Spin-multipole nuclear matrix elements in the pn quasiparticle random-phase approximation: Implications for β and ββ half-lives

Abstract

Half-lives for 148 potentially measurable 2nd-, 3rd-, 4th-, 5th-, 6th-, and 7th-forbidden unique beta transitions are predicted. To achieve this, the ratio of the nuclear matrix elements (NMEs), calculated by the proton-neutron quasiparticle random-phase approximation (pnQRPA), MpnQRPA, and a two-quasiparticle (two-qp) model, Mqp, is studied and compared with earlier calculations for the allowed Gamow-Teller (GT) 1+ and first-forbidden spin-dipole (SD) 2− transitions. The present calculations are done using realistic single-particle model spaces and G-matrix based microscopic two-body interactions. In terms of the ratio k = MpnQRPA/Mqp the studied decays fall into two groups: for GROUP 1, which consists of transitions involving non-magic nuclei, the ratio turns out to be k = 0.29 ± 0.15. For GROUP 2, consisting of transitions involving semimagic nuclei, the ratio is 0.5–0.8 for half of the decays and less than 5 × 10−3 for the other half. The magnitudes of the NMEs for several nuclei of GROUP 2 depend sensitively on the size of the used single-particle space and the energies of few key single-particle orbitals used in the pnQRPA calculation, while no such dependence is found for the transitions involving nuclei of GROUP 1. Comparing the NME ratios k of GROUP 1 with those of the earlier GT and SD calculations, where also experimental data are available, the expected “experimental” half-lives for the decays between the 0+ ground state of the even-even reference nuclei and the J π = 3+,4−,5+,6−,7+,8− states of the neighboring odd-odd nuclei are derived for possible experimental verification. The present results could also shed light to the magnitudes of the NMEs corresponding to the high-forbidden unique 0+ → J π = 3+,4−,5+,6−,7+,8− virtual transitions taking part in the neutrinoless double beta decays.