A self-consistent spectral framework for inclusive non-elastic breakup, with the Trojan Horse method as the sub-Coulomb resonant limit

TL;DR

This paper develops a spectral framework connecting the Trojan Horse Method with the inclusive non-elastic breakup theory in the sub-Coulomb regime, providing a non-perturbative resonance-strength formula.

Contribution

It introduces a diagonal isolated-pole spectral ansatz and derives a resonance-strength formula as a non-perturbative reduction of DWBA cross sections.

Findings

The inclusive cross section reduces to a sum over poles in the isolated-resonance limit.

The resonance-strength formula is derived as a non-perturbative reduction under specific approximations.

The per-pole DWBA cross section is identified as the key quantity for sub-Coulomb resonance analysis.

Abstract

The Trojan Horse Method (THM) extracts low-energy charged-particle resonance strengths through a plane-wave impulse approximation (PWIA) reduction of a three-body transfer matrix element. The Ichimura-Austern-Vincent (IAV) inclusive non-elastic breakup framework has not been brought to the sub-Coulomb astrophysical regime where THM operates. I introduce a diagonal isolated-pole spectral ansatz for the absorptive participant-target optical potential with three explicit validity conditions, two closed by $R$-matrix tabulations and the third a model-dependent continuum-decoupling diagnostic. The IAV inclusive cross section reduces in the isolated-resonance limit to a sum of per-pole distorted-wave Born approximation (DWBA) pole cross sections weighted by channel branching ratios. The factorized PWIA-THM resonance-strength formula is then identified as a non-perturbative reduction of the per-pole DWBA cross section under four approximations (plane-wave substitution on the entrance and exit distorted waves, zero-range or surface-localized treatment of the spectator-participant interaction, on-shell evaluation of the binary subreaction vertex, and post-form remnant neglect), not a multiplicative correction factor. The per-pole DWBA pole cross section is the natural extraction quantity for sub-Coulomb resonance-strength analysis.