Random-walk model of precompound decay: Dynamics and multi-particle emission

Abstract

It is demonstrated that the dynamics of precompound nuclear decay can be formulated, with regard to emission spectra as well as angular distributions, in terms of a simple random walk of the composite nuclear system. In distinction to other preequilibrium models a discrete time parameter is introduced, corresponding to the number of intranuclear interactions. This random-walk description can be employed to analytically calculate several characteristics of the equilibration process, such as the mean time to emission from an exciton state, the mean first passage time, and the attainment of isotropy. Also a simple and compact description of multi-particle emission is obtained. A necessary and sufficient condition is given for the equivalence of the random-walk and the usual exciton models. As an application some neutron emission spectra of neutron-induced reactions on 127I at E= 15 to 50 MeV have been calculated. The results show that preequilibrium effects are very important in the first-particle emission. In the emission of secondary particles preequilibrium effects need to be included at incoming energies above about 25 MeV. Preequilibrium effects in tertiary emission spectra are not significant below E = 50 MeV.

Inclusive and exclusive preequilibrium spectra in a model of independently interacting excitons

“…Already the yield from the first stage contains multi-particle emissions up to order p. Therefore, these approaches are not well suited for calculating the probability at which a certain nucleus is reached after PE emission of a specified number of protons and neutrons. This holds especially for excitation energies above approximate 25 MeV where multinucleon emission gets important [15].…”

“…p particles sharing part of the total energy U* are not emitted but induce transitions to the next stage by nucleonnucleon collisions. Hence, for P ek < U* (15) k=l the non-emission probability W is formally defined by the expression W(U*) = ~ Np -1 17 P+ (ek) (16) m=l k=l m where one has to sum over the pNp factors of the geometric mean. Since Np is a very large number and e,, is practically a continous variable the normalized sum in (18) is equivalent to the integral over a corresponding particle density PD (era, U*) : Thus the averaging problem of (16) is reduced to the determination of particle densities at a particular point of the reaction path fl [23,24].…”

“…In principal, the emission of several nucleons may be simply gained by noting the residual exciton number and excitation energy after each particle emission and then repeating the same type of calculation. However, the computational tackling of even twonucleon emission for one bombarding energy is relatively computer-time consuming and has hitherto been performed only in a few cases using either Monte Carlo integration techniques Ell, 12], matrix inversion procedures [14] or random walk techniques [15]. Furtheron, considering the applicability of the EXCITON model an interesting question arises at higher energies where multi-particle emission gets important.…”

Description of Nucleon Induced Fission in Intranuclear Cascade -Multiparticle Preequilibrium - Hauser-Feshbach Approach

“…The idea of multiparticle preequilibrium emission in the frameworks exciton statistical model was proposed a long time ago [6] but as it is known to authors was realized recently. Its meaning is clear -after the first nucleon emission to repeat the calculation of equilibration for new composite 14006-p.2 CNR*09 system etc.…”

Pre-equilibrium effect in heavy ion induced fusion

“…Among them, those which are related to the present work are the following. Akkermans and Gruppelaar [9] treated the multi-particle emission on the random walk approach without further approximation. For the heavy-ion induced reaction very few works have been published, partly because the initial distribution function is not clear.…”