L. Weinstein, Gordon 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 Quarks and Nuclear Physics 2009

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

High momentum tails: k > k F Calculable for few-body nuclei, nuclear matter. Dominated by two-nucleon short range correlations 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>>k f, even for simplest systems 3 Short Range Correlations (SRCs) 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. Deuteron Carbon NM k > 250 MeV/c 25% of nucleons 60% of KE k < 250 MeV/c 75% of nucleons 40% of KE p (GeV/c) n(p) (GeV/c)

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

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 Currents Two body currents strongly enhance the effects of correlations MEC IC What are correlations?

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

Correlations are Universal: A(e,e ’ ) Frankfurt et al, PRC (1993) Egiyan et al., PRL 96, (2006) α 2N ≈20% α 3N ≈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 Ratio of (e,e’) Cross sections 12 C/ 3 He 56 Fe/ 3 He 4 He/ 3 He Ratios to 3 He (  3/A) 2 1 Q 2 > 1.4 GeV 2 xBxB

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

12 C(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, (2003) p p p n 12 C 

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

P miss = 300, 400, 500 MeV/c e e’ n or p p P = MeV/c Ee = GeV E e ’ = GeV , 35.8, p p ~ 1.4 GeV/c Knockout the proton, look for its partner nucleon JLab Hall A C(e,e’pN) Q 2 = 2 GeV 2 x B = Q 2 /2m  = 1.2 P miss = MeV/c

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

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

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

CLAS in Maintenance Position

CLAS 3 He(e,e’pp) Detect 2 protons, reconstruct the neutron Huge electron acceptance ~ 0.8 ~ 1.8

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

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

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

pp to pn comparison (GeV 2 ) pn to pp ratio Hall A / BNL 2 / ?? 18 CLAS1-2 4 Contradiction??? Subedi et al, Science (2008) Relative np/2N pp/2N 12 C BNLHall A HALL A Hall A

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

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

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

Summary of results 1.Short Range Correlations (SRC) are universal (same momentum distribution in all nuclei) Probabilities range from 5% (d) to 25% (Fe) 2.Correlated nucleons have their momentum balanced by only one other nucleon When that nucleon is knocked out, its partner is also emitted 3.pn pairs dominate (at 300 < p rel < 500 MeV/c) Tensor correlations At large pair cm momentum, pn and pp pairs are equal 4.We have measured pair relative and total momentum distributions by hitting the third nucleon in 3 He and measuring the spectator correlated pairs Future: extend measurements to larger relative momentum to study central correlations and access higher densities See quark effects??