Some Calculated (p,α) Cross-Sections Using the Alpha Particle Knock-On and Triton Pick-Up Reaction Mechanisms: An Optimisation of the Single-Step Feshbach–Kerman–Koonin (FKK) Theory

The Feshbach–Kerman–Koonin (FKK) multi-step direct (MSD) theory of pre-equilibrium reactions has been used to compute the single-step cross-sections for some (p,α) reactions using the knock-on and pick-up reaction mechanisms at two incident proton energies. For the knock-on mechanism, the reaction was assumed to have taken place by the direct ejection of a preformed alpha cluster in a shell-model state of the target. But the reaction was assumed to have taken place by the pick-up of a preformed triton cluster (also bound in a shell-model state of the target core) by the incident proton for the pick-up mechanism. The Yukawa forms of potential were used for the proton-alpha (for the knock-on process) and proton-triton (for the pick-up process) interaction and several parameter sets for the proton and alpha-particle optical potentials. The calculated cross-sections for both mechanisms gave satisfactory fits to the experimental data. Furthermore, it has been shown that some combinations of the calculated distorted wave Born approximation cross-sections for the two reaction mechanisms in the FKK MSD theory are able to give better fits to the experimental data, especially in terms of range of agreement. In addition, the theory has been observed to be valid over a wider range of energy.