Angular distribution calculation based on the exciton model taking account of the influence of the Fermi motion and the Pauli principle

Abstract

An exact closed form solution to the time-integrated master equation of the exciton model is applied to the calculation of the angular distribution for both the preequilibrium and equilibrium decays of the neutron-induced reaction. The distribution probability of two-nucleon collision from g2 to f2' based on the Fermi gas model and the influence of the Fermi motion and the Pauli principle on the shape of the angular distribution are studied in detail. We have concluded that the influence of these effects on the shape of the angular distribution is rather significant for reactions in the energy range of several tens of MeV. As an example to compare with the experiments we have calculated the neutron-induced reaction 93Nb(n,n') at E,=15MeV. It seems that the most significant improvement of the present approach is the rise of the backward direction of the double differential cross section for the higher energy emitted neutrons.

Exciton model formulations for angular distributions and data comparison at medium energies

“…With varying assumptions altogether eight different models emerge as listed in Table I. It is shown that the model of [6], which is especially tailored to increase backward yields, is overdoing this job. The model of [9] (model IV) reproduces the data rather well except for small angles.…”

“…However, the contributions from these states to the cross section for nucleon induced reactions are small [13]. As in previous work [2][3][4][6][7][8][9][10][11] it is assumed that the spreading rate 2 factorises…”

“…For am= 1 we have the fast particle model [6]. If in an m-exciton state with p excited particles one nucleon undergoes a collision while (p-1) particles keep their energy and their direction, then…”

“…The problem in Ref. 6 and 8 was to get rid of the energy originally contained in P(m, O, e, t) via the assumptions (19) and (20).…”

“…This approach suffers from the computational difficulties compared to the previous ones. Sun Ziang et al [6] tried to take explicitly the Fermi motion into account by applying the intranuclear scattering kernel instead of the free nucleonnucleon scattering kernel of [2]. However, by averaging over all final nucleon energies the eoupling of energy and momentum is lost.…”