Gamow-Teller transition strengths in the intermediate nucleus of the ${}^{116}$Cd double-$\beta$ decay by the ${}^{116}$Cd${(p,n)}^{116}$In and ${}^{116}$Sn${(n,p)}^{116}$In reactions at 300 MeV

The double-differential cross sections for the ${}^{116}$Cd$(p,n)$ and ${}^{116}$Sn$(n,p)$ reactions were measured at 300 MeV for studying the nuclear matrix element of the ${}^{116}$Cd $\beta \beta$ decay. A multipole decomposition technique was applied to the spectra to extract the Gamow-Teller (GT) component. The integrated GT strengths up to an excitation energy of 30 MeV in the intermediate nucleus ${}^{116}$In are $40\pm 6$ and $11\pm 1$ in the $(p,n)$ and $(n,p)$ spectra, respectively, including the component from the isovector spin monopole (IVSM). The spectra are compared with those obtained from a theoretical calculation with a quasiparticle random phase approximation, where the contribution from the IVSM component as well as the interference effect between the GT and IVSM components are fully taken into account.

Figure 1

Double-differential cross sections and the MD-analysis results for the ${}^{116}$Cd$(p,n)$ (a)–(c) and for the ${}^{116}$Sn$(n,p)$ (d)–(f) reactions near $0^{\circ }$ (a), (d), $4^{\circ }$ (b), (e), and 10${}^{\circ }$ (c), (f).

Figure 2

Extracted GT strength distributions (dots) for the transitions connecting the initial ${}^{116}$Cd (a) and final ${}^{116}$Sn (b) ground states with the intermediate states of ${}^{116}$In, including the IVSM component. The shaded area in (b) represents the $B$(GT${}^{+}$) distribution by the $(d{,}^2$He) experiment [15]. The curves are the results derived through the DWIA calculations from the QRPA transition densities corresponding to GT plus IVSM (solid), GT (dashed), IVSM (dotted) excitations. (c) Values of $M_{+}^{2\nu }$ obtained from the experimental (dots) and theoretical (solid curve) GT plus IVSM strengths. The thin horizontal line shows the $M^{2\nu }$ value by the decay measurement [5]. The vertical dashed line in (b) and (c) is the upper limit of the MD analysis, above which the MD analysis for the $(n,p)$ spectra is unstable. (d) shows the magnification of (c) in the energy region up to 3 MeV.