Diffuse-Surface Optical Model Analysis of Elastic Scattering of 17- and 31.5-Mev Protons

Differential cross sections for the elastic scattering of 17- and 31.5-Mev protons by various nuclei have been analyzed according to the diffuse-surface optical model of the nucleus using a central interaction potential of the form $-\frac{\mathrm{}(V+iW)\mathrm{}}{\{1+\exp [\frac{\mathrm{}(r-R)\mathrm{}}{a}\left]\right\}}$. Calculated curves of the ratio of the differential to the Rutherford cross sections are presented and compared with experimental values. The adopted values of the four parameters of the model are those which either give best agreement with experiment or, insofar as ambiguities exist, permit the interaction radius $R$ to be expressed as $R_0{A}^{\frac{1}{3}}$ with $R_0$ constant throughout most of the periodic table. The average values of the parameters chosen in this way were found at 17 Mev to be as follows: real part of the nuclear potential $V=47\mathrm{}$ Mev, imaginary part of the nuclear potential $W=8.5\mathrm{}$ Mev, nuclear radius constant $R_0=1.33\mathrm{}\times {10}^{-13\mathrm{}}$ cm, surface rounding parameter $a=0.5\mathrm{}\times {10}^{-13\mathrm{}}$ cm. A similar analysis at 31.5 Mev gave $V=35.5\mathrm{}$ Mev, $W=15.5\mathrm{}$ Mev, $R_0=1.33\mathrm{}\times {10}^{-13\mathrm{}}$ cm, $a=0.55\mathrm{}\times {10}^{-13\mathrm{}}$ cm. Ambiguities in the quoted values due to compensating effects of changes in $V$ and $R_0$ are discussed. For intermediate and heavy nuclei like Ag and Pt, good agreement can be obtained at 17 Mev for values of $R_0$ ranging from 1.2 to 1.4×${10}^{-13\mathrm{}}$ cm, but for lighter elements like Co the range of $R_0$ is much more restricted. Theoretical curves of the reaction cross section are presented at 17 and 31.5 Mev based on quoted values of the model parameters. It is pointed out that accurate experimental measurements of this quantity may possibly resolve the ambiguity.