The ($d,{}^2\mathrm{He}$) reaction on ${}^{96}\mathrm{Mo}$ and the double-$\beta$ decay matrix elements for ${}^{96}\mathrm{Zr}$

The ${}^{96}\mathrm{Mo}(d,{}^2\mathrm{He}){}^{96}\mathrm{Nb}$ charge-exchange reaction was investigated at an incident energy of $E_d=183.5$ MeV. An excitation-energy resolution of 110 keV was achieved. The experiment was performed at KVI, Groningen, using the magnetic spectrometer BBS at three angular positions: $0^{°},2.5^{°}$, and $6^{°}$. We found that below 6 MeV almost the entire Gamow-Teller (${\mathrm{GT}}^{+}$) strength is concentrated in a single state at 0.69 MeV excitation energy. As ${}^{96}\mathrm{Mo}$ is the daughter of the $\beta \beta$ decay nucleus ${}^{96}\mathrm{Zr}$, the present result provides information about the nuclear matrix elements active in the $2\nu \beta \beta$ decay of ${}^{96}\mathrm{Zr}$.

Figure 1

Schematic representation of the $2\nu {\beta }^{-}{\beta }^{-}$ decay of ${}^{96}\mathrm{Zr}$ and the low-energy level scheme of the intermediate nucleus ${}^{96}\mathrm{Nb}$. The intermediate states in the $2\nu$ decay mode are $1^{+}$ states only. ${\mathrm{GT}}^{+}$ refers to ($n,p$)-type reactions and ${\mathrm{GT}}^{-}$ to ($p,n$)-type reactions. The single ${\beta }^{-}$ decay to ${}^{96}\mathrm{Nb}$ is energetically possible but suppressed by angular momentum. Excitation energies are given in keV.

Figure 2

Excitation-energy spectra for ${}^{96}\mathrm{Mo}(d,{}^2\mathrm{He}){}^{96}\mathrm{Nb}$. The upper spectrum covers an angular range of $0^{°}⩽{\Theta }_{\mathrm{c}.\mathrm{m}.}⩽1.5^{°}$ and the lower one a range of $1.5^{°}⩽{\Theta }_{\mathrm{c}.\mathrm{m}.}⩽3.0^{°}$. The peaks near excitation energy of $-2.3$ MeV (top panel) and around $-1.6$ MeV (bottom panel) are due to the ${}^1\mathrm{H}$ contamination and their width is due to kinematic broadening. The energy resolution is 110 keV.

Figure 3

Angular distributions for the transitions to the levels at 0.69 MeV (a) and 0.51 MeV (b) and the cluster of levels around 2.2 MeV (d) in ${}^{96}\mathrm{Nb}$. The top figures (a) and (b) show the attempt of an individual analysis of the two states in the doublet at 0.51 and 0.69 MeV and the bottom left figure (c) shows a combined analysis. The $2^{-}$ strength of the 0.51 MeV transition in part (c) was slightly scaled up compared to the one in the part (b), which could be an indication of another $2^{-}$ state appearing at the high-energy tail of the 0.69 MeV $1^{+}$ transition. For the cluster of states around 2.2 MeV a bin size from 2.1 to 2.5 MeV was taken for the combined analysis.