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arXiv · 2606.08954

Nuclear matrix element of $2\nu\beta\beta$ decay of $^{76}$Ge: roles of high-lying states and two-body currents

Hua-Yang Xu·Hao Zhou·Long-Jun Wang
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Abstract

We present a microscopic analysis of the nuclear matrix element (NME) of the two-neutrino double-$\beta$ ($2\nu\beta\beta$) decay for open-shell heavy deformed nuclei, taking into account the fact that nuclear level density increases rapidly with excitation energy as well as the contribution of two-body current (2BC). Taking $^{76}$Ge $\rightarrow$ $^{76}$Se decay as an example, we found that due to the rapid increase of the level density of the intermediate nucleus $^{76}$As with excitation energy $E_n$, the single-$\beta$ Gamow-Teller (GT) matrix elements become highly fragmented with very small magnitude, and exhibit seemingly random sign patterns at high $E_n$ region. This leads to an effective cancellation at high $E_n$ region in calculating the $2\nu\beta\beta$ NME which then turns out to converge at $E_n \lesssim 5$ MeV, indicating that the contribution of high-lying states of the intermediate nucleus to $2\nu\beta\beta$ NME is negligible. Besides, the 2BC in the transition operator is found to contribute $\sim 10\%$ quenching to the $2\nu\beta\beta$-decay NME of $^{76}$Ge.

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Hua-Yang Xu, Hao Zhou, Long-Jun Wang. 2026-06-08. Nuclear matrix element of $2\nu\beta\beta$ decay of $^{76}$Ge: roles of high-lying states and two-body currents. https://arxiv.org/abs/2606.08954

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