Determination of Total Widths and Resonance Energies of the Single-Particle Analog Resonances inBi209

Excitation functions for the inelastic scattering of protons from ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ have been obtained for incident proton energies from 14 to 18 MeV. Resonances corresponding to the first seven single-neutron isobaric analog states (IAR) of ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ are observed. Many of the inelastic-scattering excitation functions show a resonance at only one of the IAR. These excitation functions were fitted with a five-parameter formula which consists of a resonance amplitude and an energy-independent background amplitude. For some excitation functions, additional resonance amplitudes were included. The analogs of the $g_{\frac{9}{2}}$ (ground-state), $i_{\frac{11}{2}}(0.79-\mathrm{MeV})$, $j_{\frac{15}{2}}$ (1.41-MeV), $d_{\frac{5}{2}}$ (1.56-MeV), $s_{\frac{1}{2}}$ (2.03-MeV), $g_{\frac{7}{2}}$ (2.47-MeV), and $d_{\frac{3}{2}}$ (2.52-MeV) states are found to have total widths of 253±10, 224±25, 308±8, 319±15, 288±20, and 279±20 keV, respectively. In respective order, the resonance laboratory energies are 14.918±0.006, 15.716±0.010, 16.336±0.015, 16.496±0.008, 16.965±0.014, 17.430±0.010, and 17.476±0.010 MeV.