# Production of a 4He_Lambda hypernucleus in the 4He(pi, K) reactions reexamined

## TL;DR

This paper theoretically examines the production cross sections of the $^4_\Lambda$He hypernucleus in the $^4$He($\pi$, $K$) reaction, highlighting the sensitivity to wavefunctions and meson distortions, and providing specific cross section estimates.

## Contribution

It reexamines the production of $^4_\Lambda$He hypernucleus using distorted-wave impulse approximation with updated models, emphasizing the effects of wavefunctions and meson distortions.

## Key findings

- Calculated cross section at 1.05 GeV/c is approximately 11 μb/sr.
- Production cross sections are sensitive to $\\Lambda$ wavefunctions and meson distortions.
- Recoil effects and energy dependence significantly influence the results.

## Abstract

We investigate theoretically production cross sections of the $J^\pi=$ 0$^+$ ground state of a $^4_\Lambda$He hypernucleus in the $^4$He($\pi$,~$K$) reaction with a distorted-wave impulse approximation using the optimal Fermi-averaged $\pi N\to K\Lambda$ $t$ matrix. We demonstrate the sensitivity of the production cross sections to the $\Lambda$ wavefunctions obtained from $3N$-$\Lambda$ potentials and to meson distorted waves in eikonal distortions. It is shown that the calculated laboratory cross sections of the 0$^+$ ground state in $^4_\Lambda$He amount to $d\sigma/d\Omega_{\rm lab} \simeq$ 11 $\mu$b/sr at $p_{\pi}=$ 1.05 GeV/$c$ in the $K$ forward direction because of an advantage of the use of the s-shell target nucleus such as $^4$He. The importance of the recoil effects and the energy dependence of the $\pi N\to K\Lambda$ cross sections is also discussed.