1. Sources of information on V  N : Associated production of Σ Strangeness exchange reactions  atoms  N scattering THE ASSOCIATED  PRODUCTION AND THE NUCLEAR INTERACTION OF  HYPERONS J.Dąbrowski & J.Rożynek A.Sołtan Institute fot Nuclear Problems Kazimierz 2006

2. Associated production p  - P  P,   K ,  P K+ θ

4. V P0 = 46 MeV V Pls = 15 MeV R = 3.8 fm adjusted to proton separation energy and to the energies of the p1/2, p3/2, and s1/2 tates determined in (p,2p) and (e,e’) reactioms W  0   P W  0  2.5 MeV

5. A V  0 = -20 MeV B V  0 = 20 MeV C V  0 = 40 MeV D V  0 = 90 MeV E V  0 = 100 MeV [ MeV ] Kaon spectrum from (  -,K = ) on 28 Si at  K =6 o at p  =1.2 GeV/c. Data from P.K.Saha, et al., Phys.Rev.C 70, 044612(2004).

6. Strangeness exchange reaction p  - P K  P, K   ,  P  + θ

7. Π+ spectrum in the (K-,π+) Brookhaven experiments. V Σ (r)=V Σ0 θ(R-r) V Σ0 =20 MeV V Σ0 =10 MeV V Σ0 = - 10/20 MeV R. Sawafta, Nucl. Phys. A585, 103c (1995); S.Bart et al., Phys.Rev.Lrtt. 83, 5238 (1999). JD and J.Rozynek, Acta Phys. Pol. 29B, 2147 (1998).

8. Σ ATOMS Coulomb Coulomb + strong Γ ε Γ Γ

9. Σ Atoms { -(h 2 /2  )  -V C (r)+V  (r)+iW  (r) }  = (E-iΓ/2)  LDA V  (  (r))+iW  (  (r))  –  { -(h 2 /2  )  -V C (r) }  0 = E 0  0 energy shift  = E o - E width    ATOMS  JD, J.Rozynek, G.S.Agnostatos, Eur.Phys.Journ.A 14, 125 (2002).

10. The Nijmegen  N Interaction V  N V  N (models D, F, SC, NSC ) V  N (  ) (effective interaction) Yamamoto et al. Progr.Theor.Phys. Suppl. 117, 241 (1994) LOB V()V() JD Phys.ReV.C 60, 025205 (1992)

11. V 0 for Nijmegen models D,F,SC,NSC JD Nucl.Phys. A691,58c (2001).

12. Summary 1.Our simple analysis of the associated production data suggests that the  s.p. potential U  inside the nuclear core is strongly repulsive ( ~ 100 MeV). * 2.On the other hand a similar analysis of the strangeness exchange data and our analysis of the  atomic data suggests that at nuclear matter densities appearing inside nuclei. U  is less repulsive ( ~ 20 MeV). Astrophysical consequences: stiffer EOS  greater masses of neutron stars