Effects of Angular Momentum and Gamma-Ray Emission on Excitation Functions

Abstract

Excitation functions for many compound nucleus reactions are strongly dependent on the competition between gamma-ray and particle emission in the final particle-emission step. This competition depends, in turn, mainly on the energies and spins of a relatively few levels in the product nucleus, namely, on the lowest energy level at every angular momentum $J$ (these energies are herein designated by ${E}_{j}$). A method for making approximate calculations is described in which the influence of the competitive gamma-ray emission on excitation functions well above threshold is estimated, using assumed plausible distributions of the ${E}_{j}'\mathrm{s}$. It is found that larger values of the level density parameter $a$ are required to achieve agreement of calculations with experimental data when the competitive gamma-ray emission is included than when it is neglected (i.e., practically equivalent to setting ${E}_{j}=0$ for all angular momenta). An approximate analysis of experimental excitation functions for the reaction-pair ${\mathrm{Ag}}^{109}(\ensuremath{\alpha}, n){\mathrm{In}}^{112}$ and ${\mathrm{Ag}}^{109}(\ensuremath{\alpha}, 2n){\mathrm{In}}^{111}$ suggests that $a>12$ Me${\mathrm{V}}^{\ensuremath{-}1}$, assuming the level density expression $\ensuremath{\omega}(E)\ensuremath{\propto}{E}^{\ensuremath{-}2}\mathrm{exp}[2\ensuremath{\surd}(\mathrm{aE})]$, or $a>7$ Me${\mathrm{V}}^{\ensuremath{-}1}$ assuming $\ensuremath{\omega}(E)\ensuremath{\propto}\mathrm{exp}[2\ensuremath{\surd}(\mathrm{aE})]$. Alternatively, assuming $a\ensuremath{\approx}16$ Me${\mathrm{V}}^{\ensuremath{-}1}$ (in the first formula), consistent with values calculated by Lang from level spacings observed near neutron binding energies, it appears that the average value of the ${E}_{j}'\mathrm{s}$ for angular momenta of $(\frac{11}{2})\ensuremath{\hbar}$ to $(\frac{17}{2})\ensuremath{\hbar}$ in ${\mathrm{In}}^{111}$ is roughly 2 to 2.5 MeV. It is suggested that instead of trying to extract $a$ from excitation functions, it is perhaps more appropriate to try to extract information on the ${E}_{j}$ distribution, using for this purpose values of $a$ from other types of experiment.