Extended optimal Fermi averaging for near-recoilless $\Lambda$ production in the ($K^{-}$, ${\pi }^{-}$) reaction on nuclei

Abstract

We propose to extend the optimal Fermi averaging procedure theoretically in order to calculate an in-medium $K^{-}n\to {\pi }^{-}\Lambda$ amplitude for the exothermic ($K^{-}$, ${\pi }^{-}$) reaction on nuclei in the framework of a distorted-wave impulse approximation, taking into account the local momentum transfer generated by semiclassical distorted waves for $K^{-}$ and ${\pi }^{-}$ mesons. Angular distributions for the ${}^{12}$C($K^{-}$, ${\pi }^{-}$)${}_{\Lambda }^{12}$C reaction in which a momentum transfer is $q\lesssim$ 80 MeV/$c$ at $p_K=$ 800 MeV/$c$ in the ${\pi }^{-}$ forward direction, are estimated by applying the extended procedure. The result shows that the calculated angular distributions are in good agreement with those of the data, and this extension is a successful prescription making it possible to describe the reaction cross sections in near-recoilless reactions such as ($K^{-}$, ${\pi }^{-}$) in our framework.

Comments: 18 pages, 6 figures