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The first large-scale shell-model calculation of the two-neutrino double beta decay of $^{76}$Ge to the excited states in $^{76}$Se
Nuclear Theory · Submitted 28 Feb 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The experimental half-life $(1.926\pm0.094)\times10^{21}$ yr of the ground-state transition was used to derive the value $g_{\rm A}=0.80\pm0.01$ for the axial-vector coupling, which is consistent with other shell-model calculations suggesting a quenched value of $g_{\rm A}$.
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The abstract, sentence by sentence
Large-scale shell-model calculations were carried out for the half-lives and branching ratios of the $2\nu\beta\beta$ decay of $^{76}$Ge to the ground state and the lowest three excited states $2_1^+$, $0_2^+$ and $2_2^+$ in $^{76}$Se. In total, the wave functions of more than 10,000 intermediate $1^+$ states in $^{76}$As were calculated in a three-step procedure allowing an efficient use of the available computer resources. In the first step, 250 lowest states, below some 5 MeV of excitation energy, were calculated without truncations within a full major shell $0f_{5/2}-1p-0g_{9/2}$ for both protons and neutrons. The wave functions of the rest of the states, up to some 30 MeV, were computed in two more steps by introducing two consecutive stages of truncation. The computed magnitudes of the $2\nu\beta\beta$ nuclear matrix elements (including the value of the axial-vector coupling $g_{\rm A}$), $\vert M_{2\nu}\vert g_{\rm A}^2$, converged to the values 0.168$g_{\rm A}^2$, $1.2\times10^{-3}$$g_{\rm A}^2$, 0.121$g_{\rm A}^2$, and $3.1\times10^{-3}$$g_{\rm A}^2$ for the $0^+_{\rm g.s.}$, $2^+_1$, $0^+_2$, and $2^+_2$ states, respectively. Using up-to-date phase-space integrals, the corresponding branching ratios were derived to be 99.926\%, 4.4$\times10^{-5}$\%, 0.074\% and 2.5$\times10^{-7}$\%. The experimental half-life $(1.926\pm0.094)\times10^{21}$ yr of the ground-state transition was used to derive the value $g_{\rm A}=0.80\pm0.01$ for the axial-vector coupling, which is consistent with other shell-model calculations suggesting a quenched value of $g_{\rm A}$. Using this value of $g_{\rm A}$, predictions for the transition half-lives were derived.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Large-scale shell-model calculations were carried out for the half-lives and branching ratios of the $2\nu\beta\beta$ decay of $^{76}$Ge to the ground state and the lowest three excited states $2_1^+$, $0_2^+$ and $2_2^+$ in $^{76}$Se. | contribution 1.00 | 0.95 | 0.17 | asserted 0.99 |
| s1 | In total, the wave functions of more than 10,000 intermediate $1^+$ states in $^{76}$As were calculated in a three-step procedure allowing an efficient use of the available computer resources. | method 0.99 | 0.96 | 0.04 | asserted 1.00 |
| s2 | In the first step, 250 lowest states, below some 5 MeV of excitation energy, were calculated without truncations within a full major shell $0f_{5/2}-1p-0g_{9/2}$ for both protons and neutrons. | method 1.00 | 0.94 | 0.02 | asserted 1.00 |
| s3 | The wave functions of the rest of the states, up to some 30 MeV, were computed in two more steps by introducing two consecutive stages of truncation. | method 1.00 | 0.94 | 0.02 | asserted 1.00 |
| s4 | The computed magnitudes of the $2\nu\beta\beta$ nuclear matrix elements (including the value of the axial-vector coupling $g_{\rm A}$), $\vert M_{2\nu}\vert g_{\rm A}^2$, converged to the values 0.168$g_{\rm A}^2$, $1.2\times10^{-3}$$g_{\rm A}^2$, 0.121$g_{\rm A}^2$, and $3.1\times10^{-3}$$g_{\rm A}^2$ for the $0^+_{\rm g.s.}$, $2^+_1$, $0^+_2$, and $2^+_2$ states, respectively. | result 1.00 | 0.95 | 0.30 | asserted 1.00 |
| s5 | Using up-to-date phase-space integrals, the corresponding branching ratios were derived to be 99.926\%, 4.4$\times10^{-5}$\%, 0.074\% and 2.5$\times10^{-7}$\%. | result 1.00 | 0.93 | 0.13 | asserted 1.00 |
| s6 | The experimental half-life $(1.926\pm0.094)\times10^{21}$ yr of the ground-state transition was used to derive the value $g_{\rm A}=0.80\pm0.01$ for the axial-vector coupling, which is consistent with other shell-model calculations suggesting a quenched value of $g_{\rm A}$. | result 0.83 | 0.91 | 0.27 | asserted 0.58 |
| s7 | Using this value of $g_{\rm A}$, predictions for the transition half-lives were derived. | result 0.64 | 0.92 | 0.08 | asserted 0.96 |
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Original abstract
Large-scale shell-model calculations were carried out for the half-lives and branching ratios of the $2\nu\beta\beta$ decay of $^{76}$Ge to the ground state and the lowest three excited states $2_1^+$, $0_2^+$ and $2_2^+$ in $^{76}$Se. In total, the wave functions of more than 10,000 intermediate $1^+$ states in $^{76}$As were calculated in a three-step procedure allowing an efficient use of the available computer resources. In the first step, 250 lowest states, below some 5 MeV of excitation energy, were calculated without truncations within a full major shell $0f_{5/2}-1p-0g_{9/2}$ for both protons and neutrons. The wave functions of the rest of the states, up to some 30 MeV, were computed in two more steps by introducing two consecutive stages of truncation. The computed magnitudes of the $2\nu\beta\beta$ nuclear matrix elements (including the value of the axial-vector coupling $g_{\rm A}$), $\vert M_{2\nu}\vert g_{\rm A}^2$, converged to the values 0.168$g_{\rm A}^2$, $1.2\times10^{-3}$$g_{\rm A}^2$, 0.121$g_{\rm A}^2$, and $3.1\times10^{-3}$$g_{\rm A}^2$ for the $0^+_{\rm g.s.}$, $2^+_1$, $0^+_2$, and $2^+_2$ states, respectively. Using up-to-date phase-space integrals, the corresponding branching ratios were derived to be 99.926\%, 4.4$\times10^{-5}$\%, 0.074\% and 2.5$\times10^{-7}$\%. The experimental half-life $(1.926\pm0.094)\times10^{21}$ yr of the ground-state transition was used to derive the value $g_{\rm A}=0.80\pm0.01$ for the axial-vector coupling, which is consistent with other shell-model calculations suggesting a quenched value of $g_{\rm A}$. Using this value of $g_{\rm A}$, predictions for the transition half-lives were derived.
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1 arXiv paper cite this in 2 sentences
Papers citing it
Uses its data or values 1 paper
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Among these excited states transitions, the decay to the $0^+_1$ state is expected to dominate, with the most recent half-life prediction of $(2.6±0.13)·10^24$ yr [ref] .
Search for exotic physics in double-$\beta$ decays with GERDA Phase II · Statistical analysis and systematic uncertainties · 0.92
What it cites
Cites as background 1 paper
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The $2νββ$ mode is allowed in the standard model and the related half-lives have thus far been measured for more than ten nuclei [ref] .
Precise Half-Life Values for Two-Neutrino Double-$\beta$ Decay: 2020 review · Introduction · 0.81
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