Breakup of a nucleus with two weakly bound neutrons on a proton target: Single-scattering approximation

Three- and four-cluster breakup reactions in the C-16-proton scattering are studied using a three-body core-neutron-neutron model for C-16. Single-scattering approximation (SSA) of four-particle equations for transition operators is used to calculate three-and four-cluster breakup amplitudes at 200 and 300 MeV/nucleon energy near proton-neutron (pn) quasifree scattering (QFS) conditions. The differential cross section is sharply peaked at the pn QFS point and decreases rapidly whenever kinematical conditions deviate from pn QFS. The accuracy of the SSA for the three-cluster breakup is estimated from a three-body model and is found to be as good as 6% at higher reaction energies in suitable angular regimes. Furthermore, under an additional approximation the three-cluster breakup amplitude factorizes into the pn transition operator and the overlap integral of two- and three-particle bound states. That approximation usually reduces the cross section, in some cases even up to 10%. DOI: 10.1103/PhysRevC.87.034609