An IBM-2 Analysis Of Matrix Elements Of Neutrinoless Double-Beta Decay And Spectral Statistics In Deformed Nuclear System

The proton-neutron interacting boson model（IBM-2）has a good shell model foundation.The IBM-2 can be not only applied to describe nuclear structural properties closely related to micrioscopic mean-field structure but also used to simulate the spectral fluctuations in heavy nuclear systems under realistic boson number.In this thesis,we have carefully checked the IBM-2 model detail in calculating nuclear matrix elements of neutrinoless double-beta decay.Moreover,we have fitted the low-lying structures of¹⁵⁴Sm and¹⁵⁴Gd,and the results indciated that the data for excitation energies and B（E2）transitions in these two nuclei can be accurally reproduced in the framework of the IBM-2.With the fitted IBM-2 wavefucntions,we further calculated the nuclear matrix elements of the neutrinoless double-beta decay（including fermi term and Gamov-Teller term）in between two nuclei.In addition,we presented an IBM-2 analysis of the spectral fluctuations in deformed nuclear systems using two statistic schemes（the nearest neighbor level spacing distribution and spectral rigidity）.It is shown that vibrational spectra in the dynamical systems corresponding to¹⁵⁴Sm and¹⁵⁴Gd may be close to the chaotic limit,by which the conclusion obtained from the previous phenomenological analysis in the large boson number limit is justified under realistic model conditions.