The ($d,{}^2\mathrm{He}$) reaction on ${}^{76}\mathrm{Se}$ and the double-β-decay matrix elements for $A=76$

The $(d,{}^2\mathrm{He})$ charge-exchange reaction on ${}^{76}\mathrm{Se}$ was studied at an incident energy of 183 MeV. The outgoing two protons in the ${}^1{S}_0$ state, referred to as ${}^2\mathrm{He}$, were both momentum analyzed and detected by the same spectrometer and detector. The experiment was performed at KVI, Groningen, using the magnetic spectrometer BBS at three angular positions: $0^{°},2.5^{°}$, and $5^{°}$. Excitation-energy spectra of the residual nucleus ${}^{76}\mathrm{As}$ were obtained with an energy resolution of about 120 keV (FWHM). Gamow-Teller (${\mathrm{GT}}^{+}$) transition strengths were extracted up to 5 MeV and compared with those from an $(n,p)$ experiment at low resolution. Together with the ${\mathrm{GT}}^{-}$ transition strengths from the ${}^{76}\mathrm{Ge}(p,n)$ experiment leading to the same intermediate nucleus, the nuclear matrix element of the two-neutrino double-$\beta$ decay of ${}^{76}\mathrm{Ge}$ was evaluated.

Figure 1

Schematic representation of the $\beta \beta$ decay of ${}^{76}\mathrm{Ge}$ [12]. Whereas in the $2\nu \beta \beta$ mode only the intermediate $1^{+}$ states are relevant, there is a multitude of $J^{\pi }$ states involved in the neutrinoless mode.

Figure 2

Excitation-energy spectrum from the reaction ${}^{76}\mathrm{Se}(d,{}^2\mathrm{He})\hspace{0.5em}{}^{76}\mathrm{As}$. The spectrum was taken at a spectrometer angle of $0^{°}$ and covers an angular range in the center-of-mass system between $0^{°}$ and $1.3^{°}$. The $J^{\pi }$ values of individual levels (or of a conglomerate of levels) were determined by the shape of the angular distributions. In the inset, the spectrum is shown for a wider excitation-energy range to show the dominating peaks resulting from the reactions ${}^1\mathrm{H}(d,{}^2\mathrm{He})n$ and ${}^{12}\mathrm{C}(d,{}^2\mathrm{He}){}^{12}\mathrm{B}(\mathrm{g}.\mathrm{s}.)$.

Figure 3

Angular distributions of the levels excited in ${}^{76}\mathrm{As}$ sorted by excitation energy. DWBA calculations are represented by solid lines. The error bars reflect the statistical errors and an additional 10% systematic error.

Figure 4

The $\Delta L=0$, GT contribution to the ${}^{76}\mathrm{Se}(n,p)$ cross section deduced from $(n,p)$ data using the $6^{°}$-subtraction method (histogram). The GT strength distribution from the present $(d,{}^2\mathrm{He})$ analysis was folded with a 1.8 MeV energy resolution to compare with the $(n,p)$ analysis. The $(d,{}^2\mathrm{He})$ data were scaled to match the summed ${\mathrm{GT}}^{+}$ strength included in the shaded area of the $(n,p)$ data (refer to Table ). The $(n,p)$ data were taken from Ref. [36].

Figure 5

Excitation-energy spectra from the ${}^{76}\mathrm{Ge}(p,n)$ and ${}^{76}\mathrm{Se}(d,{}^2\mathrm{He})$ reactions populating the same levels in the intermediate nucleus ${}^{76}\mathrm{As}$. The shaded areas indicate predominant $1^{+}$ transitions. The $(p,n)$ spectrum was taken from Fig. 1 in Ref. [37].