Calculation of (K−,π) hypernuclear yields for stopped kaons inC12

Yields of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${\mathrm{K}}^{\mathrm{-}}$, ${\pi }^{\mathrm{-}}$ ${)}_{{\mathrm{}}^1{\mathrm{}}_{\mathrm{\Lambda }}^2}$C and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${\mathrm{K}}^{\mathrm{-}}$,${\pi }^{+}$)${}_{}^1$ ${}_{\Sigma }{}^2{}_{}{}^{}$Be stopped-kaon reactions to 1s and 1p hypernuclear states are studied in detail within the distorted wave impulse approximation, employing realistic ${\mathrm{K}}^{\mathrm{-}}$ atomic wave functions and pion distorted waves. The calculated Λ-hypernuclear yields are weaker than the Σ-hypernuclear yields by more than an order of magnitude, particularly because the outgoing pion wave is strongly damped in the Λ production region due to the proximity to the 3,3 resonance, and are sensitive to within factors of 1.5–3 to the choice of pion optical potential. The largest uncertainty, by as much as a factor of 3.5, is that for the ratio of $2^{+}$ to $0^{+}$ excitations. The calculated Σ-hypernuclear yields, on the other hand, are generally stable, to within 20%, to variations in the input parameters. The results of the calculation are compared with old and new data of stopped-kaon reactions on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and with previous theoretical reports. Yields are also calculated for production of 1$p_{\Lambda }$ states in ${}_{{\mathrm{}}^1{\mathrm{}}_{\mathrm{\Lambda }}^6}{}^{}{}_{}{}^{}\mathrm{O}$ which decay only by proton emission.