Investigation of the cause of the discrepancies between calculated running sums for nuclear matrix elements of two-neutrino double-$\beta$ decay

Abstract

A qualitative difference in the running sum for the nuclear matrix element of the two-neutrino double-$\beta$ decay of ${}^{136}$Xe was found four years ago between quasiparticle random-phase approximation (QRPA) and shell model calculations. The former result has large increase and decrease with respect to the excitation energy of the intermediate state, and the latter one is an almost monotonically and mildly increasing function. My QRPA calculations independently of the above one do not have a remarkable decrease. This discrepancy is a serious problem affecting the reliability of calculations of the neutrinoless double-$\beta$ decay, and the cause was unknown. I perform several relevant test calculations and make an analytical consideration to find the cause, which is found to be in the strength of the attractive interactions. The possible major local decrease in the running sum is also explained analytically. The interactions of my QRPA calculation are appropriate in terms of the strength, thus the almost monotonic behavior is reasonable.

13 pages, 7 figures, 1 table

References in corpus (6)

• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Disassembling the Nuclear Matrix Elements of the Neutrinoless double beta Decay
• Precision Analysis of the ${}^{136}$Xe Two-Neutrino $\beta \beta$ Spectrum in KamLAND-Zen and Its Impact on the Quenching of Nuclear Matrix Elements
• Shell-model calculations of two-neutrino double-beta decay rates of ${}^{48}$Ca with GXPF1A interaction
• Physical features of strength of isoscalar pairing interaction determined by relation between double charge change and double pair transfer
• Muon capture rates: Evaluation within the Quasiparticle Random Phase Approximation

Cited by in corpus (1)

• Supernova electron-neutrino interactions with xenon in the nEXO detector