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

Abstract

At the keV-scale energies of stellar nucleosynthesis, the resonant charged-particle reactions addressed by the Trojan Horse Method (THM) proceed through isolated near-threshold resonances, so the low-energy cross section and the resonance strength carry the same information, up to a normalization to reference resonances of known strength. Whether the standard THM working formula is accurate there has not been assessed in a controlled framework. I provide a self-consistent framework that computes the sub-Coulomb resonant THM extraction directly from the Ichimura-Austern-Vincent (IAV) inclusive non-elastic breakup cross section. The absorptive participant-target potential is represented by a diagonal isolated-pole spectral ansatz with three explicit validity conditions, two closing as dimensionless bounds from R-matrix tabulations and the third a model-dependent continuum-decoupling diagnostic. In the isolated-resonance limit the inclusive cross section reduces to a per-pole distorted-wave Born approximation (DWBA) cross section on the resonance state, carrying full entrance and exit distortions together with the post-form interaction and weighted by the channel branching ratio; this per-pole cross section is the controlled quantity for resonance-strength extraction. A three-layer Feshbach decomposition fixes the spectral pole half-width as half the non-elastic decay width, equal to half the total width in the sub-Coulomb limit, resolving the width, sign, and partial-width ambiguities of the literature. The standard factorized THM formula follows as a non-perturbative reduction under four explicit approximations, plane-wave entrance and exit waves, surface-localized spectator-participant interaction, on-shell binary amplitude, and post-form remnant neglect, so that its discarded content, the partial-wave coherence and the post-form remnant, is made explicit.