Factorization of the cross section for the 12C (p,pα)8Be(g.s.) reaction at an incident energy of 100 MeV

Knockout reactions present a direct and convenient method for the study of cluster structure in the ground state of atomic nuclei. In a-cluster knockout by means of projectiles such as energetic protons and ci-particles, distorted-wave impulse approximation (DWIA) theory is able to provide a reasonably good representation of experimental data. However, there arc indications that the reaction process may be viewed as being even simpler than implied by the full DWIA theory. For example, if spin-orbit interactions arc ignored in a (p,pa) reaction, the coincidence cross section may be formulated to display its separate observable quantities as explicit factors. This factorized expression of the coincidence cross section is written as equation in which Ep and Eα are kinetic energies of the light ejectiles, Sα is a spectroscopic factor, Fk is a kinematic factor, a half-shell two-body cross section that describes the scattering of the projectile from the bound α-cluster, and ψ is related to the bound-state wave function. Factorization would also hold if the recoiling heavy residue acts merely as spectator to the collision between the projectile and the cluster. Previous results of Roos at al. [1] for 12C(p,pα)8Be at an incident energy of 100 McV suggest a breakdown of the factorization approximation. In this work on the same target and incident energy, we explore a larger range of two-body scattering angles, which allows a better determination of the general trend. As shown in the figure, the angular distribution of the cross section for the two-body projectile-bound a-cluster system (shown as solid circles), extracted from the coincidence cross section is in remarkable agreement with classic scattering of protons from 4He (solid curve) at the same incident energy. Consequently the factorization approximation is valid to a surprising extent for this knockout reaction. Implications of this result will be discussed.(author)