Dynamical Origin of Spectroscopic Quenching in Knockout Reactions

Abstract

Nucleon-removal reactions are a primary tool for extracting single-particle structure of rare isotopes, yet the ratio $R_s=σ_{\exp}/σ_{\mathrm{th}}$ 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.

Figures (1)

• Figure 1: (a) Sequential double Feshbach projection: eliminating target excitations ($Q_A$) yields $U^{(\mathrm{nonadd})}_{bxA}$; eliminating excluded projectile configurations ($Q_{bx}$) yields $U^{(\mathrm{pol})}_{bxA}$. (b) $^{6}$Li $+$$^{209}$Bi elastic scattering at $E_{\mathrm{in}}=29.9$ MeV. Data from Ref. Keeley2003; theory from Ref. Watanabe2012. Four-body CDCC (solid red) and three-body CDCC with $U_d^{\mathrm{SF}}$ (dot-dashed purple) reproduce the data. Three-body CDCC with $U_d^{\mathrm{OP}}$ (dotted blue) underestimates the elastic cross section: the $d$-breakup DPP is double counted, producing excess absorption.