We present our attempts to determine the optical model potential U_Σ = V_Σ -iW_Σ of the Σ hyperon in nuclear matter. We analyze the following sources of information on U_Σ: Σ N scattering, Σ^- atoms, and final state interaction of Σ hyperons in the (π,K^+) and (K^-.π) reactions on nuclear targets. We conclude that V_Σ is repulsive inside the nucleus and has a shallow a tractive pocket at the nuclear surface. These features of V_Σ are consistent with the Nijmegen model F of the hyperon-nucleon interaction.

We calculate in the impulse approximation the kaon spectrum from the $({\ensuremath{\pi}}^{\ensuremath{-}},{K}^{+})$ reaction on $^{28}\mathrm{Si}$. The strength ${V}_{\ensuremath{\Sigma}}$ of the real part of the single particle potential of the $\ensuremath{\Sigma}$ hyperons produced in the reaction is obtained from the Nijmegen model F of the baryon-baryon interaction, and the strength ${W}_{\ensuremath{\Sigma}}$ of the imaginary (absorptive) part is determined by the $\ensuremath{\Sigma}N$ cross sections for the $\ensuremath{\Sigma}\ensuremath{\Lambda}$ conversion and also for the elastic $\ensuremath{\Sigma}N$ scattering (this elastic scattering introduces a strong dependence of ${W}_{\ensuremath{\Sigma}}$ on the $\ensuremath{\Sigma}$ momentum). The momentum dependence of ${V}_{\ensuremath{\Sigma}}$ is also considered. Our calculated inclusive kaon spectrum agrees reasonably with the spectrum measured at KEK. The strengths of the real and absorptive $\ensuremath{\Sigma}$ potentials used in the present calculation are compatible with these strengths determined in the analyses of $\ensuremath{\Sigma}$ atoms and of the strangeness exchange reactions.

We calculate in the impulse approximation the kaon spectrum from the (pi(-), K+) reaction on Si-28. The strength V-Sigma of the real part of the single particle potential of the Sigma hyperons produced in the reaction is obtained from the Nijmegen model F of the baryon-baryon interaction, and the strength W-Sigma of the imaginary (absorptive) part is determined by the Sigma N cross sections for the Sigma Lambda conversion and also for the elastic Sigma N scattering (this elastic scattering introduces a strong dependence of W-Sigma on the Sigma momentum). The momentum dependence of V-Sigma is also considered. Our calculated inclusive kaon spectrum agrees reasonably with the spectrum measured at KEK. The strengths of the real and absorptive Sigma potentials used in the present calculation are compatible with these strengths determined in the analyses of Sigma atoms and of the strangeness exchange reactions.

We calculate in the impulse approximation the kaon spectrum from the (pi(-), K+) reaction on Si-28. The strength V-0 of the real part of the single particle potential of the Sigma hyperons produced in the reaction is treated as a free parameter, and the strength W-0 of the imaginary (absorptive) part is determined by the Sigma N cross sections for the Sigma Lambda conversion and also for the elastic Sigma N scattering (this elastic scattering introduces a strong dependence of W-0 on the Sigma momentum). By fitting to the kaon spectrum measured at KEK, we obtain a repulsive V-0 similar or equal to 40-60 MeV. This result is much closer to previous estimates of V-0 than the results of other analyses of the KEK experiments.

The recently measured kaon spectrum from (π-, K+) reaction on 28 Si target in the region of Σ production is analyzed in impulse approximation for different strengths of the Σ single particle nuclear potential UΣ = VΣ + iWΣ. The comparison with the measured kaon spectrum leads to the conclusion that the potential VΣ inside the nuclear core is strongly repulsive. A comparison with other estimates of the strength of VΣ is presented.

The analyses of the strangeness exchange (K-,pi) and the associated production (pi(-),K+) reactions are presented. They indicate - together with the observed properties of Sigma atoms - that the Sigma single particle potential V-Sigma is repulsive inside nuclei and has a shallow attractive pocket at the nuclear surface. This conclusion is consistent with the Nijmegen model F of the hyperon-nucleon interaction. It is demonstrated how the strong-interaction shifts and widths measured in Sigma atoms may be used to obtain information on the nucleon density distributions.

It is shown that the measured cross section for the Σ production reactions, the observed properties of Σ atoms, and the two-body hyperon-nucleon data indicate that the ΣN interaction is well represented by the Nijmegen model F of the hyperon-nucleon interaction. It is demonstrated how the strong-interaction shifts and widths measured in Σ- Pb atoms may be used to obtain information on the nucleon density distributions in Pb .

The previously derived expressions for the real part of the single particle potential of a Sigma hyperon in nuclear matter, V-Sigma, are applied to investigate the dependence of V-Sigma on the nuclear matter density and Sigma momentum. Results for V-Sigma, in particular its isospin, spin, and spin-isospin dependent parts, obtained for four models of the Nijmegen baryon-baryon interaction are presented and discussed.

. The analyses of ( K - ,π) and (π - , K + ) reactions indicate that the nuclear potential of the Σ-hyperon is repulsive inside the nucleus, in agreement with the prediction of model F of the Nijmegen baryon-baryon interaction. This is consistent with the recent calculation of the strong-interaction shifts and widths of the observed levels of Σ - atoms, including the precise data on the Σ - Pb atom. In this paper, the sensitivity of this calculation to the neutron and proton density distributions is used to determine these densities in 208 Pb.

A simple theory of the interaction potential between heavy ions V, based on the local density approach and the frozen density model, is presented for nuclei with neutron excess. The energy density needed for calculating V is expressed in a simple way through the known properties of nuclear matter.

It is shown that among four models of the Nijmegen baryon-baryon interaction only model F -which leads to a repulsive potential felt by the Sigma hyperon inside the nucleus-is consistent both with the analysis of Sigma(-) atoms and of the (K-, pi) reactions. The Nijmegen models are used to determine the strong complex single-particle (s.p.) potential of Sigma(-). and to calculate the strong-interaction shifts and widths of the lowest observed levels of Sigma(-) atoms. The results obtained with model F are in best agreement with the experimental data.