Analysis of Recoil Angular and Range Distributions from Compound-Nucleus Reactions

Abstract

A method is presented for calculating the observable kinematic properties of nuclei recoiling from compound-nucleus reactions. The computations are performed by specifying center-of-mass distribution functions in angle and speed which arise from the emission of particles, and carrying out the appropriate integrations over laboratory speeds and angles. The calculated angular distributions, range distributions, and range distributions with angular restrictions (collimated ranges) are directly comparable to the corresponding properties measured in recoil experiments. Results are given for a number of compound-nucleus reactions induced by heavy ions and $\alpha$ particles, where sufficiently detailed experimental data are available for comparison. Very good agreement was obtained by assuming isotropic particle emission in the center-of-mass system and using a Maxwellian distribution of recoil speeds. The single parameter in the Maxwellian function was fixed by relating it to the mean-square velocity of the recoiling nuclei, the latter being determined from experimental angular distribution data by means of a previous analysis. The effects of different forms of the center-of-mass angular and velocity distributions on the calculated angular and range distributions are discussed. We conclude that, in all the cases investigated, the recoil angular distributions are essentially isotropic in the center-of-mass system, with no more than a small anisotropy being allowed by the experimental data. Furthermore, velocity distributions which differ greatly from the Maxwellian form are not consistent with the observations. The laboratory velocity spectrum of recoils emitted within a small angular interval about 0° has been calculated for a specific reaction, and is found to resemble rather closely a recent experimental measurement of this distribution.