ATOMS AND NUCLEON DENSITY DISTRIBUTIONS

1. Sources of information on VN :1.A Strangeness exchange reactions

1.B Associated production of Σ

1.C N scattering

2. Σ atoms and nucleon densities p , n

Strangeness exchange reaction

p-

PK

2P

)(k,

3 )r()r()rqiexp(rddEk̂dk̂d/d

P, K , P+

θ

Kkkq

Π+ spectrum in the (K-,π+) Brookhaven experiments.

VΣ(r)=VΣ0 θ(R-r)

VΣ0=20 MeV

VΣ0=10 MeV

VΣ0= - 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).

Associated production

p-

P

2P

)(k,KK

3 )r()r()rqiexp(rddEk̂dk̂d/d

P, K, PK+

θ

kkq

K

Kaon spectrum from (π-,K+) reaction on 48Si (KEK)

VΣ(r)=VΣ0 θ(R-r)

A: VΣ0 = -- 20 MeV

B: VΣ0 = + 20 MeV

C: VΣ0 = + 40MeV

H.Noumi et al., Phys.Rev.Lett. 89, 072301

JD and J,Rozynek, Aca Phys.Pol. B35,2303 (2004).

The s.p. potential of in nuclear matter.

V(k) = V0(k) + V(k)tTA/A (TA = tN)

LaneLane

V

(k) = V0(k) ½V(k) ( = [N-Z]/A)

Pion spectra from (K-,-) and (K-,) reactions on 9Be

R.Sawafta, Nucl.Phys. A585, 103c (1995).

The Nijmegen N Interaction VN

VN (models D, F, SC, NSC )

VN () (effective interaction)

Yamamoto et al. Progr.Theor.Phys. Suppl. 117, 241 (1994)

LOB

V()

JD Phys.ReV.C 60, 025205 (1992)

V0 for Nijmegen models D,F,SC,NSC

JD Nucl.Phys. A69158c (2001).

V_\tau for Nijmegen -” -

JD Acta Phys.Pol. B36 (2005) – in press

V for Nijmegen models D,F,SC,NSC

Σ ATOMS Coulomb Coulomb + strong

Γε

Γ

Γ

Σ Atoms

 

{-(h2/2) -VC(r)+V (r)+iW (r)} = (E-iΓ/2)

  LDA

V ((r))+iW ((r)) –<kN>

{-(h2/2) -VC(r) }0 = E00

    energy shift = Eo - E width

 

 

 

ATOMS 

 

 

JD, J.Rozynek, G.S.Agnostatos, Eur.Phys.Journ.A 14, 125 (2002).

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}

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

VN [MeV] [MeV] u[MeV] 2

Experiment 42256 428158 173

(A) HF n , p F 24.7 236.6 6.0 65.2

D 448.1 506.7 8.9 7.9

, , u in 208Pb calculated with the indicated densities and N interaction models with the corresponding ² values and the

experimental data.

VN [MeV] [MeV] u[MeV] 2

Experiment 42256 428158 173

(A) HF n , p F 24.7 236.6 6.0 65.2

D 448.1 506.7 8.9 7.9

(B) V = 0 F 349.9 300.2 7.0 13.4

D 762.4 743.6 10.6 45.4

, , u in 208Pb calculated with the indicated densities and N interaction models with the corresponding ² values and the

experimental data.

VN [MeV] [MeV] u[MeV] 2

Experiment 42256 428158 173

(A) HF n , p F 24.7 236.6 6.0 65.2

D 448.1 506.7 8.9 7.9

(B) V = 0 F 349.9 300.2 7.0 13.4

D 762.4 743.6 10.6 45.4

_(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.

VN [MeV] [MeV] u[MeV] 2

Experiment 42256 428158 173

(A) HF n , p F 24.7 236.6 6.0 65.2

D 448.1 506.7 8.9 7.9

(B) V = 0 F 349.9 300.2 7.0 13.4

D 762.4 743.6 10.6 45.4

_(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.

HF densities p,n and the modified densities and p p

~

s(A) HF n , p

__

(C) p p = Z/N)n

5.51 5.45 5.62 0.17

5.68 5.62 5.62 0 __

(D) p ̃p = p + _

5.50 5.44 5..62 0.18

[fm] [fm] [fm] [fm]

ch2

r n2

r

p2r

Mean square radia of charge, proton, and neutron distributions in Pb

α( r ) = [ρp( r )– ρn( r )]/ρ( r ) in 208Pb

(N – Z)/A

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

HF densities and the modified proton density p~

p n ,

VN [MeV] [MeV] u[MeV] 2

Experiment 42256 428158 173

(A) HF n , p F 24.7 236.6 6.0 65.2

SC 250.1 367.7 7.5 19.6

, , u in 208Pb calculated with the indicated densities and N interaction models with the corresponding ² values and the

experimental data.

VN [MeV] [MeV] u[MeV] 2

Experiment 42256 428158 173

(A) HF n , p F 24.7 236.6 6.0 65.2

SC 250.1 367.7 7.5 19.6

(B) V = 0 F 349.9 300.2 7.0 13.4

S.C. 235.5 380.5 7.6 21.0

, , u in 208Pb calculated with the indicated densities and N interaction models with the corresponding ² values and the

experimental data.

VN [MeV] [MeV] u[MeV] 2

Experiment 42256 428158 173

(A) HF n , p F 24.7 236.6 6.0 65.2

SC 250.1 367.7 7.5 19.6

(B) V = 0 F 349.9 300.2 7.0 13.4

S.C. 235.5 380.5 7.6 21.0

_(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.

VN [MeV] [MeV] u[MeV] 2

Experiment 42256 428158 173

(A) HF n , p F 24.7 236.6 6.0 65.2

SC 250.1 367.7 7.5 19.6

(B) V = 0 F 349.9 300.2 7.0 13.4

S.C. 235.5 380.5 7.6 21.0

_(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.