Spallation-Fission Competition in Heavy-Element Reactions:Th232+He4andU233+d

Abstract

Cross sections and excitation functions have been determined for spallation and fission products from bombardments of ${\mathrm{Th}}^{232}$ with helium ions (15 to 46 Mev) and ${\mathrm{U}}^{233}$ with deuterons (9 to 24 Mev). This work extends a series of investigations of charged particle ($\ensuremath{\alpha}$, $d$, and $p$) induced reactions in heavy elements ($Z\ensuremath{\ge}88$). Radiochemical methods were employed to isolate products corresponding to the following spallation reactions: neutron emission, ($\ensuremath{\alpha}, 4n$), ($\ensuremath{\alpha}, 5n$), ($d, n$), ($d, 2n$), and ($d, 3n$); emission of one proton and neutrons ($\ensuremath{\alpha}, p$), ($\ensuremath{\alpha}, \mathrm{pn}$), ($\ensuremath{\alpha}, p2n$), and ($\ensuremath{\alpha}, p3n$); and emission of two protons and neutrons, ($\ensuremath{\alpha}, 2p$), ($\ensuremath{\alpha}, 2pn$), and ($\ensuremath{\alpha}, \ensuremath{\alpha}n$), and ($d, \ensuremath{\alpha}n$). In addition, the following fission products were isolated from one or more bombardments: ${\mathrm{Zn}}^{72}$, ${\mathrm{Ge}}^{77}$, ${\mathrm{As}}^{77}$, ${\mathrm{Br}}^{82,83}$, ${\mathrm{Rb}}^{86}$, ${\mathrm{Sr}}^{89,91}$, ${\mathrm{Y}}^{93}$, ${\mathrm{Zr}}^{95,97}$, ${\mathrm{Nb}}^{96}$, ${\mathrm{Mo}}^{99}$, ${\mathrm{Ru}}^{103,105,106}$, ${\mathrm{Pd}}^{109,112}$, ${\mathrm{Ag}}^{111}$, ${\mathrm{Cd}}^{115,115m,117}$, ${\mathrm{I}}^{131,133}$, ${\mathrm{Cs}}^{136}$, ${\mathrm{Ba}}^{139,140}$, ${\mathrm{La}}^{140}$, ${\mathrm{Ce}}^{141,143,144}$, ${\mathrm{Nd}}^{147}$, ${\mathrm{Eu}}^{157}$, and ${\mathrm{Gd}}^{159}$.The results show that fission is the predominant reaction at all energies for ${\mathrm{Th}}^{232}$ and to an even greater extent for ${\mathrm{U}}^{233}$. The data for the surviving spallation products are consistent with several mechanisms of reaction, including compound-nucleus formation and evaporation, direct interactions between nucleons of the incoming helium ion or deuteron and nucleons of the nucleus, and a combination of these types of processes (direct interaction followed by evaporation). In general, the results confirm and extend previously established concepts.The neutron-emission spallation reactions as well as fission are best explained as proceeding through compound-nucleus formation. The shapes and magnitudes of ($\ensuremath{\alpha}, 4n$), ($d, 2n$), and ($d, 3n$) excitation functions correlate well with a compound-nucleus treatment modified to include fission competition. According to this treatment, ratios of neutron to total-reaction level width, $\frac{{\ensuremath{\Gamma}}_{n}}{\ensuremath{\Sigma}{i}^{}{\ensuremath{\Gamma}}_{i}}$, are 0.49 for ${\mathrm{U}}^{236\ensuremath{-}233}$ [from ${\mathrm{Th}}^{232}(\ensuremath{\alpha}, 4n)$], 0.17 for ${\mathrm{Np}}^{235\ensuremath{-}234}$ [from ${\mathrm{U}}^{233}(d, 2n)$], and 0.20 for ${\mathrm{Np}}^{235\ensuremath{-}233}$ [from ${\mathrm{U}}^{233}(d, 3n)$]. In addition the total-reaction excitation functions (consisting mostly of the fission excitation functions) are consistent with theoretical cross sections for compound-nucleus formation calculated with a nuclear radius parameter ${r}_{0}=1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{A}^{\frac{1}{3}}$.The fission mass-yield curves are similar to those found for other heavy target isotopes (for elements from thorium to plutonium). The minimum in the curves in the region of mass 120 tends to disappear as helium-ion or deuteron energy is increased.The ($\ensuremath{\alpha}, \mathrm{pxn}$), ($\ensuremath{\alpha}, 2pxn$), ($\ensuremath{\alpha}, \ensuremath{\alpha}n$), ($d, n$), and ($d, \ensuremath{\alpha}n$) products are attributed to direct interactions, with complex particles emitted in preference to a series of protons and neutrons. Thus ($\ensuremath{\alpha}, d$), ($\ensuremath{\alpha}, t$), and ($\ensuremath{\alpha}, \mathrm{tn}$) mechanisms would account for most of the ($\ensuremath{\alpha}, \mathrm{pn}$), ($\ensuremath{\alpha}, p2n$), and ($\ensuremath{\alpha}, p3n$) products, respectively. In the case of the ($\ensuremath{\alpha}, t$) and ($\ensuremath{\alpha}, \mathrm{tn}$) reactions, analysis of the ratio $\frac{\ensuremath{\sigma}(\ensuremath{\alpha}, tn)}{\ensuremath{\sigma}(\ensuremath{\alpha}, t)}$ leads one to the conclusion that with 35-Mev helium ions only 9% of outgoing tritons leave the residual nucleus with sufficient energy to evaporate a neutron or undergo fission, and with 44-Mev helium ions only 20% do so. The ($d, n$) product probably results from the stripping reaction.