Research on nuclear thermodynamical properties via microscopic theories and applications to nuclear astrophysics

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We have studied thermodynamical properties of atomic nuclei and related topics, and have obtained the following results.1. We have developed a convenient technique of angular-momentum projection in the shell model Monte Carlo method, and have applied it to investigate spin-dependence of nuclear level densities. By numerical calculations on Fe-Ni nuclei, we have found that the pair correlation influences low-energy densities of even-even nuclei, which disappears as the energies goes higher, and that such effects are not viewed in odd nuclei.2. We have implemented calculation of level densities of well-deformed nuclei in the rare-earth region, such as ^<162>Dy, and succeeded in reproducing experimental data in wide energy region.3. We have reformulated quantum-number projection in finite-temperature mean-field theories, and moreover, have formulated a BCS-type theory in canonical ensembles for the first time. These have been applied to investigate role of conservation laws in phase transition in finite systems for increasing temperature, the superfluid-to-normal transition in particular. We have pointed out that the S-shape heat capacity of nuclei, which had been suggested to be a fingerprint of the superfluid-to-normal transition, comes out because of the particle-number conservation.4. We have developed a new algorithm for Hartree-Fock-Bogolyubov calculations by applying the Gaussian expansion method, in order to investigate shell structure in unstable nuclei and effects of the pairing correlation. Shell structure around the new magic numbers N=16 and 32 depends on effective interactions. However, the shell gap is almost compensated by the pairing gap in the HFB calculations.