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

Abstract

We investigate theoretically production cross sections of the $J^{\pi }=$ 0${}^{+}$ ground state of a ${}_{\Lambda }^4$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 ${}_{\Lambda }^4$He amount to $d\sigma /d{\Omega }_{\mathrm{lab}}\simeq$ 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.

Comments: 26 page, 8 figures, 4 Tables