Shell-model Study On Nuclear Matrix Elements And Convergence For Two-Neutrino Double-Beta Decay Of Medium Mass Nuclei

Double-β decay is one of the most significant topics in modern nuclear physics and particle physics,which will help not only to understand the laws of strong and weak interactions,but also to investigate new physical mechanisms beyond the standard model.It is well known that the experiment of neutrinoless double-β decay(0νββ)is an important method to explore the properties of neutrinos,but it is usually difficult to detect.However,no evidence of the existence of 0νββ decay has been found in experiments so far,and the relevant theoretical calculation results are not completely consistent.The detailed measurements and calculations of the half-lives of two-neutrino double-β(2vββ)decays open up a new perspective for the study of 0νββ decay and provide a good reference for the development on physics related fields.There are 90 kinds of nuclei that can undergo double-βdecays,but only 14 of them have been measured experimentally so far,so it is necessary to conduct theoretical research on them.In this paper,the characteristics of wave function,nuclear matrix element and phase-space factor are calculated for the six nuclei in the region of Z=40-50 within the framework of nuclear shell model,and we also theoretically predicted the double-β decay half-lives of four nuclei.Our study shows that 94Zr and 104Ru have relatively short half-lives.Considering the large isotopic abundance,their decays may be detected in the near future.Finally,by studying the convergence problem of nuclear matrix elements,the single state dominance(SSD)property is newly discovered for the nucleus 94Zr.The main contents of paper include:1.The research of double-β decay is a hotspot in modern nuclear physics and particle physics.In this paper,the significance and progress of double-β decay are summarized,and we also introduce the basic theory of double-β decays,including neutrino double-β decays(2νββ)and neutrinoless double-β decays(0νββ).2.In this paper the double-β decay properties are studied under the theoretical framework of nuclear shell model for the range of Z=40-50 nuclei.The shell model is one of the reliable nuclear structure models,whose calculated results have important reference value for experiment and theory.The theory of the shell model is introduced in detail,as well as the detail problems that involved in the calculation,i.e.,the model space,the effective interaction and the quenching factor.3.The 2vββ decays of unstable nuclei in the proton number Z=40-50 are calculated,whose results are listed,including the half-lives,nuclear matrix elements,phasespace factors,etc.In addition,the study of the convergence problem of nuclear matrix elements will help to improve the accuracy of double-β decay properties.If the single state domination(SSD)theory is confirmed,then the half-life of 2vββ decay can be determined from the single β-decay and electron capture(EC)measurements.By studying the convergence of the nuclear matrix elements,it is concluded that the SSD holds for the nuclei 94Zr and 96Zr.4.Finally,the research work of the paper is summarized,and the practical results obtained in the research are presented,which provides a reference for the future research on the double-β decay theory.In addition,the future work is also prospected.