Occupation probabilities of single particle levels using the microscopic interacting boson model: Application to some nuclei of interest in neutrinoless double-$\beta$ decay

We have developed a new method to calculate the occupancies of single particle levels in atomic nuclei. This method has been developed in the context of the microscopic interacting boson model, in which neutron and proton degrees of freedom are treated explicitly. The energies of the single particle levels constitute a very important input for the calculation of the occupancies in this method. In principle these energies can be considered as input parameters that can be fitted to reproduce the experimental occupancies. Instead of fitting, in this study we have extracted the single particle energies from experimental data on nuclei with a particle more or one particle less than a shell closure. We provide the sets of these single particle energies suitable for several major shells and apply our method to calculate the occupancies of several nuclei of interest in neutrinoless double-$\beta$ decay using these sets. Our results are compared with other theoretical calculations and experimental occupancies, when available.

Figure 1

IBM-2 occupations in (a) ${}^{76}\mathrm{Ge}$, (b) ${}^{76}\mathrm{Se}$, and (c) their change for neutrons, compared with experimental [1, 2], BCS [22, 42], and ISM [21, 43] results.

Figure 2

Same as Fig. 1 for protons.

Figure 3

IBM-2 occupations in (a) ${}^{100}\mathrm{Mo}$, (b) ${}^{100}\mathrm{Ru}$, and (c) their change for neutrons, compared with experimental [4] and BCS [7, 42] results.

Figure 4

Same as Fig. 3 for protons.

Figure 5

IBM-2 occupations in (a) ${}^{130}\mathrm{Te}$, (b) ${}^{130}\mathrm{Xe}$, and (c) their change for neutrons, compared with experimental [3], BCS [41], and ISM [8] results.

Figure 6

Same as Fig. 5 for ${}^{128}\mathrm{Te}$ and ${}^{128}\mathrm{Xe}$.

Figure 7

IBM-2 occupations in (a) ${}^{130}\mathrm{Te}$, (b) ${}^{130}\mathrm{Xe}$, and (c) their change for protons, compared with experimental [5], BCS [41], and ISM [8] results.

Figure 8

Same as Fig. 7 for ${}^{128}\mathrm{Te}$ and ${}^{128}\mathrm{Xe}$.

Figure 9

IBM-2 occupations in (a) ${}^{136}\mathrm{Xe}$, (b) ${}^{136}\mathrm{Ba}$, and their change (c) for protons, and (d) predicted IBM-2 occupations in ${}^{136}\mathrm{Ba}$ for neutrons.

Figure 10

IBM-2 occupations in (a) ${}^{150}\mathrm{Nd}$, (b) ${}^{150}\mathrm{Sm}$, and (c) their change for neutrons using the single particle energies of Set I.

Figure 11

IBM-2 occupations in (a) ${}^{150}\mathrm{Nd}$, (b) ${}^{150}\mathrm{Sm}$, and (c) their change for neutrons using the single particle energies of Set II.

Figure 12

IBM-2 occupations in (a) ${}^{150}\mathrm{Nd}$, (b) ${}^{150}\mathrm{Sm}$, and (c) their change for protons using the single particle energies of Set I.

Figure 13

IBM-2 occupations in (a) ${}^{150}\mathrm{Nd}$, (b) ${}^{150}\mathrm{Sm}$, and (c) their change for protons using the single particle energies of Set II.

Figure 14

(a) Different single particle energies for neutrons. (b) Different single particle energies for protons. (c) Evolution of occupancies for neutrons. (d) Evolution of occupancies for protons.

Figure 15

Same as Fig. 14.