Factorization in quasifree breakup reactions with two bodies left behind
Phys. Rev. C 114, 044616 – Published 14 October, 2026
DOI: https://doi.org/10.1103/8tl3-5vgm
Abstract
We consider scenarios in which a shallow bound state undergoes breakup by a probe whose energy is high compared to the binding energy. The first two scenarios, which serve as warm-up exercises, involve a single heavy particle bound to a light particle, analogous to a core nucleus bound to a neutron. We show that in quasifree kinematics, the leading effect comes from the heavy particle being knocked out by the probe, with corrections suppressed by inverse powers of the probe momentum. This formally justifies extracting neutron form factors from high-energy deuteron breakup in quasifree kinematics. In scenario 1, the probe is a local current; in scenario 2, it is hadron scattering. In scenarios 3 and 4 we consider, respectively, a local current and hadron scattering, but now on a three-body bound state of a heavy particle and two light particles. Hard knockout of the heavy particle leaves two low-energy particles behind, which can interact with one another. In all four scenarios, we prove that the amplitude is dominated by the nearby on-shell pole of the heavy-particle propagator and derive a closed-form expression for this contribution. When two bodies are left behind, the leading amplitude is the product of the scattering of the two light particles, a dynamical function depending on the probe, and a real function related to the bound-state wave function. Thus, quasifree removal of a core nucleus from a system with halo neutrons provides access to on-shell data on multineutron interactions. The resulting amplitudes are relativistic and satisfy unitarity for the remnant subsystem exactly. We also provide complementary nonrelativistic derivations. While the derivations are for spinless particles, the generalization to spin is straightforward, since the results depend only on quasifree knockout kinematics; we make no assumptions about the interparticle dynamics.
