Analysis of Fragmented Analog-State Resonances by Coupled Optical Equations with Effective Nonlocal Potentials

The fragmentation of single-particle analog resonances in proton elastic scattering is accomplished here by means of an effective nonlocal optical potential added to the Lane equations. This potential is inferred from the analogous potential in the parent isobaric nucleus, where it arises from the coupling of the single-neutron states to other degrees of freedom in that system. The new coupled equations are solved numerically by an iterative procedure for the case of ${\mathrm{Sr}}^{88}$+$p$ using an average set of optical-model parameters and the known ($d, p$) spectroscopic factors. The elastic excitation functions calculated in this way compare closely to experiment over a range of energies of $E_p=4.8\mathrm{} \mathrm{to} 8.1$ MeV, which includes six $2d_{\frac{5}{2}}$, $2d_{\frac{3}{2}}$, $3s_{\frac{1}{2}}$, and $1g_{\frac{7}{2}}$ resonances. The sensitivity of the calculations to the various input parameters indicates that the method may be useful for providing independent determinations of both optical-model parameters and spectroscopic factors. Some shortcomings of the model are discussed and future improvements indicated.