AN ITERATIVE METHOD FOR CALCULATION OF NUCLEAR LEVEL DENSITIES

An improved method is presented for the calculation of nuclear level densities from single particle energy levels. The calculation is performed using a statistical approach but avoiding the usual mathematical approximations. Recursion relations are given for the calculation of coefficients of a finite order partition function for the case of non-interacting fermions and for the case in which the effect of residual interactions is approximated by a diagonal pairing energy for doubly degenerate states. Computer calculations of the level density are demonstrated for several simple models exhibiting structure in the single-particle level scheme and for the deformed nucleus single-particle Nilsson levels for the nuclei 30Si, 31P, 32P and 32S as a function of deformation parameter η and pairing energy Δ. Non-zero values of both parameters are required to obtain reasonable agreement with observed level densities at or below 8 MeV. © 1969.