Excitation Functions and Nuclear Charge Dispersion in the Fission of Uranium by 0.1- to 6.2-GeV Protons

Abstract

Cross sections for formation of cesium and rubidium isotopes produced by bombardment of uranium with protons ranging in energy from 0.1 to 6.2 GeV were measured both radiochemically and mass spectrometrically. Independent yields were determined for ${\mathrm{Rb}}^{84}$, ${\mathrm{Rb}}^{86}$, ${\mathrm{Cs}}^{127}$, ${\mathrm{Cs}}^{129}$, ${\mathrm{Cs}}^{130}$, ${\mathrm{Cs}}^{131}$, ${\mathrm{Cs}}^{132}$, ${\mathrm{Cs}}^{134}$, ${\mathrm{Cs}}^{136}$, and, at some energies, ${\mathrm{Rb}}^{83}$ and ${\mathrm{Cs}}^{135}$. In addition, the independent yield of ${\mathrm{Ba}}^{131}$ and the chain yields of ${\mathrm{Cs}}^{125}$, ${\mathrm{Cs}}^{127}$, ${\mathrm{Cs}}^{129}$, ${\mathrm{La}}^{131}$, ${\mathrm{Cs}}^{135}$, ${\mathrm{Cs}}^{137}$, ${\mathrm{Rb}}^{83}$, ${\mathrm{Rb}}^{87}$, and ${\mathrm{Ba}}^{140}$ were obtained. The formation cross sections of the Cs and Ba products on the neutron-excess side of stability decrease monotonically with increasing energy above 0.1 GeV, whereas the excitation functions for independent formation of the more neutron-deficient products in the Cs-Ba region and of ${\mathrm{Rb}}^{84}$ and ${\mathrm{Rb}}^{86}$ all go through maxima. The proton energies at which these maxima occur fall on a smooth curve when plotted against the neutron-proton ratio of the product, with the peaks moving to higher energies with decreasing neutron-proton ratio. Under the assumption that the mass-yield curve in the region $125lAl140$ is rather flat at each proton energy, the cross-section data in the Cs region can be used to deduce the charge dispersion in this mass range. Plots of $log\ensuremath{\sigma}$ vs $\frac{N}{Z} (or Z\ensuremath{-}{Z}_{A})$ show symmetrical bell-shaped peaks up to a bombarding energy of 0.38 GeV, with full width at half-maximum increasing from $3.3 Z$ units at 0.10 GeV to about $5 Z$ units at 0.38 GeV, and with the peak position (${Z}_{p}$) moving from ${Z}_{A}\ensuremath{-}1.44$ to ${Z}_{A}\ensuremath{-}0.85$ over the same energy range. At all higher energies, a double-peaked charge distribution was found, with a neutron-excess peak centered at $\frac{N}{Z}\ensuremath{\sim}1.515({Z}_{p}\ensuremath{\sim}{Z}_{A}\ensuremath{-}1.9)$, and having approximately constant width and height at bombarding energies greater than 1 GeV. The peak on the neutron-deficient side which first becomes noticeable at 0.68 GeV appears to become broader and shift slightly to smaller $\frac{N}{Z}$ values with increasing energy. The two peaks are of comparable height in the GeV region, and the peak-to-valley ratio is only \ensuremath{\sim}2. The total formation cross section per mass number in the Cs region decreases from \ensuremath{\sim}52 mb at 0.1 GeV to about 29 mb at 1 GeV and then stays approximately constant; the contribution of the neutron-excess peak above 1 GeV is about 12 mb. The neutron-excess peak corresponds in width and position to that obtained in fission by \ensuremath{\sim}50-MeV protons. The recoil behavior of ${\mathrm{Ba}}^{140}$ leands support to the idea that the neutron-excess products are formed in a low-deposition-energy process. The recoil behavior of ${\mathrm{Ba}}^{131}$ indicates that it is formed in a high-deposition-energy process. Post-fission neutron evaporation is required to account for the observed characteristics of the excitation functions of the rubidium isotopes and the neutron-deficient species in the Cs region. The correlation between neutron-proton ratios and positions of excitation function maxima is semiquantitatively accounted for if fission with unchanged charge distribution, followed by nucleon evaporation, is assumed.