论文标题
$^{76} $ ge的两个中性双β衰减的第一个大型外壳模型计算$^{76} $^{76} $ se
The first large-scale shell-model calculation of the two-neutrino double beta decay of $^{76}$Ge to the excited states in $^{76}$Se
论文作者
论文摘要
对$^{76} $ ge的$2νβ$衰减的半衰期和分支比进行了大规模的壳模计算，并将最低的三个激发态$ 2_1^+$，$ 0_2^+$和$ 2_2^+$ 2_2^+$ in $^{76} $ se进行。总的来说，在三步过程中计算出的$^{76} $中的10,000多个中间$ 1^+$状态的波函数，允许有效地使用可用的计算机资源。在第一步中，在完整的主要外壳内无截断$ 0f_ {5/2} -1p-0g_ {9/2} $，在质子和中子中计算出250个最低状态，低于5 me的激发能量。通过引入两个连续的截断阶段，将其余状态的波函数（最高30 MEV）分为两个步骤。 $2νβ$核矩阵元素的计算幅度（包括轴向矢量耦合$ g _ {\ rm a} $的值$ 1.2 \ times10^{ - 3} $$ g _ {\ rm a}^2 $，0.121 $ g _ {\ rm a}^2 $和$ 3.1 \ times10^{ - 3} $ g _ {\ rm a}^$ 0^+_ $ _ { $ 0^+_ 2 $和$ 2^+_ 2 $状态。使用最新的相位空间积分，相应的分支比率为99.926 \％，4.4 $ \ times10^{ - 5} $ \％，0.074 \％\％和2.5 $ \ times10^{ - 7} $ \％。 The experimental half-life $(1.926\pm0.094)\times10^{21}$ yr of the ground-state transition was used to derive the value $g_{\rm A}=0.80\pm0.01$ for the axial-vector coupling, which is consistent with other shell-model calculations suggesting a quenched value of $g_{\rm a} $。使用$ g _ {\ rm a} $的此值，得出了过渡半衰期的预测。
Large-scale shell-model calculations were carried out for the half-lives and branching ratios of the $2νββ$ decay of $^{76}$Ge to the ground state and the lowest three excited states $2_1^+$, $0_2^+$ and $2_2^+$ in $^{76}$Se. In total, the wave functions of more than 10,000 intermediate $1^+$ states in $^{76}$As were calculated in a three-step procedure allowing an efficient use of the available computer resources. In the first step, 250 lowest states, below some 5 MeV of excitation energy, were calculated without truncations within a full major shell $0f_{5/2}-1p-0g_{9/2}$ for both protons and neutrons. The wave functions of the rest of the states, up to some 30 MeV, were computed in two more steps by introducing two consecutive stages of truncation. The computed magnitudes of the $2νββ$ nuclear matrix elements (including the value of the axial-vector coupling $g_{\rm A}$), $\vert M_{2ν}\vert g_{\rm A}^2$, converged to the values 0.168$g_{\rm A}^2$, $1.2\times10^{-3}$$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.
