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

我们对原子核的热力学性质及相关课题进行了研究，取得了以下结果。我们在壳模型蒙特卡罗方法中发展了一种简便的角动量投影技术，并将其应用于研究核能级密度与自旋的关系。通过对Fe-Ni核的数值计算，我们发现偶关联对偶偶核的低能密度有影响，这种影响随着能量的升高而消失，而在奇核中则不存在这种影响。实现了稀土区大变形核能级密度的计算，并成功地重现了宽能区的实验数据。我们重新表述了有限温度平均场理论中的量子数投影，并首次建立了正则系综下的BCS型理论。这些都被用来研究守恒定律在有限系统升温相变中的作用，特别是从超流到正常的相变。我们指出，由于粒子数守恒，曾经被认为是超流到正常相变的指纹的核热容S形状出现了。为了研究不稳定核中的壳层结构和配对关联的影响，我们应用高斯展开方法发展了一种新的Hartree-Fock-Bogolyubov计算算法。新魔数N=16和32周围的壳层结构取决于有效的相互作用。然而，在HFB计算中，壳层间隙几乎被配对间隙所补偿。

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.