Pairing properties of the double-$\beta$ emitter ${}^{116}\mathrm{Cd}$

The pairing properties of the neutrinoless double-$\beta$ decay candidate ${}^{116}\mathrm{Cd}$ have been investigated. Measurements of the two-neutron removal reactions on isotopes of ${}^{114,116}\mathrm{Cd}$ have been made in order to identify $0^{+}$ strength in the residual nuclei up to $\approx 3$ MeV. No significant $L=0$ strength has been found in excited states indicating that the Bardeen-Cooper-Schrieffer (BCS) approximation is a reasonable basis to describe the neutrons in the ground state. This approximation avoids complications in calculations of double-$\beta$ decay matrix elements that use the quasiparticle random-phase approximation (QRPA) techniques. However this is not the case for the protons, where pair vibrations are prevalent and the BCS approximation is no longer valid, complicating the use of traditional QRPA techniques for this system as a whole.

Figure 1

Calculated angular distributions for the ${}^{116}\mathrm{Cd}(p,t){}^{114}\mathrm{Cd}$ reaction for $L=0$ (black), 2 (red), and 4 (green) transfer to $0^{+},2^{+}$, and $4^{+}$ states in the residual nucleus. Dashed lines highlight the angles where cross sections were measured in this work. Details on the calculations can be found in the main body of the text.

Figure 2

Excitation energy spectra for the residual nuclei populated via the ($p,t$) reactions on ${}^{114}\mathrm{Cd}$ and ${}^{116}\mathrm{Cd}$ targets. Sections of the spectra to the right of the dashed vertical lines have been multiplied by the indicated factor. Peaks identified from reactions on contaminants in the target are labeled with an asterisk (*).

Figure 3

Ratio of cross sections measured at $8^{\circ }$ and ${15}^{\circ }$ for reactions on ${}^{114}\mathrm{Cd}$ (squares) and ${}^{116}\mathrm{Cd}$ (circles). Solid black points are known $L=0$ states in the residual nuclei, while solid red points are known states with $L>0$. Empty points are states with no previous firm assignment in the literature. States in ${}^{112}\mathrm{Cd}$ (up-triangle) and ${}^{114}\mathrm{Cd}$ (down-triangle) where cross sections at ${15}^{\circ }$ could only be assigned as an upper limit, and therefore the ratio is a minimum limit, are included.