 GeV/c proton beam impinging on a lead spallation target. The facility combines a very high instantaneous neutron flux, an excellent time of flight resolution due to the distance between the experimental area and the production target (185 meters), a low intrinsic background and a wide range of neutron energies, from thermal to GeV neutrons. These characteristics provide a unique possibility to perform neutron-induced capture and fission cross-section measurements for applications in nuclear astrophysics and in nuclear reactor technology. The most relevant measurements performed up to now and foreseen for the future will be presented in this contribution. The overall efficiency of the experimental program and the range of possible measurements achievable with the construction of a second experimental area (EAR-2), vertically located 20 m on top of the n_TOF spallation target, might offer a substantial improvement in measurement sensitivities. A feasibility study of the possible realisation of the installation extension will be also presente

Microscopic description of α-decay as super-asymmetric fission

The fine structure of α-decay is treated with fission-like models. The single particle levels are calculated along a least action path connecting the ground state of the parent nucleus and the configuration of two spherical tangent nuclei. The probabilities to find different seniority-1 configurations are obtaining by solving the time-dependent pairing equations generalized by including the Landau-Zener effect and the Coriolis coupling. The theoretical results for the α-decay of 211Po and 211Bi are compared with experimental data showing a good agreement

Study of the Effect of Newly Calculated Phase Space Factor on β-Decay Half-Lives

We present results for β-decay half-lives based on a new recipe for calculation of phase space factors recently introduced. Our study includes fp-shell and heavier nuclei of experimental and astrophysical interests. The investigation of the kinematics of some β-decay half-lives is presented, and new phase space factor values are compared with those obtained with previous theoretical approximations. Accurate calculation of nuclear matrix elements is a prerequisite for reliable computation of β-decay half-lives and is not the subject of this paper. This paper explores if improvements in calculating the β-decay half-lives can be obtained when using a given set of nuclear matrix elements and employing the new values of the phase space factors. Although the largest uncertainty in half-lives computations come from the nuclear matrix elements, introduction of the new values of the phase space factors may improve the comparison with experiment. The new half-lives are systematically larger than previous calculations and may have interesting consequences for calculation of stellar rates

New Phase Space Calculations for β

We revisit the computation of the phase space factors (PSF) involved in the positron decay and EC processes for a large number of nuclei of experimental interest. To obtain the electron/positron wave functions, we develop a code for solving accurately the Dirac equation with a nuclear potential derived from a realistic proton density distribution in the nucleus. The finite nuclear size (FNS) and screening effects are included through recipes which differ from those used in previous calculations. Comparing our results with previous calculations, performed with the same Q-values, we find a close agreement for positron decays, while, for the EC process, there are relevant differences. For the EC process, we also find that the screening effect has a notable influence on the computed PSF values especially for light nuclei. Further, we recomputed the same PSF values but using the most recent Q-values reported in literature. In several cases, the new Q-values differ significantly from the older ones, leading to large differences in the PSF values as compared with previous results. Our new PSF values can contribute to more reliable calculations of the beta-decay rates, used in the study of nuclei far from the stability line and stellar evolution