A theory of isobaric-spin analogue resonances is developed by considering a potential model which has an isobaric-spin-dependent component. The occurrence of isobaric states as compound-nucleus resonances is shown to be a natural consequence of the formalism previously used to explain the excitation of isobaric analogue states by the direct-interaction charge-exchange mechanism. The results are then generalized on the basis of the $R$-matrix theory of nuclear reactions because of the expectation that isobaric spin is relatively pure within a sphere of dimensions similar to those of the charge distribution. The interpretation of analogue resonances as giant resonances is considered and shown to be different from the conventional optical giant resonances. Formulas are derived which are mainly applicable to the elastic scattering of protons below the Coulomb barrier. The importance of the external and internal regions with respect to isobaric-spin mixing is investigated for the case of ${\mathrm{Mo}}^{92}(p, p){\mathrm{Mo}}^{92}$, and results are obtained which verify the importance of external mixing for this nucleus. Various limitations of the theory are discussed and further developments are indicated.

• Received 19 August 1964

DOI:https://doi.org/10.1103/PhysRev.137.B535