Many-body correlations as the origin of Gamow-Teller quenching in nuclear $β$-decay

Abstract

The longstanding quenching problem of Gamow-Teller (GT) strength in nuclear $β$-decay is attributed to missing contributions in the transition operator and/or incomplete nuclear correlations in the many-body wavefunction. Recent studies have predominantly emphasized operator renormalization, including chiral two-body currents, while the effects of many-body correlations--especially in heavy open-shell nuclei--remain underappreciated. We present a large-configuration shell-model calculation that incorporates chiral two-body weak current and treats both mechanisms on equal footing. Taking the neutrinoless double $β$-decay candidate $^{76}$Ge as an example, we demonstrate that strong nuclear correlations drive a substantial portion of GT strength to high excitation energies, leading to a pronounced suppression of low-energy strength responsible for the apparent quenching. We identify that the quenching originates mainly from deformation, cross-shell correlations, and mixing among densely-spaced highly excited states. In contrast, the chiral two-body current contributes only a modest $5-15\%$ reduction, depending on the coupling constants employed. Our results thus suggest many-body correlations as the primary origin of GT quenching and provide a unified microscopic explanation for this phenomenon in nuclear $β$-decay.

Figures (4)

• Figure 1: (Color online) Cumulative sum of GT transition strengths from the $0_1^+$ ground state of $^{76}$Ge to all $1_f^+$ states of $^{76}$As within the excitation $E_f \leqslant 5.0$ MeV. The charge-exchange reaction data 76Ge_BGT_PRC_2012 are compared to the PSM results with different calculation conditions: (1) with different deformation parameters, (2) with small (up to 2qp) and large (up to 4qp) configuration spaces, and (3) for cases when only one-body current (OBC) or when both OBC and two-body current (TBC) are considered. See the text for details.
• Figure 2: (Color online) Calculated GT strength distribution for individual transitions (with only one-body current considered), for (a) small (up to 2qp) configuration space, and (b) large (up to 4qp) configuration space. (c) Calculated cumulative sum of numbers of $1^+$ levels in $^{76}$As for case (b), as compared with the known experimental $1^+$ levels in Ref. NNDC.
• Figure 3: (Color online) The ratio of strengths calculated with the two-body currents to those without the two-body currents, i.e., $\langle \Psi_{1^+_f} \| (\hat{ \mathcal{J}}_{1b} + \hat{ \mathcal{J}}_{2b}) \| \Psi_{0^+_1} \rangle^2 / \langle \Psi_{1^+_f} \| \hat{ \mathcal{J}}_{1b} \| \Psi_{0^+_1} \rangle^2$, for each individual transition with index $f$ and excitation energy $E_f$. The couplings are adopted as $c_3 = -3.2$, $c_4 = 5.4$ and $c_D = -2.0$ in the two-body currents.
• Figure 4: (Color online) Effect of the two-body current (TBC) with increasing level density. Cumulative sum of GT transition strengths from the $0_1^+$ ground state of $^{76}$Ge to all $1_f^+$ states of $^{76}$As with $E_f \lesssim 20.0$ MeV, calculated by the PSM with fixed large configuration space and the one-body current (OBC) are compared with the calculations that further considered TBC. The charge-exchange reaction data Madey_PRC_1989, without giving error bars, are shown as reference.