Off- Fermi Shell Protons in the Superdense Nuclear Ma9er

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1 Off- Fermi Shell Protons in the Superdense Nuclear Ma9er & New Vistas in the Dynamics of Neutron Stars Protons in the Nuclear Medium Misak Sargsian Florida Interna-onal University Obergurgle, 24- Feb- 2011

2 q APS DNP invited session 2008 q GRC10 on Photonuclear Reactions q Miami 10 on QCD and Nuclear Physics

3 q How to Probe High Density Fluctuations in Nuclei q What can we Learn about Structure of Super-Dense Nuclear Matter

q How to probe high density fluctuations in nuclei 1. Pr o b e n u c l e o n w i t h l a r g e virtuality 2. Probe large relative momenta n(r)r 2 0.2 0.1 0 0.04 0.02 0 0.01 0.

72 Fm for Deuteron 1 k 2 m 2 +i 1 m( k2 2m + B i) E m k2 2m 100 MeV n(r) = Θ(k p) Ψ d (p) 2 e ip r d 3 p k 300 MeV/c! d (r) 2 r 2 0 0.01 0.005 0 0.004 0.002 0 0.5 1 1.5 2 2.

4 q How to probe high density fluctuations in nuclei 1. Pr o b e n u c l e o n w i t h l a r g e virtuality 2. Probe large relative momenta n(r)r k = 100 MeV/c, r rms = 2.36 Fm k = 200 MeV/c, r rms = 2.21 Fm k = 300 MeV/c, r rms = 1.72 Fm for Deuteron 1 k 2 m 2 +i 1 m( k2 2m + B i) E m k2 2m 100 MeV n(r) = Θ(k p) Ψ d (p) 2 e ip r d 3 p k 300 MeV/c! d (r) 2 r k = 500 MeV/c, r rms = 1.07 Fm k = 700 MeV/c, r rms = 1.65 Fm Probe large missing energies and relahve momenta x

5 q How to probe high density fluctuations in nuclei for A > 3 Probe large inihal momenta of nucleon in the nucleus and large excitahon energy of residual A- 1 nucleus E B k2 2m i=2,..a T i)ψ A = i=2,...a V (k k i )ψ A (k, k i,...k j,...k A ) d3 k i (2π) 3 + i=2,...a V (ki k i )ψ A(k, k i,...k j,...,k A ) d3 k i (2π) 3, If at large k, V NN (k) 1 k n and n>1 in k 2 /2m N E B limit ψ A V NN(k) k 2 f(k 3,...k A ), Frankfurt & Strikman PR 81 where f(k 3,...k A ) is a smooth function of spectator nucleon s momenta with k 2 k.

6 q Probe large initial nucleon momenta and nuclear excitation energy Transferred energy to nuclei Transferred momentum to nuclei >> V NN >> 2k F ermi Frankfurt, MS Strikman IJMP 2010 nk nk Iron p, MeV/c Lead p, MeV/c

7 q Signatures that 2N Short Range Correlations are Probed - nuclear momentum distribu-on in the high momentum tail is similar to that of NN system/deuteron n A, (GeV -3 ) dash-dotted - 16 O dotted - 4 He dashed - 3 He solid - 2 d k, (GeV/c)

V NN (r) V c (r)+v t (r) S 12 (r)+v LS L S S 12 = 3(σ 1 ˆr)(σ 2 ˆr) σ 1 σ 2 S

8 q Signatures that 2N Short Range Correlations are Probed - Nuclear momentum distribution at k>k F should reflect the dynamics of V NN rather than V Nucl V NN (r) V c (r)+v t (r) S 12 (r)+v LS L S S 12 = 3(σ 1 ˆr)(σ 2 ˆr) σ 1 σ 2 S 12 pp =0 S 12 nn =0 S 12 pn =0 S 12 pn =0 Isospin 1 states Isospin 0 states 3 He

9 q Signatures that 2N Short Range Correlations are Probed V nucl (r) = i<j V ij + i,j,k V ijk nk nk Iron p, MeV/c Lead p, MeV/c Any given nucleon feels the average nuclear field in which only total central and some LS part survived And proton and neutron come almost idenhcal in the nuclei

10 q Theory of High Energy and Momentum Transfer Nuclear Reactions I. Momenta involved in the reactions q p f > few GeV/c. e q e p f A new small parameters M A p s Q 2 2 q 2 E mm = 1 2(1+ q 0 2mx ) E mm << 1

11 N N N N N,,.. (c) (a) (b) (d) (a) What we want to study: (b) Should be understood: InteracHon with deeply bound nucleon, relahvishc effects, etc (virtual nucleon, Light Cone approximahon ) Generalized Eikonal ApproximaHon (c) Can be suppressed by choosing (d) Can be suppressed by choosing Q 2 > 1 GeV 2 and by choosing kinemahcs away from the inelashc threshold Generalized Eikonal ApproximaHon

12 q Generalized Eikonal Approximation P D P1 T1 T2 T3 P3 DNN Ps1 Ps 2 P4 Ps O( p f p f+ ) MS, Int. J.Mod.Phys, 2001 P1 T1 T2 T3 P3 P 1 FNN P 3 j P4 P 4 P D P D j DNN Ps DNN P s

13 EffecHve Feinman Rules Frankfurt, Strikman, MS Phys. Re. C 1997 q p +q 1 F... F F F 1 k k+1 n p f MS, Int. J.Mod.Phys, 2001 P A p 1 p 2 p p n+1 p n+2 2 p n+1 P A 1 Ciofi degli A_, Kaptari, 2001 Ciofi degli A_, Kaptari, 2007 p A MS, Abrahamyan, Frankfurt, Strikman Phys. Rev.C 2005 MS, Phys. Rev. C 2010 Resca9erings conserve the light cone momentum frachon of nucleons

14 e + d e + p + n q q N P N f P f P D P D P s P DNN DNN s Ps (a) (b) e + 3 He e + p + p + n 3 He NNN q N P1 P2 P f Pr2 P 3 He P3 + NN Pr 3 P P 3 He 3 He q N P1 3 He NNN + F a NN P 2 P2 P3 q b N FNN P1 P2 P 3 P3 3 He NNN + NN + NN P f P f P P P P r 2 r 3 r 2 r 3 (a) (b) P 3 He P 3 He q F F a b NN NN N P f P1 P2 P 2 P r 2 (a) P 3 P He NN Pr 3 NNN q N P1 3 He NNN P 3 F b NN P2 + F a NN P 3 P 2 + NN P f P r 2 P r 3 (b)

15 e + d e + p + n 4 3 GEA GA 2 p s =400MeV/c (E m =82MeV) p s =400MeV/c p s =100MeV/c (E m =6MeV) p s =200MeV/c (E m =22MeV) p s =200MeV/c pq

16 Recoil-Neutron s Angular Distributions - I P R E L I M I N A R Y Next7years, June 04 K. Egiyan et al, PRL07

17 Recoil-Neutron Angular Distributions; Hall A Exp. Werner Boeglin Luminita Coman, PhD 2007 PRELIMINARY Next7years, June 04 K. Egiyan

18 Back to SRCs Inclusive Scattering Inclusive Sca9ering From the Black Box How Bjorken x becomes a correlahon parameter q What we can learn about BB without detechng it? the Black Box has constituents - the probe knocks-out one of such constituents without breaking it - the remnant of the BB was a spectator to this action

20 Invariant with respect to Lorentz transformahon in z

21 If BB = nucleus CorrelaHon Parameter knocked out constituent is nucleon Momentum Fraction of Nucleus carried by the constituent nucleon For finite Q2

22 signatures for short range correlations at least 2 nucleons are needed at least 3 nucleons are needed at least j+1 nucleons are neede Frankfurt & Strikman PR 88 PredicHon for Scaling if only 2 nucleons then if only 3 nucleons then if only j+1 nucleons then scales scales scales

23 First such analysis was done using different SLAC data sets R = 2 σ ea A σ ed σ ea/d = dσ ea/d de e dω e Day, Frankfurt,MS, Strikman PRC 93

24 More refined experiment at JLAB measured 3 σ ea A σ e 3 He p i 250 MeV/c x Bj > 1.5 Q GeV 2

25 A(e,e / ) 3 C12 /12 He Q 2 =2.5 Q 2 = a) 3 Fe56 /56 He Q 2 =2.5 Q 2 =1.5 X b =Q 2 /2m p 0.5 b) Day, Frankfurt, MS, Strikman, PRC 1993 X b =Q 2 /2m p

26 A(e,e / ) 3 C12 /12 He Q 2 =2.5 Q 2 = a) X b =Q 2 /2m p 3 Fe56 /56 He Q 2 =2.5 Q 2 = b) Egiyan, et al PRC 2004 X b =Q 2 /2m p

27 A(e,e / ) 3 C /12 He Q 2 < a) X b =Q 2 /2M 3 C /12 He Q 2 > b) X b =Q 2 /2M

28 x Bj > 2 3 σ ea A σ e 3 He

29 signatures for short range correlations at least 2 nucleons are needed at least 3 nucleons are needed at least j+1 nucleons are neede PredicHon for Scaling if only 2 nucleons then if only 3 nucleons then if only j+1 nucleons then scales scales scales

30 Egiyan, et al PRL 2006

31 introduce Meaning of the scaling values In the situahon when scaling is established a 2 (A) = σ ea σ ed a 3 (A) = σ ea σ e 3 He where σ ea = dσ ea de e dω e (A Z)σ en +Zσ ep Probability of finding 2N or 3N SRCs relahve to deuteron and helium 3 FracHon of High momentum component of nuclear wave funchon due to 2N SRC P 2N a 2 (A) k F ψ d (p) 2 d 3 p 3N SRC P 3N a 3 (A) ψ3 He(p) 2 d 3 p k 3N

32 P 2N P 3N 3 He He C Fe

33 " high energy inclusive probe at x>1 and large Q2 can detect high density fluctuahons " and measure their probabilihes

34 What are these correlations/fluctuations made of

35 proton proton Brookhaven NaHonal Lab proton neutron

36 Eli Pasetzky TAU A. Tang et al, PRL 2003

37 Brookhaven Experiment A. Tang et al, PRL 2003 Theoretical Analysis Piasetzky, Sargsian, Frankfurt, Strikman, Watson PRL 2007 relative probability of finding pn SRC in the px configuration that contains a proton with

38 " 92% of the Hme two- nucleon high density fluctuahons are proton and neutron " at most 4% of the Hme proton- proton or neutron- neutron

39 proton p and 6n neutron rate 92% calculated upper limit of proton rate 4%

40 electron electron Jeferson Lab Experiment R. Shneor et al. PRL 07 proton neutron/proton

41 Combined Analysis R.Subdei, et al Science, 2008 SRC Pair Fraction (%) pp/np from [ C(e,e pp) / C(e,e pn) ] / pp/2n from [ C(e,e pp) / C(e,e p) ] / np/2n from C(e,e pn) / C(e,e p) np/2n from C(p,2pn) / C(p,2p) pn pp nn Missing Momentum [GeV/c]

42 Combined Analysis R.Subdei, et al Science, 2008

9t Press releases on SRC:! protonsrcfinal.pdf! EVA-SRC-discoverbnl.pdf! Protons Pair Up with Neutrons (from BNL News, pdf)! Science Magazine: Probing Cold Dense Nuclear Matter (pdf)!

Brookhaven National News: Protons Pair Up with Neutrons! Press release from Kent State University! ScienceDaily (Penn State University)! ScienceDaily (Penn State University)! ScientistLive (Penn State University)!

43 9t Press releases on SRC:! protonsrcfinal.pdf! EVA-SRC-discoverbnl.pdf! Protons Pair Up with Neutrons (from BNL News, pdf)! Science Magazine: Probing Cold Dense Nuclear Matter (pdf)! Nature Physics (Research Highlights: Unequal pairs (pdf))! Protons Pair Up With Neutrons, EurekAlert, May 29, 2008! Jefferson Lab in the News: Nuclear Pairs! Brookhaven National News: Protons Pair Up with Neutrons! Press release from Kent State University! ScienceDaily (Penn State University)! ScienceDaily (Penn State University)! ScientistLive (Penn State University)! On Target! Physics Today! (July, 2008) PHYSORG.com! NFC (in hebrew)! Tel Aviv University Press (in hebrew)! (July, 2008) CERN Courier article: "Protons and neutrons certainly prefe each oether's! R&D magazine! company"! The A to Z of Nanotechnology! analitica-world! Matter News! Softpedia! Old Dominion! from h9p://tauphy.tau.ac.il/eip

44 Some Conclusions - We learned to probe directly the short range correlations in nuclei with relative momenta MeV/c" - SRC s are dynamically high-density fluctuations" - Final State Interactions are localized in SRCs" - There is a strong suppression (factor of 20) of pp and nn" SRCs as compared to pn SRCs" " - this disparity is related to the dominance of the " strong tensor force at intermediate to short distances "

45 " Relativism and core of the NN interaction" Dominance of T=0 channel of NN interachon

46 a 2 (A) a 2 (A, Z) a 2 (A, y) y = 1 2x p x p = Z A P 2N (A) P p/n (A, Z) a 2 (A, Z) k F (p/n) ψ NN (p) 2 d 3 p

47 a 2 (A, y) a 2 (ρ,y) y = 1 2x p x p Z A (1) (2) a 2 (A, y) =a sym 2 (A) f(y) For a sym 2 (A) and for other A s use the relahon where ρ 2 A,sym = 1 A we analyze data for symmetric nuclei a sym ρa,sym (r) 2 d 3 r 2 (A) =C ρ 2 A,sym (3) NeglecHng contribuhons due to pp and nn SRCs one obtains boundary condihons f(0) = 1 and f(1) = 0 M. McGauley, MS Feb arxiv

48 World Data on Inclusive A(e,e )X and d(e,e )X Data a 2 = σ A σd with σ A = dσ/de e /dω e Zσ p +(A Z)σ n for x 1.5 and Q 2 1.5GeV 2. we found data for d, 3 He, 4 H 12 C, 27 Al, 56 Fe, 197 Au

49 a 2 (A) f(y) (a) a 2 sym HF A (b) y a sym 2 data for 4 He and 12 C Remaining a sym 2 (A) =C ρ 2 A,sym where ρ 2 sym = 1 A ρ 2 A,sym (r)d 3 r, using ρ A,sym = ρ A,mf + ρ A,SRC and ρ A,SRC ρ A,mf ρ 2 A,sym (r)d3 r ρ 2 A,mf (1 + 2 ρ A,SRC ρ A,mf )d 3 r ρ A,mf (r) 2 d 3 r

50 nk nk Iron p, MeV/c Lead p, MeV/c ρ 2 A,sym (r)d3 r ρ 2 A,mf (1 + 2 ρ A,SRC ρ A,mf ρ A,mf (r) 2 d 3 r )d 3 r

51 a 2 (A) f(y) (a) a 2 sym HF A (b) y a sym (A) =C ρ 2 2 sym 1 ρ 2 A A,mf (r)d 3 r. C = 47.5 ± 2.5 ExtracHng data for f(y) Al 27 y = Fe56 y = Au197 y = He y = f(0) = 1 and f(1) = 0 f(y) =(1 y)(1 0.6y)cor(y)

52 ExtrapolaHon to infinite and superdense nuclear ma9er a 2 (A, y) =a sym 2 (A) f(y) with a sym 2 (A) =C ρ 2 A,sym For the symmetric nuclear matter at saturation densities ρ 0 using: R = r 0 A 1 3 we obtain: ρ 2 INM sym = 1 A and a 2 (ρ 0, 0) 6.8 ± 0.4 ρ 2 A,sym(r)d 3 r = 4π 3 ρ2 0r fm 3 compare a 2 (ρ 0, 0) 8 ± 1.24 C.Ciofi degli A_, E. Pace, G.Salme, PRC 1991

53 Asymmetric and superdense nuclear ma9er a 2 (ρ,y)=ρ 2 INM sym f(y) Consider β equilibrium e p n superdense asymmetric nuclear matter at the threshold of URCA processes x p = 1 9 (y = 7 9 ). At x p < 1 9 the URCA processes n p + e + ν e, p+ e n + ν e will stop in the standard model of superdense nuclear matter consisting of degenerate protons and neutrons.

54 For x p = 1 9 and y = 7 9 and using k F,N =(3π 2 x N ρ) 1 3 P p/n (ρ,y)=a 2 (ρ,y) ψ d (p) 2 d 3 p k f Fractions protons n(k) n(k) neutrons / k, GeV/c k, GeV/c

55 Some ImplicaHon of our Results Cooling of Neutron Star: Large concentration of the protons above the Fermi momentum will allow the condition for Direct URCA processes p p +p e >p n to be satisfied even if x p < 1 9. This will allow a situation in which intensive cooling of the neutron stars will be continued well beyond the critical point x p = 1 9. Superfluidity of Protons in the Neutron Stars: Transition of the protons to the high energy momentum spectrum will smear out the energy gap which will remove the superfluidity condition for the protons. Transition of the protons to the high energy momentum spectrum will smear out the energy gap which will remove the superfluidity condition for the protons. This will result also in significant changes in the mechanism of the generation of the magnetic fields of the neutron stars.

56 Protons in the Neutron Star Cores: Some ImplicaHon of our Results The concentration of the protons in the high momentum tail will result to the proton densities ρ p p 3 p kf,p 3. This will result to the equilibrium conditions with high density of protons that will populate the core rather than the crust of the neutron stars. This situation may provide very different dynamically condition for generation of the magnetic filed of the stars. Isospin Locking and Large Masses of the Neutron Stars With an increase of the densities more and more protons move to the high momentum tail where they are in short range tensor correlations with neutrons. In this case on will expect that high density nuclear matter will be dominated by configurations with quantum numbers of tensor correlations S = 1 and I = 0. In such scenario protons and neutrons at large densities will be locked in the NN isosinglet state. Such situation will double the threshold of inelastic excitation from NN N to NN (NN ) transition thereby stiffening the equation of the state. This situation my explain the observed neutron star masses in Ref.[?] which are in agreement with the calculation of equation state that include only nucleonic degrees of freedom

57 " Transition from hadronic to quark degrees of freedom in high density nuclear matter SRC Pair Fraction (%) pp/np from [ C(e,e pp) / C(e,e pn) ] / pp/2n from [ C(e,e pp) / C(e,e p) ] / np/2n from C(e,e pn) / C(e,e p) np/2n from C(p,2pn) / C(p,2p) for internal momenta up to 600 MeV/c nucleonic degrees freedom are dominant for up to 600 MeV/c Missing Momentum [GeV/c]

Nuclear Short Range Correlations

Nuclear Short Range Correlations Larry Weinstein Old Dominion University What are Correlations? Neutron stars EMC effect Hit the correlated pair Spectator correlated pairs np vs pp pairs Summary Elba Workshop,