Partial restoration of isospin symmetry for neutrinoless double $\beta$ decay in the deformed nuclear system of ${}^{150}\mathrm{Nd}$

In this work, we calculate the matrix elements for the $0\nu \beta \beta$ decay of ${}^{150}\mathrm{Nd}$ using the deformed quasiparticle random-phase approximation $(pn$-QRPA) method. We adopted the approach introduced by Rodin and Faessler [Phys. Rev. C 84, 014322 (2011)] and Simkovic et al. [Phys. Rev. C 87, 045501 (2013)] to restore the isospin symmetry by enforcing $M_F^{2\nu }=0$. We found that with this restoration, the Fermi matrix elements are reduced in the strongly deformed ${}^{150}\mathrm{Nd}$ by about 15 to 20%, while the more important Gamow-Teller matrix elements remain the same. The results of an enlarged model space are also presented. This enlargement increases the total (Fermi plus Gamow-Teller) matrix elements by less than 10%.

Figure 1

The decomposition of $0\nu \beta \beta$ matrix elements for different values of $K^{\pi }$. Here, “Msp” is an abbreviation for “model space,” where “Msp I” refers to the $N=4$–6 space and “Msp II” refers to the $N=0$–7 space. “ISR” denotes “isospin symmetry restoration.”