A three-body model for the analysis of quasi-free 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 by an expansion in terms of $p$-$n$ or $p$-$p$ 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 in order to make this expansion finite and numerically tractable. The proposed formalism is non-relativistic 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 ${}^{12}$C($p$,$2p$), ${}^{12}$C($p$,$pn$) and ${}^{23}$O($p$,$pn$) at $\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.

14 pages, 11 figures, to be published in Phys. Rev. C

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• Determining $B(E1)$ distributions of weakly bound nuclei from breakup cross sections using Continuum Discretized Coupled Channels calculations. Application to ${}^{11}$Be
• Indirect methods in nuclear astrophysics with relativistic radioactive beams
• Nuclear Spectroscopy with Heavy Ion Nucleon Knockout and (p,2p) Reactions
• Toward a reliable description of $(p,pN)$ reactions in the distorted-wave impulse approximation
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• Single-particle spectroscopic strength from nucleon transfer reactions with a three-nucleon force contribution
• Exploring continuum structures in reactions with three-body nuclei
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