Dynamical Origin of Spectroscopic Quenching in Knockout Reactions

TL;DR

This paper derives an exact three-body Hamiltonian for knockout reactions, revealing missing induced interactions that explain the observed spectroscopic quenching and its energy dependence.

Contribution

It introduces a precise theoretical framework accounting for induced interactions, clarifying the dynamical origin of spectroscopic quenching in knockout reactions.

Findings

The derived Hamiltonian includes non-additive and polarization terms.

Standard models overestimate cross sections by neglecting these interactions.

Validation with $^{6}$Li data supports the new framework.

Abstract

Nucleon-removal reactions are a primary tool for extracting single-particle structure of rare isotopes, yet the ratio $R_s=\sigma_{\exp}/\sigma_{\mathrm{th}}$ of measured to theoretical cross sections drops systematically below unity for deeply bound nucleons. I derive the exact effective three-body Hamiltonian for composite-projectile reactions using a sequential double Feshbach projection and show that the standard additive model misses two induced interactions: a non-additive term from virtual target excitations and a polarization potential from excluded projectile configurations. Their omission overestimates the stripping cross section, producing apparent quenching distinct from genuine nuclear-structure correlations. This mechanism offers a dynamical origin for the strong separation-energy dependence of the quenching ratio, a feature unique to knockout analyses. Existing four-body CDCC calculations for $^{6}$Li validate the framework: the proper Feshbach reference reproduces elastic scattering data, while a phenomenological optical potential double counts the breakup absorption and fails.