Research On Convergence Of The Nucleus Matrix Elements For Double-β Decay Based On The Nuclear Shell Model

As a far-reaching subject in modern nuclear physics and particle physics,the two-neutrino double-βdecay（2νββ）of the nuclei is an extremely special second-order weak interaction process.The study of 2νββdecay is not only important for understanding the laws of strong and weak interactions,but also helps to find new effective nucleon-nucleon interactions.Although the neutrinoless double-βdecay（0νββ）experiments are important methods to explore the properties of neutrinos,the detailed measurement and calculations of the decay half-life opens up a new perspective for decay experiments and provides good references for finding new physics.The double-βdecay experiment requires an extremely clean background environment and highly enriched analyte,and the entire experimental process is challenging,so it is of necessary to study the related theoretical approach.In this paper,the characteristics of 2νββdecays for six nuclei(³⁶Ar,⁴⁶Ca,⁴⁸Ca,⁵⁰Cr,⁷⁰Zn and ¹³⁶Xe)in a mass range A=36-136 are studied within the framework of nuclear shell model,and the convergence problem of the nucleus decay nucleus matrix element is studied.The main content of paper includes:1.The energy level of the nuclear ³⁶Cl and theγtransition probability of them are calculated by the shell model method;Gamow-Tellerβdecay nuclear matrix elements of the nuclei ³⁶Ar,³⁶Cl,³²Cl,³²P,⁴⁶Ca and ⁴⁸Ca are calculated,and the results fully satisfy the Gamow-Teller sum rule.The results show that shell method is feasible to compute the wave function of the nucleus.2.The characteristics of 2νββdecays for six nuclei(³⁶Ar,⁴⁶Ca,⁴⁸Ca,⁵⁰Cr,⁷⁰Zn and ¹³⁶Xe)within the mass range A=36-136 are studied under frame of the shell model.Calculations are presented for the half-lives,nuclear matrix elements and phase space factors.In addition,the applicability of single-state dominance（SSD）hypothesis to these nuclei is discussed.3.The calculation of nuclear matrix element involves a large number of 1⁺states in the middle nuclear,and there is no discussion on the convergence of kernel matrix element.Thus,the convergence of six nuclear decay matrix elements is studied systematically in this paper.According to the calculations of shell model,the empirical formulas for convergence of nuclear matrix element are summarized,and the applicability and feasibility of them for different model spaces and different interactions are verified.In this paper,we study the convergence of the nuclear matrix element of 2νββdecay based on shell model method,which provides important theoretical support and good reference for calculating the nuclear matrix element of 2νββdecay theory,and also provides a new perspective for exploring the neutrino properties of 0νββdecay theory.