Inverse scattering problem with a bare state

In hadron physics, molecular-like multihadron states can interact with compact multiquark states. The latter are modeled as bare in the Hilbert space of a potential model. this work, we study several models relevant to state, and solve their inverse scattering problems. first model, called ``cc,'' is separable We show that it approximate (single-channel short-range) $S$-wave near-threshold physics an error $\mathcal{O}({\ensuremath{\beta}}^{3}/{M}_{V}^{3})$, where $\ensuremath{\beta}$ sets maximum momentum region ${M}_{V}$ typical scale potential. second ``bc,'' serves bare-state-dominance approximation, interaction between continuum ignored. Under even though state always crucial for bound state's generation, shallow naturally tends have small bare-state proportion. Therefore, need other quantities quantify importance state. last ``bcc,'' combination two models. This model not only correction but also be used understand interplay quark degrees freedom. leads presence Castillejo-Dalitz-Dyson (CDD) zero. consider energy decomposition ratio bare-continuum self-interaction proposed how generated. Model independently, inequality derived. Based on CDD zero estimate ratio. Finally, apply these studies deuteron, $\ensuremath{\rho}$ meson, ${D}_{s0}^{*}(2317)$, analyze properties.