ar X iv : n uc l - th / 9 90 20 34 v 1 1 5 Fe b 19 99 Submitted to Physical Review C FSU - SCRI - 99 - 07 Relativistic Treatment of Hypernuclear Decay

We compute for the first time the decay width of Λ-hypernuclei in a rela-tivistic mean-field approximation to the Walecka model. Due to the small mass difference between the Λ-hyperon and its decay products—a nucleon and a pion—the mesonic component of the decay is strongly Pauli blocked in the nuclear medium. Thus, the in-medium decay becomes dominated by the non-mesonic, or two-body, component of the decay. For this mode, the Λ-hyperon decays into a nucleon and a spacelike nuclear excitation. In this work we concentrate exclusively on the pion-like modes. By relying on the analytic structure of the nucleon and pion propagators, we express the non-mesonic component of the decay in terms of the spin-longitudinal response function. This response has been constrained from precise quasielastic (p, n) measurements done at LAMPF. We compute the spin-longitudinal response in a relativistic random-phase-approximation model that reproduces accurately the quasielastic data. By doing so, we obtain hypernuclear decay widths that are considerably smaller—by factors of two or three—relative to existing nonrelativistic calculations.