Level density based on the degenerate single particle levels

Level density for the equidistant level scheme is derived with keeping the degeneracy of the single particle levels. The derivation is sufficiently accurate within the framework of the model, and the only approximation introduced is the saddle point approximation in the Darwin-Fowler integral. The results are discussed in comparison with those by the Rosenzweig approximation and those of the continuous approximations. It is found that the Rosenzweig approximation is accurate for a rather broad range of the nuclear temperature in the case of large systems. The deviation from the more accurate calculation appears only below the excitation energy of a few times the single particle level spacing. Discussion is presented on the quantitative relationship among the continuous approximation, the Rosenzweig model and the present method, in the light of the result of the level counting. (auth.)