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

Abstract

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 linearand angular-momentum state densities is discussed, and we show how the familiar Gaussian angularmomentum 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-particleone-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 of the use of the Gaussian form of state densities with linear momentum, we calculate the angular distributions of emitted particles in the preequilibrium reaction Ho(n, p), E = 109 MeV. Our calculations account for the experimental angular distributions well, even at large backward angles where many semiclassical approaches fail. PACS number(s): 24.10.i, 24.60.Gv, 25.40. Ep, 25.40.Fq

Comparison of approximations to the transition rate in the DDHMS preequilibrium model

“…[2] The model was extended by Blann and Chadwick to calculate double differential spectra (DDHMS) using approximate expressions obtained from considerations of linear momentum conservation for the energy-dependent angular distributions of the particles and holes created. [4,5] Because the DDHMS uses only two-body transitions to two-particle-one-hole (2p-1h) or one-holetwo-particle (1h-2p) states, the transitions can be calculated in more complex approximations than that used in the original work. The simplest extension would be to substitute the exciton model densities and transition rates, based on equally spaced levels, with Fermi gas densities and transition rates that better reflect the nuclear single-particle density of states.…”

Iwamoto-Harada model of pre-equiluibrium cluster emission: Should we care about angular momentum?

“…The approach was much improved in [34], together with a method to calculate the densities with specified linear momentum.…”

“…Incorporation of spin variables into the pre-equilibrium exciton model [29,34] has been developed for the equilibration process, nucleon and γ emissions. Obviously, if we calculate the time spent in the n-exciton state by solving the set of master equations [30], this set becomes much larger (from tens of thousands coupled equations up to millions of them).…”

The density of available states of the DDHMS pre-equilibrium model

“…An additional advantage of the HMS model compared to earlier models is that it easily permits multiple emissions from the precompound nucleus. Two years later, Blann and Chadwick, generalized the model to the DDHMS (double differential hybrid Monte Carlo simulation) [9] model by including the calculation of angular distributions based on the work of Chadwick and Obložinský [10,11]. We show how the double differental transition densities of the DDHMS can be easily sampled using Monte Carlo methods.…”