Constraint on $0\nu \beta \beta$ Matrix Elements from a Novel Decay Channel of the Scissors Mode: The Case of ${}^{154}\mathrm{Gd}$

The nucleus ${}^{154}\mathrm{Gd}$ is located in a region of the nuclear chart where rapid changes of nuclear deformation occur as a function of particle number. It was investigated using a combination of $\gamma$-ray scattering experiments and a $\gamma \gamma$-coincidence study following electron capture decay of ${}^{154}\mathrm{Tb}^m$. A novel decay channel from the scissors mode to the first excited $0^{+}$ state was observed. Its transition strength was determined to $B(M1;1_{sc}^{+}\to 0_2^{+})=0.031(4){\mu }_N^2$. The properties of the scissors mode of ${}^{154}\mathrm{Gd}$ imply a much larger matrix element than previously thought for the neutrinoless double-$\beta$ decay to the $0_2^{+}$ state in such a shape-transitional region. Theory indicates an even larger effect for ${}^{150}\mathrm{Nd}$.

Figure 1

Simplified decay scheme for the $\beta \beta$ decay of ${}^{154}\mathrm{Sm}$. The $0\nu \beta \beta$ decay to the $0_2^{+}$ state of ${}^{154}\mathrm{Gd}$ could offer a coincidence tag with the prompt $0_2^{+}\to 2_1^{+}$ and $2_1^{+}\to 0_1^{+}$ $\gamma$ rays. Excitation energies of states of ${}^{154}\mathrm{Gd}$ are given in MeV.

Figure 2

Photon-scattering spectrum of ${}^{154}\mathrm{Gd}$. At energies of 2811 and 2934 keV, deexciting transitions from the strongly excited $1^{+}$ state to the ground state and first $2^{+}$ are visible. Photon-scattering cross sections are measured relative to well-known cross sections in ${}^{27}\mathrm{Al}$ [26], which is irradiated simultaneously (marked “Al”). The labels “BG” and “SE” denote background lines or single-511 keV escape signals, respectively.

Figure 3

(a) Part of the $\gamma$-ray spectrum recorded following the EC decay of the $0^{+}$ low-spin isomer ${}^{154}\mathrm{Tb}^m$ populated in the ${}^{154}\mathrm{Gd}(p,n)$ reaction. (b) Part of the $\gamma \gamma$-coincidence spectrum gated on the $0_2^{+}\to 2_1^{+}$ transition. The coincident observation of the 2253-keV transition establishes the population of the $0_2^{+}$ state at 681 keV from the $1^{+}$ state at 2934 keV. Please note the different scaling of the $y$ axis. (c) Simplified decay scheme of the $1_{sc}^{+}$ state populated in the EC decay and the respective relative decay intensities.

Figure 4

Comparison of the $B(M1)$ branching ratio $br=B(M1;1_{sc}^{+}\to 0_2^{+})/B(M1;1_{sc}^{+}\to 0_1^{+})$ in % (red) of the $1^{+}$ scissors mode state of ${}^{154}\mathrm{Gd}$, the dimensionless $0\nu \beta \beta$ NME $M^{(0\nu )}[0_1^{+}]$ (blue), and $M^{(0\nu )}[0_2^{+}]$ (green) for previous [15] and new IBM-2 parameters and experimental data, where available.

Figure 5

(a) Collective wave functions for the initial ${}^{154}\mathrm{Sm}$ ground state (black solid) and the final $0_1^{+}$ (red dashed) and $0_2^{+}$ (blue dotted) states of ${}^{154}\mathrm{Gd}$ as a function of the quadrupole deformation ($\beta$). (b) Accumulated NMEs for transitions from ${}^{154}\mathrm{Sm}$ to the ground (red dashed) and first excited $0^{+}$ (blue dotted) states of ${}^{154}\mathrm{Gd}$.