Weak-interaction and nuclear-structure aspects of nuclear double beta decay

Recent experimental data and progress in nuclear structure modeling have led to improved descriptions of astrophysically important weak-interaction processes. This review discusses these advances and their applications to hydrostatic solar and stellar burning, to the slow and rapid neutron-capture processes, to neutrino nucleosynthesis, and to explosive hydrogen burning. Special emphasis is given to the weak-interaction processes associated with core-collapse supernovae. Despite significant progress, improvements in the modeling of these processes are still warranted and are expected to come from future radioactive ion-beam facilities.

Nuclear weak-interaction processes in stars

The nuclear shell model towards the drip lines

The last decades brought impressive progress in synthesizing and studying properties of nuclides located very far from the beta stability line. Among the most fundamental properties of such exotic nuclides, the ones usually established first are the half-life, possible radioactive decay modes, and their relative probabilities. When approaching limits of nuclear stability, new decay modes set in. First, beta decays are accompanied by emission of nucleons from highly excited states of daughter nuclei. Second, when the nucleon separation energy becomes negative, nucleons start being emitted from the ground state. A review of the decay modes occurring close to the limits of stability is presented. The experimental methods used to produce, identify, and detect new species and their radiation are discussed. The current theoretical understanding of these decay processes is reviewed. The theoretical description of the most recently discovered and most complex radioactive process---the two-proton radioactivity---is discussed in more detail.

Radioactive decays at limits of nuclear stability

Assessment of uncertainties in QRPA $0νββ$-decay nuclear matrix elements

\ensuremath{\beta}-decay properties of nuclei are studied in the framework of proton-neutron quasiparticle random-phase approximation with a schematic Gamow-Teller residual interaction Particle-hole and particle-particle terms of the separable Gamow-Teller force are consistently included for both ${\mathrm{\ensuremath{\beta}}}^{+}$ and ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}}$ directions, and their strengths are fixed as smooth functions of mass number A of nuclei in such a way that the calculation reproduces observed \ensuremath{\beta}-decay properties of nuclei Using the fixed interaction strengths, \ensuremath{\beta}-decay half-lives of nuclei up to A=150 are calculated, and generally good agreement with experiment is obtained A schematic force which is relevant to the unique first-forbidden decay is also included in a similar way to the Gamow-Teller force, and its effects are studied \textcopyright{} 1996 The American Physical Society

Systematic study of nuclear beta decay

A comprehensive representation is presented of a generalized form of the proton-neutron quasiparticle RPA model, originally introduced by Halbleib and Sorensen almost thirty years ago. The model uses separable Gamow-Teller forces, including, in addition to the particle-hole force of the former model, the particle-particle force, which is of decisive importance for β+ decay andββ decay. The above model has further been extended to the treatment of odd-odd nuclei. An extension is also made to transitions from nuclear excited states. This is essential for calculations of nuclear weak transition rates in the high-temperature interior of massive stars. Complementing the discussion of Halbleib and Sorensen on the particle-hole force, the structure of the RPA dispersion relation is discussed with emphasis on effects of the particle-particle force.

Proton-neutron quasiparticle RPA with separable Gamow-Teller forces

Nuclear matrix elements of the two-neutrino and neutrinolessββ decays of48Ca(0 g.s. + )→48Ti(0 g.s. + ) are calculated by shell model and QRPA. The two-neutrino matrix elementM GT 2v is rather reliably evaluated in the QRPA approach by a careful fit of the particle-particle interaction strength in the 1+ channel, which governs the spinisospin ground-state correlations. The shell-model value ofM GT 2v depends not only on the 1+ interaction but largely on the pairing and quadrupole interactions. Concerning the neutrinoless-mode nuclear matrix elements, the shell model gives generally smaller values than the QRPA. A detailed analysis indicates that the discrepancies originate mainly from the truncation of shell-model configurations (fp-space). The QRPA calculation in a larger model space well takes into account transitions from/to single-particle orbits far from the Fermi surface, and those transitions give rise to sizable contributions because of large momentum transfers due to the exchange of a virtual neutrino.

A comparative study of double beta decay by shell model and quasiparticle RPA

Allowed {beta}{sup +}-decay branches of very proton-rich {ital sd}-shell nuclei up to the proton drip line are calculated by the complete {ital sd}-space shell model. The {beta}{sup +}-decay half-lives calculated with the global quenching factor ({ital g}{sub {ital A}}{sup eff}/{ital g}{sub {ital A}}){sup 2}=0.60 are in reasonable agreement with existing experimental data. However, considerable deviations of the quenching factor from the global value are obtained in a comparison of the theoretical and experimental {ital ft} values in the large-{ital Q}-value window. Probable candidates for the {beta}-delayed two-proton emission are suggested with the predicted {beta}{sup +}-decay branching strengths to states above the proton-emission threshold energy.

E. Bender

Papers

Systematic study of nuclear beta decay

Proton-neutron quasiparticle RPA with separable Gamow-Teller forces

A comparative study of double beta decay by shell model and quasiparticle RPA

beta + decays of very proton-rich sd-shell nuclei.