Level Density of a Fermi System: Nonperiodic Perturbations of the Energy‐Level Scheme

The level density of a degenerate Fermi system is modified by the perturbation in the position of a single‐particle level. To study this effect, miscellaneous exact relations between the level densities of the perturbed and unperturbed system are derived. For the special case of the perturbed uniform model, these connections become a set of recursion relations which lead to a complete solution of the problem. Results are also obtained in the saddle‐point approximation, and these have a simple interpretation in terms of the usual Fermi occupation probabilities. If a single‐particle level is deleted from the scheme, the resultant diminution in the level density persists indefinitely with increasing excitation energy. Information about the adequacy of the saddle‐point approximation is obtained by comparison with some exact solutions.