Precision Hypernuclear Structure from Interaction Cross Sections

Abstract

We establish interaction cross sections as a quantitative structural observable for hypernuclei. Using the hypertriton, ${}_{\Lambda }^3\mathrm{H}$, as the most stringent benchmark, microscopic three-body wave functions are combined with a finite-range coupled-channel Glauber calculation and Bayesian inversion. For ${}_{\Lambda }^3\mathrm{H}+{}^{12}\mathrm{C}$ at 1.5 GeV/nucleon, the interaction cross section decreases from about 1150 to 750 mb as the $\Lambda$ separation energy $B_{\Lambda }$ increases from 0.1 to 0.5 MeV, while propagated reaction-model uncertainties remain near 5\%. A measurement therefore supplies a direct inversion ${\sigma }_I\to r_m\to B_{\Lambda }$, constraining both the matter radius and the $\Lambda$ 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.

6 pages, 3 figures, supplemental material included. Accepted for publication in Physical Review Letters