Shell model study for the nuclear beta transitions and supernova explosion

本项目首先利用核壳模型研究核β跃迁，其次利用核壳模型研究获得的结果研究超新星爆炸。我们开发了能够计算p壳、sd壳和fp壳核的核弱和电磁跃迁概率的核壳模型计算机程序。以下是使用该计算机程序获得的结果摘要，并发表在期刊上。(1)在全（sd）^n基下计算的sd-壳核的总Ml激发强度约为j-耦合单粒子极限的50%。与计算值相比，观察到的Ml强度通常降低了20%。与自旋电流相比，轨道电流的贡献几乎与质量数无关。从超多乘子SU(4)对称的角度解释了^<20>Ne的轨道自旋比大，并计算了伽莫夫-泰勒激发的总强度。(2)利用求和规则技术计算了偶偶sd壳核的总Gamow-Teller （GT）强度s。基态波函数由全（sd）^n空间的壳模型计算得到。结果表明，质子-中子相关效应使总GT强度显著降低。构型混合引起的S_-中同位旋分量的减少随着同位旋的增加而变得更加明显。(3)在f<n(1)7/2>+f<n (1)7/2>+f<n-1(1)7/2> (f_<5/2>p_<3/2>p_<1/2>)^1构型空间中，研究了轨道电流对o<+(1)gr>->1^+ Ml激发的作用。大部分的轨道贡献集中在最低的1^+态。与单纯的f<n(1)7/2>模型相比，一阶修正项显著提高了轨道自旋比。在^<46>Ti中，0 <+(1)gr>->1<+(1+1>) Ml跃迁的轨道自旋比得到了很好的重现。在本项目期间，重恒星坍缩阶段的电子俘获率的计算及其在超新星爆炸研究中的应用尚未能够进行，但目前正在进行中。少

This project aims firstly to study the nuclear beta transitions using nuclear shell model and secondly to study supernova explosion applying obtained results of this nuclear shell model study. We have developed the nuclear shell model computer program which is able to calculate nuclear weak and electromagnetic transition probabilities in the p-shell, sd-shell and fp-shell nuclei. The followings are abstracts of the results obtained by using this computer program and published in the journals.(1) It is shown that the total Ml excitation strengths of the even-even sd-shell nuclei calculated in the full (sd)^n basis are about 50% of the jj-coupling single-particle limit. Compared with the calculated values, the observed Ml strengths are reduced by typically 20%. It is found that the orbital current contribution is almost independent of the mass number, in contrast to the spin current. A large orbital-to-spin ratio for ^<20>Ne is explained from the viewpoint of supermultiplet SU(4) symmetr … More y. The total strength of Gamow-Teller excitation is also calculated.(2) We have calculated the total Gamow-Teller (GT) strength s in the even-even sd-shell nuclei making use of the sum rule technique. The ground state wavefunction is obtained from the shell model calculation in the full (sd)^n space. It is shown that the proton-neutron correlation effect causes a considerable amount of reduction of the total GT strength. It is also shown that the reduction of the isospin component in S_- induced by the configuration mixing becomes more significant with increasing isospin.(3) The role of orbital current for the o<+(1)gr>->1^+ Ml excitations in the even-even f_<7/2> shell nuclei is studied in the full f<n(1)7/2>+f<n-1(1)7/2> (f_<5/2>p_<3/2>p_<1/2>)^1 configuration space. Most of the orbital contribution is concentrated in the lowest 1^+ state. The first order correction term enhances appreciably the orbital-to-spin ratios compared with the pure f<n(1)7/2> model. The observed orbital-to-spin ratio for the o<+(1)gr>->1<+(1+1> Ml transition in ^<46>Ti is well reproduced.Calculations of the electron capture rates at the collapsing stage of the heavy stars and their application to the study of supernova explosion have not been able to be carried out during the term of this project, but they are now in progress. Less