Theory of (a,xn) Reactions

A new method for the study of ($a,xn$) reactions is presented ($a=n,p,\alpha ,\gamma ,\mathrm{HI}$). The method is applicable to reactions in which first a compound nucleus is created and later $x$ neutrons are evaporated. The method allows the calculation of excitation functions for the emission of a specified number of neutrons, average neutron energies, and neutron spectra. The equations governing a succession of neutron emissions are derived from first principles. The effect of $\gamma$ decay is incorporated. The effect of spin on decay rates is treated rigorously. The theory is used to calculate the excitation function for the reactions ${\mathrm{Ag}}^{109}(\alpha ,n){\mathrm{In}}^{112m}$, ${\mathrm{Ag}}^{109}(\alpha ,n){\mathrm{In}}^{112g}$, and ${\mathrm{Ag}}^{109}(\alpha ,2n){\mathrm{In}}^{111}$. The comparison between measured and calculated values is discussed.