High-Energy Multiple Scattering for Large Angles

Abstract

A formalism for high-energy multiple scattering is presented which is similar to the Glauber approach but which replaces the small-angle approximation by the larger-angle theory of Schiff. This formalism is applied to the scattering of fast protons from ${\mathrm{He}}^4$ with a very simple model, and Glauber's small-angle approximations are shown to be accurate only out to about 6° for an incident momentum $\approx 1\frac{\mathrm{BeV}}{c}$. A more realistic model using simple harmonic oscillator $S$ waves for the nuclear wave functions is then shown to fit the recent 1-BeV scattering data of Palevsky et al. quite well even at the maximum which occurs at $q^2=9.4\mathrm{}$ ${\mathrm{fm}}^{-2\mathrm{}}$, where the simple Glauber approach falls short. Using modified nuclear wave functions and the Glauber formalism, Bassel and Wilkin can also fit this maximum. In the present paper, a good fit is obtained by improving the basic scattering theory, rather than by using a small-angle theory at fairly large angles and then modifying the nuclear model.