Three-body model for the analysis of quasifree scattering reactions in inverse kinematics

Abstract

A new method to calculate cross sections for $(p,pn)$ and $(p,2p)$ reactions measured under inverse kinematics conditions is proposed. The method uses the prior form of the scattering transition amplitude and replaces the exact three-body wave function appearing in this expression with an expansion in terms of $p\ensuremath{-}n$ or $p\ensuremath{-}p$ states, covering the physically relevant excitation energies and partial waves. A procedure of discretization, similar to that used in continuum-discretized coupled-channels calculations, is applied to make this expansion finite and numerically tractable. The proposed formalism is nonrelativistic, but several relativistic kinematical corrections are applied to extend its applicability to energies of current interest. The underlying optical potentials for the entrance and exit channels are generated microscopically by folding an effective density-dependent $G$ matrix with the density of the composite nucleus. Numerical calculations for $^{12}\mathrm{C}$($p,2p$), $^{12}\mathrm{C}$($p,pn$), and $^{23}\mathrm{O}$($p,pn$) at $\ensuremath{\sim}400$ MeV/nucleon are presented to illustrate the method. The role of final-state interactions and Pauli principle between the outgoing nucleons is also discussed.