Examinations of the consistency of the quasiparticle random-phase approximation approach to double-$\beta$ decay of ${}^{48}$Ca

Abstract

The nuclear matrix elements (NMEs) of the neutrinoless and two-neutrino double-$\beta$ decays of ${}^{48}$Ca are calculated by the quasiparticle random-phase approximation (QRPA) with emphasis on the consistency examinations of this calculation method. The main new examination points are the consistency of two ways to treat the intermediate-state energies in the two-neutrino double-$\beta$ NME and comparison with the experimental charge-exchange strength functions obtained from ${}^{48}$Ca$(p,n)$ and ${}^{48}$Ti$(n,p)$ reactions. No decisive problem preventing the QRPA approach is found. The obtained neutrinoless double-$\beta$ NME adjusted by the ratio of the effective and bare axial-vector current couplings is lowest in those calculated by several groups and close to one of the QRPA values obtained by another group.

13 pages, 13 figures. Discussions added to the previous version. Addition and removal of figures and tables

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Cited by in corpus (7)

• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• Time-reversed particle-vibration loops and nuclear Gamow-Teller response
• Physical features of strength of isoscalar pairing interaction determined by relation between double charge change and double pair transfer
• Isoscalar pairing interaction for the quasiparticle random-phase approximation approach to double-$\beta$ and $\beta$ decays
• Estimation of nuclear matrix elements of double-$\beta$ decay from shell model and quasiparticle random-phase approximation
• Theory of nuclear collective vibrations
• Investigation of the cause of the discrepancies between calculated running sums for nuclear matrix elements of two-neutrino double-$\beta$ decay