Study of the Interaction of PositiveKMesons

Continuing our program on the study of positive $K$ mesons, we have investigated the interactions of $K$ mesons with hydrogen and complex nuclei in photographic emulsions primarily in the energy interval 100 to 220 Mev. We are reporting on interactions found in 320 meters of ${K}^{+}$ track length followed, of which 227 meters were in the energy interval 100 to 220 Mev. The exposure was made to an enriched $K$-meson beam at the Berkeley Bevatron. The ratio of $K$ mesons to minimum ionizing background particles ranged from 1:1 to 1:3 across our stack. Thirteen new $K$-hydrogen scattering events were found and added to those previously published. We find the $K$-H cross section to be energy-independent in the energy interval from 20 to 200 Mev. The average cross section over this energy interval is 14.5\ifmmode\pm\else\textpm\fi{}2.2 mb. The differential cross section appears to be due predominantly to $S$-wave scattering.The data obtained on inelastic collisions with complex nuclei have been analyzed by using an independent-particle model for the nucleus. Using this model and correcting for (a) nucleon shading, (b) Coulomb repulsion, (c) Pauli exclusion principle, and (d) repulsive potentials, we obtained the average $K$-nucleon cross section as a function of energy. This cross section appears energy-independent in the energy interval 60 to 180 Mev. The values for the elementary cross sections obtained in this analysis for ${T}_{K}=60 \mathrm{to} 180$ Mev with $V={V}_{N}+{V}_{C}=35$ Mev were $\overline{\ensuremath{\sigma}}(\mathrm{the}\mathrm{average} K\ensuremath{-}\mathrm{n}\mathrm{u}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{o}\mathrm{n}\phantom{\rule{0ex}{0ex}}\mathrm{c}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}\phantom{\rule{0ex}{0ex}}\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n})=11.8\ifmmode\pm\else\textpm\fi{}1.3$ mb, ${\ensuremath{\sigma}}_{\mathrm{KN}}=9.8\ifmmode\pm\else\textpm\fi{}3.0$ mb (with ${\ensuremath{\sigma}}_{\mathrm{Kn}}={{\ensuremath{\sigma}}_{n}}^{+}+{{\ensuremath{\sigma}}_{n}}^{0}$ where ${{\ensuremath{\sigma}}_{n}}^{+}$ is direct neutron scattering and ${{\ensuremath{\sigma}}_{n}}^{0}$ is charge-exchange scattering), ${{\ensuremath{\sigma}}_{n}}^{+}=5.8\ifmmode\pm\else\textpm\fi{}3.1$ mb, and ${{\ensuremath{\sigma}}_{n}}^{0}=4.0\ifmmode\pm\else\textpm\fi{}0.8$ mb. In this case the ratio ${\ensuremath{\sigma}}_{\mathrm{Kp}}:{{\ensuremath{\sigma}}_{n}}^{+}:{{\ensuremath{\sigma}}_{n}}^{0}\ensuremath{\approx}3.6:1.5:1$. We observe a backward peaking in the differential cross section and believe that this is due to a small $P$-wave contribution.These results lead us to believe that the $K$-nucleon scattering is a short-range force interaction and does not proceed through single $\ensuremath{\pi}$-meson exchange. The latter would require high-angular-momenta contributions and would presumably result in a strongly energy-dependent cross section.A repulsive potential was necessary to explain the behavior of the fractional energy loss as a function of energy. The magnitude of the potential necessary for a best fit $V\ensuremath{\approx}30$ Mev agrees very well with the results of a partial wave analysis of the elastic-scattering data.