Particle-hole state densities with linear momentum and angular distributions in preequilibrium reactions

We present two methods for the calculation of state densities with linear momentum. The first is exact, convoluting single-particle and hole densities in momentum space, and can be used for nuclear excitations with small numbers of particles and holes. The second, based on statistical arguments, is applicable for excitations of many particles and holes and leads to state densities with a Gaussian linear-momentum dependence. Together, these two techniques allow state densities with linear momentum to be determined for any particle-hole excitation. The relationship between linear- and angular-momentum state densities is discussed, and we show how the familiar Gaussian angular-momentum distribution of states can be obtained from state densities with linear momentum. We argue that these state densities provide the most elegant and straightforward means for obtaining angular distributions in semiclassical preequilibrium theories, avoiding inconsistencies inherent in the commonly adopted procedure of using a nucleon-nucleon scattering kernel. In our approach the angular distribution of preequilibrium particles emitted from a two-particle–one-hole state is identical to that found by Kikuchi and Kawai. Angular distributions from more complex particle-hole states do, however, differ from a convolution of Kikuchi-Kawai scattering kernels, since we do not make a leading-particle approximation. As an illustrative example to the use of the Gaussian form of state densities with linear momentum, we calculate the angular distributions of emitted particles in the preequilibrium reaction ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$(α,p), ${\mathit{E}}_{\mathrm{\alpha }}$=109 MeV. Our calculations account for the experimental angular distributions well, even at large backward angles where many semiclassical approaches fail.