Optimal Fermi-averaging t-matrix for (${\pi }^{+}$,$K^{+}$) reactions in $\Lambda$ quasi-free region

Abstract

We propose an optimal Fermi-averaging for an elementary ${\pi }^{+}$+$n$$\to$$K^{+}$+$\Lambda$ t-matrix under the on-energy-shell condition, in order to describe (${\pi }^{+}$,$K^{+}$) reactions on a nuclear target in the framework of a distorted-wave impulse approximation. We apply it to calculate $\Lambda$ quasi-free spectra from ${}^{12}$C(${\pi }^{+}$,$K^{+}$) reactions at $p_{\pi }$= 1.20 GeV/c and 1.05 GeV/c, and compare them with experimental data. The results show that the calculated spectra are in excellent agreement with the data, because the energy-dependence originates from the nature of the optimal Fermi-averaging t-matrix.

Comments: 10 pages, 3 figures