Configuration mixing effects on neutrinoless $ββ$-decay nuclear matrix elements

Abstract

Mixing and coexistence of intrinsic nuclear shapes play an important role to determine the low-energy structure of heavy nuclei, and are expected to affect nuclear matrix elements (NMEs) of neutrinoless double beta ($0νββ$) decay. This problem is addressed in the interacting boson model with configuration mixing that is formulated by using the nuclear energy density functional theory. It is shown that significant amounts of mixing of normal and deformed intruder configurations are present in the ground and excited $0^+$ states in the even-even nuclei that are parent or daughter nuclei of the $0νββ$ decay. An illustrative application to the $0νββ$ decays of $^{76}$Ge, $^{96}$Zr, $^{100}$Mo, $^{116}$Cd, and $^{150}$Nd shows that the inclusion of the configuration mixing reduces the NMEs for most of the $0^+_1$ $\to$ $0^+_1$ $0νββ$ decays.

Figures (6)

• Figure 1: Potential energy surfaces in terms of the triaxial quadrupole $(\beta,\gamma)$ deformations for the nuclei of interest in the IBMCM that is based on the RHB and HFB SCMF calculations. The global and local minima are indicated by the solid circles and open triangles, respectively.
• Figure 2: Calculated excitation energies for the $2^+_1$, $4^{+}_1$, $0^+_2$, and $2^+_2$ states in the IBMCM that is based on the RHB and HFB SCMF methods. The results obtained from the IBM without configuration mixing are adopted from nomura2025bb. Experimental data are taken from the NNDC database data.
• Figure 3: Fractions of the intruder configurations in the IBMCM wave functions of the $0^+_1$ and $0^+_2$ states for the even-even nuclei under consideration.
• Figure 4: Predicted (a) $M^{0\nu}(0^+_1\,\to\,0^+_1)$ and (b) $M^{0\nu}(0^+_1\,\to\,0^+_2)$ for the studied even-even nuclei, computed by the mapped IBM with and without inclusion of the configuration mixing (CM).
• Figure 5: Decomposition of (a) $M_{\mathrm{GT}}^{0\nu}(0^+_1\,\to\,0^{+}_1)$ and (b) $M_{\mathrm{GT}}^{0\nu}(0^+_1\,\to\,0^{+}_2)$ into the monopole and quadrupole components calculated with and without the configuration mixing. Note that in (b) the sign of the monopole and quadrupole parts of $M_{\mathrm{GT}}^{0\nu}(0^+_1\,\to\,0^{+}_2)$ is set so that the former is positive. The RHB-SCMF calculation is performed to provide the microscopic input.