Analysis of Thick-Target Recoil Studies of High-Energy Nuclear Reactions

The effect of broad velocity distributions on the vector-model analysis of average projected ranges obtained in thick-target experiments has been explored. The Monte Carlo technique was used to construct laboratory velocity distributions on the basis of impact ($v_{\parallel }$) and breakup ($V$) velocity distributions inferred from differential recoil studies. A range-velocity relation for fission products in uranium was constructed and used to convert the laboratory velocities to average projected ranges. The latter were then analyzed by means of equations based on the vector model to yield values of $〈v_{\parallel }〉$ and $〈V〉$ which could be compared with the respective average values of the input velocity distributions. The calculation was performed for ${\mathrm{Mo}}^{99}$, ${\mathrm{Pd}}^{103}$, and ${\mathrm{Ba}}^{131}$ formed in the high-energy fission of uranium, as well as for several simple velocity distributions. The effects tend to be rather small (0-20%), although in most cases the vector-model analysis does tend to overestimate the value of $〈V〉$ and underestimate that of $〈v_{\parallel }〉$.