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 $E_j\text{'}\mathrm{s}$. 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 $E_j=0\mathrm{}$ for all angular momenta). An approximate analysis of experimental excitation functions for the reaction-pair ${\mathrm{Ag}}^{109}(\alpha , n){\mathrm{In}}^{112}$ and ${\mathrm{Ag}}^{109}(\alpha , 2n){\mathrm{In}}^{111}$ suggests that $a>\mathrm{}12\mathrm{}$ Me${\mathrm{V}}^{-1\mathrm{}}$, assuming the level density expression $\omega \mathrm{}\left(E\right)\mathrm{}\propto E^{-2\mathrm{}}\exp \left[2\mathrm{}\surd \mathrm{}\right(\mathrm{aE}\left)\right]$, or $a>\mathrm{}7\mathrm{}$ Me${\mathrm{V}}^{-1\mathrm{}}$ assuming $\omega \mathrm{}\left(E\right)\mathrm{}\propto \exp \left[2\mathrm{}\surd \mathrm{}\right(\mathrm{aE}\left)\right]$. Alternatively, assuming $a\approx 16$ Me${\mathrm{V}}^{-1\mathrm{}}$ (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 $E_j\text{'}\mathrm{s}$ for angular momenta of $\left(\frac{11}{2}\right)\hslash$ to $\left(\frac{17}{2}\right)\hslash$ 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.