Studies on the double-β decay nucleus ${}^{64}\mathrm{Zn}$ using the ($d$,${}^2\mathrm{He}$) reaction

The ($d,{}^2$He) charge-exchange reaction on the double-β decay ($\beta \beta$) nucleus ${}^{64}\mathrm{Zn}$ has been studied at an incident energy of 183 MeV. The two protons in the ${}^1{S}_0$ state (indicated as ${}^2\mathrm{He}$) were both momentum analyzed and detected simultaneously by the BBS magnetic spectrometer and its position-sensitive detector. ${}^2\mathrm{He}$ spectra with a resolution of about 115 keV (FWHM) have been obtained allowing identification of many levels in the residual nucleus ${}^{64}\mathrm{Cu}$ with high precision. ${}^{64}\mathrm{Zn}$ is one of the rare cases undergoing a $\beta \beta$ decay in ${\beta }^{+}$ direction. In the experiment presented here, Gamow-Teller (GT${}^{+}$) transition strengths have been extracted. Together with the GT${}^{-}$ transition strengths from ${}^{64}\mathrm{Ni}$(${}^3\mathrm{He}$,$t$) data to the same intermediate nucleus ${}^{64}\mathrm{Cu}$, the nuclear matrix elements of the $\beta \beta$ decay of ${}^{64}\mathrm{Zn}$ have been evaluated. Finally, the GT${}^{\pm }$ distributions are compared with shell-model calculations and a critical assessment is given of the various residual interactions presently employed for the $\mathit{pf}$ shell.

Figure 1

Schematic representation of the $\beta \beta$ decay of ${}^{64}\mathrm{Zn}$. The transitions are given together with the corresponding $Q$ values. In the final nucleus the first excited state in ${}^{64}\mathrm{Ni}$ is at 1.346 MeV [34].

Figure 2

Excitation-energy spectra for ${}^{64}\mathrm{Zn}$ ($d,{}^2$He)${}^{64}\mathrm{Cu}$ (upper panel) and ${}^{64}\mathrm{Ni}$(${}^3\mathrm{He}$,$t$)${}^{64}\mathrm{Cu}$ (lower panel, from Ref. [35]). The ($d,{}^2$He) 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 $J^{\pi }$ of individual levels were determined by the shape of the cross-section angular distributions. A weak hydrogen contamination in the ($d,{}^2$He) reaction appears around 0.2 MeV, although it is not readily visible in the spectrum.

Figure 3

Angular distributions of the transitions discussed in the text sorted by excitation energy. DWBA calculations are represented by solid lines. The increased error bars (red) for the cross sections of the $0.2$ MeV$⩽E_x⩽0.6$ MeV energy bin at small angles are due to the hydrogen contamination (see text). For all other data points the error bars reflect the statistical errors and an additional uncorrelated 10% systematic error due to the procedure of counting rate extraction.

Figure 4

Bar plot of the extracted GT${}^{\pm }$ strength in ${}^{64}\mathrm{Cu}$ from the ($d,{}^2$He) and (${}^3\mathrm{He}$,$t$) reactions. States above 4 MeV are dimmed to indicate uncertainties arising from the multipole decomposition. $B$(GT${}^{-}$) values were taken from Ref. [35].

Figure 5

Running sum of the GT${}^{+}$ (top) and GT${}^{-}$ strength (middle) deduced in ($d,{}^2$He) and (${}^3\mathrm{He}$,$t$) reactions, respectively. (${}^3\mathrm{He}$,$t$) data are taken from Ref. [35]. The cumulative sum of the $M_{\mathrm{DGT}}^{(2\nu )}$ is shown in the lower plot.

Figure 6

GT${}^{+}$ and GT${}^{-}$ strength distributions and their running sums for the daughter nucleus ${}^{64}\mathrm{Cu}$ at low excitation energies calculated with KB3G, its gap-corrected version KB3Gmod, GXPF1, and KBF effective interactions. The shaded area represents the experimental curve.