Shell-Model Calculations of the Lowest-Energy Nuclear Excited States of Very High Angular Momentum

A combinatorial calculation is used to estimate the few (about ten) lowest-energy nuclear excited states at every angular momentum, out to very large angular momenta (e.g., out to about $70\hslash$). It is useful to have these estimates to interpret many nuclear reactions, especially reactions induced by heavy ions and proceedings through the compound-nucleus mechanism. The calculation is based on a spherical shell model of fermions assumed to be noninteracting, except that pairing forces are taken into account. Several calculated examples are given. It is found that the division of nuclear excitation energy into "thermall" and "rotational" energies in computing level densities may not be very useful near to or far from closed shells, but may accidentally be useful for some intermediate cases. For convenience, however, the calculated levels can be thought of as embodying simultaneously the effects of pairing energy, rotational energy, and shell closure, which are often introduced separately and ad hoc into analyses of nuclear reaction data. The rate of increase of the nuclear level density at energies just above the lowest excited level at every angular momentum also depends sensitively on the proximity of the nucleus to closed shells. The "brute-force" calculation described here is only practicable if the energies of very many configurations can be computed and compared in a short time, a circumstance facilitated by use of a spherical model nuclear potential. However, it is found that an extension of this type of calculation to include nonspherical potentials should be feasible. Since, in discussing many nuclear reactions, it is necessary to call attention repeatedly to the lowest excited level at every angular momentum, it is desirable to give these levels a special name. It has been proposed that the lowest-energy excited state at a given angular momentum be called "yrast" level for that angular momentum.