Parity mixing of elastic scattering resonances: General theory and application toN14

Abstract

We consider the elastic scattering of nucleons from spin ½ targets via parity-mixed resonances and derive expressions for the longitudinal parity nonconserving analyzing power. We neglect any direct parity nonconserving processes—the parity nonconservation being assumed to be due solely to the resonances. We then consider a particularly interesting example—the scattering of protons by ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ over $0^{+}$ and $0^{-}$ $I=1\mathrm{}$ resonances. We show that in this case longitudinal analyzing power measurements yield, with little theoretical uncertainty, the parity nonconserving matrix element between the $0^{+}$ and $0^{-}$ levels. The large width of the $0^{-}\left(2\mathrm{}{s}_{\frac{1}{2}}\right)$ resonance compared to that of the $0^{+}\left(1\mathrm{}{p}_{\frac{1}{2}}\right)$ resonance produces a significant enhancement of the predicted effect. Because of the large size of elastic scattering cross sections a longitudinal analyzing power experiment can achieve small statistical errors. The ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ resonances are especially interesting because the mixing is essentially pure $\Delta I=0\mathrm{}$.