Pb 208 ( O 16 , O 15 ) Pb 209 reaction

The neutron levels in $^{209}\mathrm{Pb}$ have been studied with the $^{208}\mathrm{Pb}$($^{16}\mathrm{O}$,$^{15}\mathrm{O}$) reaction at a bombarding energy of 139 MeV. Spectroscopic factors ($S$) have been deduced using a finite-range distorted-wave Born approximation (DWBA) with recoil. The $2{g}_{\frac{9}{2}}$, $1{i}_{\frac{11}{2}}$, $2{g}_{\frac{7}{2}}$, and $3{d}_{\frac{3}{2}}$ levels are found to have $S\ensuremath{\gtrsim}0.9$ while $S\ensuremath{\approx}0.7$ for the $1{j}_{\frac{15}{2}}$ level at 1.4 MeV excitation. Evidence is found for other $1{j}_{\frac{15}{2}}$ fragments being at 3.05 MeV and \ensuremath{\sim} 3.8 MeV with $S\ensuremath{\approx}0.08 \mathrm{and} 0.26$, respectively, which would place the centroid of the $1{j}_{\frac{15}{2}}$ level at ${E}_{x}\ensuremath{\approx}2.2$ MeV. DWBA predicts a shift in the maxima of the angular distributions as a function of $Q$ value which is not observed experimentally. A comparison with the proton transfer reaction $^{208}\mathrm{Pb}$($^{16}\mathrm{O}$,$^{15}\mathrm{N}$)$^{209}\mathrm{Bi}$ has been used to deduce the geometrical parameters of a neutron shell-model potential appropriate for nuclei with $A\ensuremath{\gtrsim}200$. The parameters of this Woods-Saxon potential are: ${V}_{R}=\ensuremath{-}50.5$ MeV ${r}_{R}=1.19$ fm, ${a}_{R}=0.75$ fm, ${V}_{\mathrm{so}}=\ensuremath{-}5.5$ MeV, ${r}_{\mathrm{so}}=1.01$ fm, and ${a}_{\mathrm{so}}=0.75$ fm.