Optical Model Analysis of Elastic Scattering of 125-MevK+Mesons in Nuclear Emulsions

The diffuse-surface optical model has been used to analyze the elastic scattering and interaction cross-section data obtained from 94 meters of positive $K$-meson track in nuclear emulsion between energies of 100 and 150 Mev. The analysis was carried out on the SWAC digital computer through the use of the existing proton code which required but slight modification, such as the use of the Klein-Gordon equation. A thorough investigation was made of the number of energy intervals and representative emulsion nuclei that were required for adequate accuracy in the computed averaged cross sections. This number was found to be one energy and two representative emulsion nuclei (heavy and light). The four parameters ($R_0$, the radius parameter; $a$, the edge thickness; $V$, the real part of the potential; and $W$, the imaginary part of the potential) were varied and the goodness of fit was tested by means of the ${\chi }^2$ probability, there being nine degrees of freedom. An attractive real potential is fairly clearly ruled out and good fits were obtained for a repulsive real potential for a fairly wide range of physically acceptable geometrical parameters. If the $R_0$ and $a$ are chosen from electron-scattering experiments, then $V=21\mathrm{}\pm 4$ Mev and $W=-11.0\mathrm{}\pm 1.5$ Mev. If $R_0$ is increased to 1.20×${10}^{-13\mathrm{}}$ cm, then $V=14\mathrm{}\pm 2.5$ Mev and $W=-7\mathrm{}\pm 1$ Mev.