Competition Between Neutron and Gamma-Ray Emission Following Formation of the Compound Nucleus ${\mathrm{Po}}^{210}$ in the Systems ${\mathrm{Pb}}^{206}$+$\alpha$ and ${\mathrm{Bi}}^{209}$+$p$

We report measurements of the cross-section ratio $R_x=\frac{\sigma \left({\mathrm{Po}}^{208}\right)}{\left[\sigma \right({\mathrm{Po}}^{208})+\sigma ({\mathrm{Po}}^{209}\left)\right]}$ for the reactions ${\mathrm{Pb}}^{206}(\alpha , n){\mathrm{Po}}^{209}$, ${\mathrm{Pb}}^{206}(\alpha , 2n){\mathrm{Po}}^{208}$, and ${\mathrm{Bi}}^{209}(p, n){\mathrm{Po}}^{209}$, ${\mathrm{Bi}}^{209}(p, 2n){\mathrm{Po}}^{208}$ for bombarding energies up to 2.7 and 2.3 MeV above the respective $\alpha$, $2n$ and $p$, $2n$ thresholds. The shape of $R_{\alpha }$ as a function of energy is clearly different from the shape of $R_p$. Moreover, using threshold energies determined "internally" by extrapolation of the data we show that $R_{\alpha }>R_p$ at any given excitation energy of the ${\mathrm{Po}}^{210}$ compound nucleus over the entire range of energies studied. Despite this observed dependence of decay on the mode of formation, we find that our results are completely consistent with the compound nucleus mechanism if we take into account (1) the competition between gamma-ray emission and neutron emission, and (2) the different distributions of angular momenta characterizing the compound nucleus ${\mathrm{Po}}^{210}$ for the two different target-projectile systems. From a detailed analysis of the data nearest threshold we find the value of the level density parameter $a$ to be about 11 Me${\mathrm{V}}^{-1\mathrm{}}$ (to within about ±20%), in agreement with values of $a$ from other types of data in the mass region $A=204\mathrm{} \mathrm{to} 210$. Simultaneously we also obtain an estimate for the ratio of mean radiation width to mean level spacing in ${\mathrm{Po}}^{209}$ at excitation energies near the neutron binding energy, which estimate agrees well with the value expected from systematics. We also report measurements of the ratio ${\mathcal{R}}_{\gamma }=\frac{\sigma \left({\mathrm{Po}}^{210}\right)}{\left[\sigma \right({\mathrm{Po}}^{208})+\sigma ({\mathrm{Po}}^{209})+\sigma ({\mathrm{Po}}^{210}\left)\right]}$ where the