1.  ATOMS AND NUCLEON DENSITY DISTRIBUTIONS 1. Sources of information on V  N : 1.A Strangeness exchange reactions 1.B Associated production of Σ 1.C  N scattering 2. Σ atoms and nucleon densities  p,  n

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

3. 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).

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

5. Kaon spectrum from (π-,K+) reaction on 48Si (KEK) V Σ (r)=V Σ0 θ(R-r) A: V Σ0 = -- 20 MeV B: V Σ0 = + 20 MeV C: V Σ0 = + 40MeV H.Noumi et al., Phys.Rev.Lett. 89, 072301 JD and J,Rozynek, Aca Phys.Pol. B35,2303 (2004).

6. The s.p. potential of  in nuclear matter. Lane V  (k  ) = V 0 (k  ) + V  (k  )t  T A /A (T A =  t N ) Lane V   (k  ) = V 0 (k  )  ½V  (k  )  (  = [N-Z]/A)

7. Pion spectra from (K-,  -) and (K-,  ) reactions on 9Be R.Sawafta, Nucl.Phys. A585, 103c (1995).

8. 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)

9. V 0 for Nijmegen models D,F,SC,NSC JD Nucl.Phys. A69158c (2001).

10. V_\tau for Nijmegen -” - JD Acta Phys.Pol. B36 (2005) – in press V  for Nijmegen models D,F,SC,NSC

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

12. 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).

13. Σ Pb atoms and nucleon densities  p,  n R.J.Powers et al., Phs.RevC 47, 1263 (1993). JD, J.Rozynek,G.S.Anagnostatos, Eur.Phys.J.A 25, 137 (2005). In  Pb atom: {n = 10, l = 9}  {n = 9, l = 8}

14. , R²,  R² in the circular n=9 Σ orbit in 208Pb

15. V  N  [MeV]  [MeV]  u [MeV] 22 Experiment 422  56 428  158 17  3 (A) HF   n,  p F 24.7 236.6 6.065.2 D 448.1 506.7 8.97.9 , ,  u in 208Pb calculated with the indicated densities and  N interaction models with the corresponding  ² values and the experimental data.

16. V  N  [MeV]  [MeV]  u [MeV] 22 Experiment 422  56 428  158 17  3 (A) HF   n,  p F 24.7 236.6 6.065.2 D 448.1 506.7 8.97.9 (B) V  = 0F 349.9 300.2 7.013.4 D 762.4 743.6 10.645.4 , ,  u in 208Pb calculated with the indicated densities and  N interaction models with the corresponding  ² values and the experimental data.

17. V  N  [MeV]  [MeV]  u [MeV] 22 Experiment 422  56 428  158 17  3 (A) HF   n,  p F 24.7 236.6 6.065.2 D 448.1 506.7 8.97.9 (B) V  = 0F 349.9 300.2 7.013.4 D 762.4 743.6 10.645.4 _ (C)  p   p = (Z/N)  n F 266.6 495.0 15.3 8.2 D 688.2 891.6 19.4 31.9 , ,  u in 208Pb calculated with the indicated densities and  N interaction models with the corresponding  ² values and the experimental data.

18. V  N  [MeV]  [MeV]  u [MeV] 22 Experiment 422  56 428  158 17  3 (A) HF   n,  p F 24.7 236.6 6.065.2 D 448.1 506.7 8.97.9 (B) V  = 0F 349.9 300.2 7.013.4 D 762.4 743.6 10.645.4 _ (C)  p   p = (Z/N)  n F 266.6 495.0 15.3 8.2 D 688.2 891.6 19.4 31.9 _ _ _ (D)  p   ̃ p =  p +   p F 272.7 467.8 15.1 7.6 D 658.2 770.6 18.3 22.7 , ,  u in 208Pb calculated with the indicated densities and  N interaction models with the corresponding  ² values and the experimental data.

19. HF densities  p,  n and the modified densities and

20. s (A) HF   n,  p __ (C)  p   p = Z/N)  n 5.51 5.45 5.62 0.17 5.68 5.62 0 __ (D)  p   ̃ p =  p +  _ 5.50 5.44 5..62 0.18 [fm] Mean square radia of charge, proton, and neutron distributions in Pb

21. α( r ) = [ρ p ( r )– ρ n ( r )]/ρ( r ) in 208Pb (N – Z)/A

22. Summary 1.The analysis of the new strangeness exchange and associated production data indicates that the  s.p. potential V  inside the nuclear core is repulsive. * 2.Among the Nijmegen models of the  interaction only model F leads to a V  repulsive at nuclear matter densities appearing inside nuclei. 3.Assuming that model F is a realistic picture of the  interaction, the analysis of the  atomic data leads to information on  n,  p at the nuclear periphery. Astrophysical consequences: stiffer EOS  greater masses of neutron stars

23. HF densities and the modified proton density

24. V  N  [MeV]  [MeV]  u [MeV] 22 Experiment 422  56 428  158 17  3 (A) HF   n,  p F 24.7 236.6 6.065.2 SC 250.1 367.7 7.519.6 , ,  u in 208Pb calculated with the indicated densities and  N interaction models with the corresponding  ² values and the experimental data.

25. V  N  [MeV]  [MeV]  u [MeV] 22 Experiment 422  56 428  158 17  3 (A) HF   n,  p F 24.7 236.6 6.065.2 SC 250.1 367.7 7.519.6 (B) V  = 0F 349.9 300.2 7.013.4 S.C. 235.5 380.5 7.621.0 , ,  u in 208Pb calculated with the indicated densities and  N interaction models with the corresponding  ² values and the experimental data.

26. V  N  [MeV]  [MeV]  u [MeV] 22 Experiment 422  56 428  158 17  3 (A) HF   n,  p F 24.7 236.6 6.065.2 SC 250.1 367.7 7.519.6 (B) V  = 0F 349.9 300.2 7.013.4 S.C. 235.5 380.5 7.621.0 _ (C)  p   p = (Z/N)  n F 266.6 495.0 15.3 8.2 SC 268.6 626.6 16.6 9.1 , ,  u in 208Pb calculated with the indicated densities and  N interaction models with the corresponding  ² values and the experimental data.

27. V  N  [MeV]  [MeV]  u [MeV] 22 Experiment 422  56 428  158 17  3 (A) HF   n,  p F 24.7 236.6 6.065.2 SC 250.1 367.7 7.519.6 (B) V  = 0F 349.9 300.2 7.013.4 S.C. 235.5 380.5 7.621.0 _ (C)  p   p = (Z/N)  n F 266.6 495.0 15.3 8.2 SC 268.6 626.6 16.6 9.1 _ _ _ (D)  p   ̃ p =  p +   p F 272.7 467.8 15.1 7.6 SC 270.4 582.4 16.2 8.4 , ,  u in 208Pb calculated with the indicated densities and  N interaction models with the corresponding  ² values and the experimental data.