Theory of K-shell ionization during nuclear resonance scattering

Recently the measured proton-induced C K-shell ionization probability was found to vary significantly near the 0.461-MeV j = 1/2+ elastic resonance in 12C. Since the resonance was so wide that time-delay effects on K-shell ionization should be very small, it was hypothesized that this effect was due to the exchange of angular momentum between the projectile motion and electron. Assuming a potential description of the nuclear scattering, we make a completely quantum-mechanical calculation of the ionization probability in the distorted-wave Born approximation and show that angular momentum effects do not account for these results. We also show how the amplitude for monopole excitation is augmented by the ''shake-off'' or ''sticking'' term found in the semiclassical theory of Ciocchetti and Molinari, and display the formal correspondence between the semiclassical and quantum-mechanical theories. Numerical calculations of the ionization probability show only a slight dip at the minimum in the p-C elastic cross section, opposite in sign and of much smaller magnitude than the reported variation