Precision Hypernuclear Structure from Interaction Cross Sections

We establish interaction cross sections as a quantitative structural observable for hypernuclei. Using the hypertriton, _{Λ}^{3}H, as the most stringent benchmark, microscopic three-body wave functions are combined with a finite-range coupled-channel Glauber calculation and Bayesian inversion. For _{Λ}^{3}H+^{12}C at 1.5  GeV/nucleon, the interaction cross section decreases from about 1150 to 750 mb as the Λ separation energy B_{Λ} increases from 0.1 to 0.5 MeV, while propagated reaction-model uncertainties remain near 5%. A measurement therefore supplies a direct inversion σ_{I}→r_{m}→B_{Λ}, constraining both the matter radius and the Λ separation energy. The framework provides the missing quantitative link between proposed interaction-cross-section measurements and the spatial structure of an already formed hypernucleus. Although demonstrated for the hypertriton, the methodology is readily extendable to other weakly bound hypernuclei.