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

Abstract

. (2016). Occupation probabilities of single particle levels using the microscopic interacting boson model: Application to some nuclei of interest in neutrinoless double-β decay. Physical Review C, 94 (3), 034320. doi:10.1103/PhysRevC.94.034320 2016 PHYSICAL REVIEW C 94, 034320 (2016) Occupation probabilities of single particle levels using the microscopic interacting boson model:Application to some nuclei of interest in neutrinoless double-β 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-β decay using these sets. Our results are compared with other theoretical calculations and experimental occupancies, when available.

Rearrangement of valence neutrons in the neutrinoless double- β decay of Xe136

“…Recent work by Entwisle et al [8] measured the π0h 11/2 occupancy to be small, 0.62, about 5% of the full shell, as would be expected below the [8] and the neutron data from the present work. The three different theoretical calculations are from the shell model, SM1 [14] and SM2 [50], and the interacting boson model, IBM [51]. The discrepancy between the theoretical calculations and the experimental data is shown on the right where the error bars show the experimental uncertainty.…”

Role of Single-Particle Energies in Microscopic Interacting Boson Model Double Beta Decay Calculations

“…The single-particle energies may be considered as input parameters to be fitted to reach an optimal correspondence with the data, or alternatively they can be calculated using a mean field potential, or they can be extracted from available experimental data. In Reference [50] the single-particle and single-hole energies for protons and neutrons were extracted from experimental data and discussed in detail. The underlying motivation in [50] was to estimate the validity of the single-particle energies and check the reliability of the used IBM-2 wave functions by calculating occupancies of the appropriate singleparticle levels.…”

“…In Reference [50] the single-particle and single-hole energies for protons and neutrons were extracted from experimental data and discussed in detail. The underlying motivation in [50] was to estimate the validity of the single-particle energies and check the reliability of the used IBM-2 wave functions by calculating occupancies of the appropriate singleparticle levels. These kinds of tests are particularly important in the case of nuclei involved in DBD, as they directly affect the evaluation of the nuclear matrix elements and thus their reliability [66].…”

“…These kinds of tests are particularly important in the case of nuclei involved in DBD, as they directly affect the evaluation of the nuclear matrix elements and thus their reliability [66]. In Reference [50], single-particle energies for several major shells were updated to values given in Tables 1-4 and marked as set (I). These single-particle energy sets were then used to calculate the occupancies of several nuclei of interest in neutrinoless double beta decay.…”

“…Such experiments have been carried out for several candidates participating in 0νββ decay in a series of experiments [16][17][18][19][20]. The obtained results offer an important test for theoretical models used to calculate nuclear properties [19,20,[47][48][49][50]. The comparison of calculated occupation probabilities with experimentally obtained ones serves the purpose of assessing the goodness of the chosen single-particle energies, as well as the used wave functions.…”