Semiclassical Treatment of Direct Nuclear Reactions

Abstract

A semiclassical method is employed to discuss the angular distributions of direct nuclear reactions. The method considers the incident and outgoing particles to be described by rays which follow classical paths; these rays can be refracted, reflected, and absorbed by a "clouded-crystal-ball" nucleus. Any given incident ray is considered to have a certain probability of suffering a major "scattering" at each point within a nucleus, this "scattering" not only changing the direction of the ray but also its wavelength. A condition of angular momentum conservation is imposed on this direct-scattering event, such that the angular momentum change in this process is equal to that required by the direct reaction under consideration.On this picture it is seen that the oscillations in the angular distributions which often occur with direct reactions arise as a result of interference between direct scatterings in different regions of the nucleus. Thus these oscillations are to be likened to the interference maxima and minima which arise when light is scattered, for example from a soap film. Effects due to compound nucleus absorption and of refraction and reflection of the incident and outgoing rays can be discussed fairly simply on this model. An investigation of the basis of the semiclassical method indicates that it should be reliable over a wide range of interesting conditions. *

Study of (He3,d) and (HeWegner1, Hall2 1960Phys. Rev.58220View full textAdd to dashboardCite

“…This calculation, as well as other recent work, 25 could be applied to these data by appropriate extensions of the calculations.…”

Simple Realistic Treatment of Nuclear Direct-Interaction Processes

“…In that example the simple jL{KR) of the Butler formula was replaced by a sum of terms jv (KR) with coefficients whose squared moduli were interpreted as the probability that the angular momentum transfer in the inelastic episode is V rather than L. On the other hand, Eq. (17) does not seem to have this type of structure, and only one Bessel function appears to be present. However, the argument of the Bessel function in (17) is not simply KR, and the perfect resolution of angular momentum is associated with Bessel functions of this argument, and in particular with the fact that for particular momentum transfers \JL(KR)\ 2 is strictly zero.…”

“…Lastly, the relative magnitudes of successive peaks is controlled by the thickness parameter X. Predictions of (16) and (17) are compared in Fig. 5 and typical fits for (a,a') scattering from sulfur and magnesium targets using (15') are shown in Figs.…”

“…Equation (18) displays clearly the poor resolution for angular momentum transfer, but also spoils the great simplicity of our result. In the form (17) or (15') the lack of resolution for angular momentum transfer, shows up through the nonzero minima of da/dtt.…”

“…Consequently there can be a very large contribution to the cross section from jo(KR) even though in fact the angular momentum transfer L is 2. Butler, Austern, and Pearson 17 have given what appears to be an alternative explanation of the anomalous forward scattering typical of (p,p') experiments, namely that the bending of the incoming beam introduces an extra transverse component of momentum which permits a scattering to take place which one might naively expect to be forbidden by angular momentum conservation. This is really not a different interpretation, however.…”