6533b85afe1ef96bd12b9409

RESEARCH PRODUCT

Schematic model for narrowΔ(1232)resonances bound in a nucleus

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description

A schematic model explaining the recent evidence for bound states of the $\ensuremath{\Delta}(1232)$ resonance in ${}^{12}\mathrm{C}$ with a width of about 5 MeV found in the ${}^{12}\mathrm{C}{(e,e}^{\ensuremath{'}}p{\ensuremath{\pi}}^{\ensuremath{-}}{)}^{11}{\mathrm{C}}_{\mathrm{g}.\mathrm{s}.}$ is suggested. It interprets the observed narrow resonances as coherent bound states enforcing a fixed phase relation for the rescattering of the decay $\ensuremath{\pi}$'s in the nucleus. The coherent summing of the rescattering diagrams results in a cancellation of the tails of the resonance and a constructive interference in the maximum of the resonance leading to the observed narrow states at the maximum of the $\ensuremath{\Delta}(1232)$ shifted by the binding energy. The same mechanism may contribute to narrow $\ensuremath{\Sigma}$ hypernuclear states and explains their successful and failed observation, respectively.