Quantitative evidence of weak isospin mixing in the low-lying isobaric analog resonances in 209Bi

The excitation functions of ${}^{208}\text{Pb}\text{(}\text{p}\text{,}\text{p}{}_0\text{)}{}^{208}\text{Pb}$ have been measured in the energy range E_p = 14.2 to 17.4 MeV in 50 keV steps at θ_lab = 120°, 140° and 160°. The isobaric analog resonances of the parent states in ²⁰⁹Pb up to E_x = 2.5 MeV and the optical-model background were fit simultaneously at all energies and angles. The spreading widths and the values of a parameter β², which measures the isospin purity of the IAR, were determined for the $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{,}\text{i}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{,}\text{j}{}_{\mathrm{<mtext>15</mtext><mtext>2</mtext>}}\text{,}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, and $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ resonances. An average value of the isospin purity of β² = 66% was found.