The Nucleons Went Two By Two: Short Range Correlations in Nuclei

1. The Nucleons Went Two By Two: Short Range Correlations in Nuclei Larry Weinstein Old Dominion University • Theory Overview • What are Correlations? • How big are they? • np vs pp pairs • Summary L. Weinstein, Gordon 2004 Quarks and Nuclear Physics 2009

2. Comprehensive Theory Overview Nuclear Theory - circa 2000 Nuclear Theory - today: 1, 2, 3, … 12, … many

3. k > 250 MeV/c 25% of nucleons 60% of KE Deuteron Carbon k < 250 MeV/c 75% of nucleons 40% of KE NM n(p) (GeV/c)-3 0.2 0.8 p (GeV/c) High momentum tails: k > kF Calculable for few-body nuclei, nuclear matter. Dominated by two-nucleon short range correlations Short Range Correlations (SRCs) Poorly understood part of nuclear structure NN potential models not applicable at p > 350 MeV/c Uncertainty in SR interaction leads to uncertainty at k>>kf, even for simplest systems Looking for quarks in the nucleus is like looking for the mafia in Sicily. Everyone knows they are there, but evidence is hard to find. 3

4. Two nucleon short range correlations (NN-SRC) NN-SRC  ~ 50 ~1.0 fm 1.7 fm 0 = 0.16 fm-3 • Studying NN-SRC concerns: • High momentum part of the nuclear wave function • Short distance behavior of nucleons - overlapping?? • Cold dense nuclear matter • Neutron Stars

5. What are correlations? Average Two Nucleon Properties in the Nuclear Ground State Responsible for the high momentum part of of the Nuclear WF Two-body currents are not Correlations Correlations Two body currents strongly enhance the effects of correlations MEC IC Currents

6. Why are Correlations Interesting? Responsible for high momentum part of Nuclear WF Momentum Density Continuum Continuum p-15N breakup p-d breakup Correlations Corr Momentum (1/fm) Momentum (1/fm) Ciofi degli Atti, PRC 53 (1996) 1689

7. Ratios to 3He (3/A) 4He/3He Q2 > 1.4 GeV2 12C/3He Ratio of (e,e’) Cross sections 56Fe/3He 2 1 Correlations are Universal: A(e,e’) xB α2N ≈20% α3N ≈1% Scaling (flat ratios) indicates a common momentum distribution. 1 < x < 1.5: dominated by different mean field n(k) 1.5 < x < 2: dominated by 2N SRC x > 2.3: dominated by 3N SRC Frankfurt et al, PRC48 2451 (1993) Egiyan et al., PRL 96, 082501 (2006)

8. What are Correlations? Average Two Nucleon Properties in the Nuclear Ground State Not Two-Body Currents An Experimentalist’s Definition: • A high momentum nucleon whose momentum is balanced by one other nucleon • NN Pair with • Large Relative Momentum • Small Total Momentum • Whatever a theorist says it is

9.  12C p p p n 12C(p,ppn) EVA/BNL cos Large neutron momentum p opposite n Small neutron momentum p isotropic High momentum nucleons are paired Tang et al, PRL 90, 042301 (2003)

10. south linac north linac injector Hall C Hall B CLAS Hall A Jefferson Lab Site

11. Knockout the proton, look for its partner nucleonJLab Hall A C(e,e’pN) Pmiss = 300, 400, 500 MeV/c Q2 = 2 GeV2 xB = Q2/2m = 1.2 Pmiss = 300-600 MeV/c Ee’ = 3.724 GeV e’ Ee = 4.627 GeV 19.50 e 50.40 40.1, 35.8, 32.00 pp ~ 1.4 GeV/c P = 300-600 MeV/c n or p p

12. High momentum protons have partners +8 -18 pn R. Subedi et al., Science, 2008 Yield Ratio [%] 96 ± 23 % BNL Experiment measurement was 92 % 9.5 ± 2 % R. Shneor et al., PRL 99, 072501 (2007) Yield Ratio [%] pp/pN = 5% Since the electron can hit either proton pp Missing momentum [MeV/c] (proton initial momentum)

13. 2.2 and 4.7 GeV electrons Inclusive trigger Almost 4 detector 3He(e,eX) in JLab CLAS

14. TOF CAL CER DC3 DC2 DC1 Sectors 1 and 4 CLAS Event Display Beamline

15. CLAS in Maintenance Position

16. CLAS3He(e,e’pp) Detect 2 protons, reconstruct the neutron <Q2> ~ 0.8 Huge electron acceptance <Q2> ~ 1.8

17. 3He(e,e’pp)n nucleon energy balance: p > 250 MeV/c Pair has back-to-back peak! pn pair Select peaks in Dalitz plot Cut on leading nucleon perpendicular momentum

18. I don’t want to get involved:spectator correlated pairs Small forward momentum (described by theory) Isotropic! pn pair 2 GeV 2 GeV 2 GeV pn pair 4.7 GeV leading p pn pair 4.7 GeV cos(neutron q angle)

19. pn pairs pn pairs 2 GeV 4.7 GeV 5.3 Golak 2.2 + =1-Body Golak 4.7 5.3 pp pairs pp pairs Results: 2.2 GeV (Q2≈0.8 GeV2)4.7 GeV (Q2≈1.5 GeV2) 4.7 GeV scaled by 5.3 • Similar momentum distributions • Relative • Total • pn:pp ratio ~ 4 • Theory (Golak) • Describes 2 GeV OK • Prel too low • Too low at 4.7 GeV

20. BNL Hall A pp to pn comparison np/2N pp/2N Subedi et al, Science (2008) HALL A Hall A 12C Relative Contradiction???

21. Why is np/pp so dominant at prel=300-500 MeV/c? 3He 3He np np pp pp V18 Bonn Pair relative momentum 3He8Be pn The s-wave momentum distribution has a minimum The np minimum is filled in by strong tensor correlations pp 0 400 1000 Ciofi degli Atti, Alvioli; Schiavilla, Wiringa, Pieper, Carlson Sargsian, Abrahamyan, Strikman, Frankfurt

22. pp to pn resolution: pp/pn ratio increases with pair total momentum Ptot 300 < Prelative < 500 MeV/c Tensor Correlations! CLAS Hall A / BNL Larger Ptot pp pair wave fn minimum fills in Hall A: small Ptot less pp CLAS: large Ptot  more pp

23. Correlations and Neutron Stars ‘Classical’ neutron star: fermi gases of e, p and n Low temperature  almost filled fermi spheres  limited ability of pn decays (Urca process) Correlations  high momentum tail and holes in the fermi spheres Why does this matter? Cooling should be dominated by the Urca process: Correlations-caused holes in the proton fermi sphere should enhance this process by large factors and speed neutron star cooling. L. Frankfurt, PANIC 2008

24. Summary of results • Short Range Correlations (SRC) are universal (same momentum distribution in all nuclei) • Probabilities range from 5% (d) to 25% (Fe) • Correlated nucleons have their momentum balanced by only one other nucleon • When that nucleon is knocked out, its partner is also emitted • pn pairs dominate (at 300 < prel < 500 MeV/c) • Tensor correlations • At large pair cm momentum, pn and pp pairs are equal • We have measured pair relative and total momentum distributions by hitting the third nucleon in 3He and measuring the spectator correlated pairs Future: extend measurements to larger relative momentum to study central correlations and access higher densities See quark effects??