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

TL;DR

This study investigates the breakup reactions of ${}^{16}$C on a proton target at high energies using a three-body model and single-scattering approximation, providing insights into reaction mechanisms and approximation accuracy.

Contribution

It introduces a three-body model combined with single-scattering approximation to analyze ${}^{16}$C breakup reactions at 200 and 300 MeV/nucleon, assessing approximation accuracy.

Findings

SSA accurately predicts three-cluster breakup within 6% at high energies.

Differential cross section peaks sharply at pn quasi-free scattering conditions.

Factorization approximation can underestimate cross sections by up to 10%.

Abstract

Three- and four-cluster breakup reactions in the ${}^{16}$C-proton scattering are studied using three-body core-neutron-neutron model for ${}^{16}$C. 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 ($pn$) quasi free scattering (QFS) conditions. The differential cross section is sharply peaked at $pn$ 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\%.