Shell model study for the nuclear beta transitions and supernova explosion

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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