Angular distributions and differential ranges of Ba products from the interactions ofU238with 0.8-400-GeV protons

Angular distributions and differential ranges at ${90}^0$ to the beam of ${}_{}{}^{128}{}_{}{}^{}\mathrm{Ba}$, ${}_{}{}^{131}{}_{}{}^{}\mathrm{Ba}$, ${}_{}{}^{135}{}_{}{}^{}\mathrm{Ba}_{}^m{}_{}{}^{}$, and ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ba}$ emitted in the interaction of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ with 0.8-400 GeV protons have been measured. The angular distributions of ${}_{}{}^{128}{}_{}{}^{}\mathrm{Ba}$ and ${}_{}{}^{131}{}_{}{}^{}\mathrm{Ba}$ change from forward-peaked to sideward-peaked between 3 and 11.5 GeV, while those of ${}_{}{}^{135}{}_{}{}^{}\mathrm{Ba}_{}^m{}_{}{}^{}$ and ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ba}$ are sideward-peaked and independent of bombarding energy in the above regime. Momentum distributions of all products are Gaussian at 0.8 GeV with a mean value increasing from 120 ${\left(\mathrm{M}\mathrm{e}\mathrm{V}\mathit{A}\right)}^{1/2}$ for ${}_{}{}^{128}{}_{}{}^{}\mathrm{Ba}$ to 139 ${\left(\mathrm{M}\mathrm{e}\mathrm{V}\mathit{A}\right)}^{1/2}$ for ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ba}$. The momenta of the neutron-deficient products decrease by nearly a factor of 2 with increasing proton energy and the distributions broaden and become asymmetric. On the other hand, the momentum distributions of ${}_{}{}^{135}{}_{}{}^{}\mathrm{Ba}_{}^m{}_{}{}^{}$ and ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ba}$ are independent of proton energy. The results are analyzed with the two-step model and compared with the kinematics of the coherent interaction model. The implications of the results and comparisons for the reaction mechanism are considered.