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

TL;DR

This paper extends the optimal Fermi averaging method to better calculate in-medium reaction amplitudes for near-recoilless ($K^-$, $\pi^-$) reactions on nuclei, achieving good agreement with experimental angular distributions.

Contribution

The authors develop an extended optimal Fermi averaging procedure that incorporates local momentum transfer, improving theoretical predictions of reaction cross sections.

Findings

Extended method accurately reproduces experimental angular distributions.

The approach successfully describes near-recoilless ($K^-$, $\pi^-$) reactions.

Good agreement with data validates the extended framework.

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($K^-$, $\pi^-$)$^{12}_\Lambda$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.