Medium effects in ${\Lambda}K^+$ pair production by 2.83 GeV protons on nuclei

We study ${\Lambda}K^+$ pair production in the interaction of protons of 2.83 GeV kinetic energy with C, Cu, Ag, and Au target nuclei in the framework of the nuclear spectral function approach for incoherent primary proton--nucleon and secondary pion--nucleon production processes, and processes associated with the creation of intermediate ${\Sigma^0}K^+$ pairs. The approach accounts for the initial proton and final $\Lambda$ hyperon absorption, final $K^+$ meson distortion in nuclei, target nucleon binding, and Fermi motion, as well as nuclear mean-field potential effects on these processes. We calculate the $\Lambda$ momentum dependence of the absolute ${\Lambda}K^+$ yield from the target nuclei considered, in the kinematical conditions of the ANKE experiment, performed at COSY, within the different scenarios for the $\Lambda$-nucleus effective scalar potential. We show that the above observable is appreciably sensitive to this potential in the low-momentum region. Therefore, direct comparison of the results of our calculations with the data from the ANKE-at-COSY experiment can help to determine the above potential at finite momenta. We also demonstrate that the two-step pion--nucleon production channels dominate in the low-momentum ${\Lambda}K^+$ production in the chosen kinematics and, therefore, they have to be taken into account in the analysis of these data.