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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

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Strangeness exchange reaction p - P K P, K , P + θ

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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).

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Associated production p - P P, K , P K+ θ

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

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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)

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

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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, (1992)

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

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

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Σ ATOMS Coulomb Coulomb + strong Γ ε Γ Γ

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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).

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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}

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

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V N [MeV] [MeV] u [MeV] 22 Experiment 422 3 (A) HF n, p F D , , u in 208Pb calculated with the indicated densities and N interaction models with the corresponding ² values and the experimental data.

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V N [MeV] [MeV] u [MeV] 22 Experiment 422 3 (A) HF n, p F D (B) V = 0F D , , u in 208Pb calculated with the indicated densities and N interaction models with the corresponding ² values and the experimental data.

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V N [MeV] [MeV] u [MeV] 22 Experiment 422 3 (A) HF n, p F D (B) V = 0F D _ (C) p p = (Z/N) n F D , , u in 208Pb calculated with the indicated densities and N interaction models with the corresponding ² values and the experimental data.

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V N [MeV] [MeV] u [MeV] 22 Experiment 422 3 (A) HF n, p F D (B) V = 0F D _ (C) p p = (Z/N) n F D _ _ _ (D) p ̃ p = p + p F D , , u in 208Pb calculated with the indicated densities and N interaction models with the corresponding ² values and the experimental data.

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HF densities p, n and the modified densities and

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s (A) HF n, p __ (C) p p = Z/N) n __ (D) p ̃ p = p + _ [fm] Mean square radia of charge, proton, and neutron distributions in Pb

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

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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

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HF densities and the modified proton density

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V N [MeV] [MeV] u [MeV] 22 Experiment 422 3 (A) HF n, p F SC , , u in 208Pb calculated with the indicated densities and N interaction models with the corresponding ² values and the experimental data.

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V N [MeV] [MeV] u [MeV] 22 Experiment 422 3 (A) HF n, p F SC (B) V = 0F S.C , , u in 208Pb calculated with the indicated densities and N interaction models with the corresponding ² values and the experimental data.

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V N [MeV] [MeV] u [MeV] 22 Experiment 422 3 (A) HF n, p F SC (B) V = 0F S.C _ (C) p p = (Z/N) n F SC , , u in 208Pb calculated with the indicated densities and N interaction models with the corresponding ² values and the experimental data.

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V N [MeV] [MeV] u [MeV] 22 Experiment 422 3 (A) HF n, p F SC (B) V = 0F S.C _ (C) p p = (Z/N) n F SC _ _ _ (D) p ̃ p = p + p F SC , , u in 208Pb calculated with the indicated densities and N interaction models with the corresponding ² values and the experimental data.

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