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
L.Elba Weinstein, Workshop, Gordon June 2004 2010 1 Two nucleon short range correlations (NN-SRC) 2N-SRC
ρ ~ 5ρ0
~1.0 fm 1.7 fm
-3 ρ0 = 0.16 fm Studying NN-SRC concerns: • High momentum part of the nuclear wave function • Short distance behavior of nucleons - overlapping?? • EMC Effect • Neutron Stars Short Range Correlations (SRCs)
High momentum tails: k > kF Calculable for few-body nuclei, nuclear matter. Dominated by two-nucleon Deuteron
short range correlations -3 Carbon )
Poorly understood part of NM nuclear structure k > 250 MeV/c GeV/c 25% of nucleons 60% of KE NN potential models not n(p) ( k < 250 MeV/c applicable at p > 350 MeV/c 75% of nucleons 40% of KE Uncertainty in SR interaction 0.2 0.8 p (GeV/c) leads to uncertainty at k>>kf, even for simplest systems
Nucleons are like people … Why are Correlations Interesting?
Responsible for high momentum part of Nuclear WF
Continuum Continuum
p-d p-15N
Momentum Density breakup Corr breakup Correlations
Momentum (1/fm) Momentum (1/fm) Ciofi degli Atti, PRC 53 (1996) 1689 (See also Schiavilla, Van Orden, and many others) 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. (This is already included phenomenologically in the ‘modified Urca process.) L. Frankfurt, PANIC 2008 Correlations are Universal: A(e,e’) Ratio (2/56) Fe/d Ratios to 3He (×3/A)
4 3 Q2=0.9 He/ He
Q2 > 1.4 GeV2
12 3 Q2=1.8 C/ He ) Cross sections ’
56Fe/3He Q2=2.9 Ratio of (e,e
1 2 1 2 xB 2 xB xB=Q /2mω Scaling (flat ratios) indicates a common momentum distribution. α2N ≈20% 1 < x < 1.5: dominated by different mean field n(k) α3N ≈1% 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) EMC Effect Ratio to 3He
and Correlations EMC SRC a2n Ratios to 3He (×3/A) 4He 3 (2-5) 1.9 12C 4 (3-7) 2.5 Not very good agreement But: need to correct for d SRC Ratio to 3He EMC SRC SRC EMC Slope A A d a2n (a2n -a2n ) 4He 3 (2-5) 1.9 2.9 12C 4 (3-7) 2.5 4.0 Fe ??? 3.0 5.1 (see earlier talk by P. Solvignon) EMC Effect and SRC: Another Look The deuteron is not a free np pair Ratios to 3He (×3/A) SRC ratio 3He/d = 2.0 ⇒If the EMC effect is due to SRC then the d EMC slope (relative to a free np pair) should be half of the 3He EMC slope ⇒ d EMC slope = 0.07 ⇒ 3He corrected EMC slope = 0.14 ⇒ add 0.07 to all measured EMC slopes Ratio to 3He EMC Slope EMC SRC Wow! corrected EMC is caused by 4He 2 1.9 SRC! 12C 2.5 2.5
(Warning: large uncertainties) 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 MEC IC strongly enhance the effects of correlations Currents 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 12C(p,ppn) EVA/BNL γ cos p p
γ p 12C
n
Large neutron momentum n opposite pinit Small neutron momentum n isotropic
High momentum nucleons are paired Tang et al, PRL 90, 042301 (2003) Jefferson Lab Site
north linac south linac
injector
Hall C
Hall B CLAS
Hall A Knock out a correlated pair JLab Hall A C(e,e’pN) - selected kinematics P = 300, 400, Q2 = 2 GeV2 miss 2 500 MeV/c xB = Q /2mω = 1.2 Ee’ = 3.724 GeV Pmiss = 300-600 MeV/c e’ Ee = 4.627 GeV 19.50 e 50.40 40.1, 35.8, 32.00 p p ~ 1.4 GeV/c
! * n or p p P = 300-600 MeV/c
Detect the proton, look for its partner nucleon High momentum protons have partners
R. Subedi et al., Science 320, 1476 (2008)
12C(e,e' pn) BNL Experiment +8 Yield Ratio [%] 12 extrapolated C(e,e' p) 96 ± 23 % measurement was 92-18 %
12C(e,e' pp) extrapolated 12C(e,e' p) 9.5 ± 2 % R. Shneor et al., PRL 99, 072501 (2007)
pp/pN = 5% Yield Ratio [%] Since the electron can hit either proton Missing momentum [MeV/c] 3 e2a and e2b He(e,eX) in 2.2 and 4.7 GeV electrons CLAS Inclusive trigger Sectors 1 and 4 CLAS TOF CAL Event CER Display DC3 DC2 DC1 Beamline CLAS in Maintenance Position CLAS 3He(e,e’pp)
Detect 2 protons, reconstruct the
Huge electron acceptance
Proton 2 Kinetic Energy/Omega Mostly pp knockout with a low energy neutron pp knockout dominated by rescattering
90 degree pp opening angle
Rescattering! Energy balance (Dalitz plot): 3He(e,e’pp)n events with spectator neutron 90 But let’s look more closely … pp knockout: a closer look
Two active nucleons:
pneutron< 200 MeV/c
Try to minimize FSI:
1. Two forward protons XB>1 θ(pq) < 35o 2. Slower backward proton o XB<1, θ(pslowq) > 100 Plot vs Prel=(Pfast-q-Pslow)/2 XB>1 pp knockout: o θ<35 correlations? data
Full Avoiding FSI: 1. x<1 and x>1 data completely disagree 1 Body 2. Laget calculation does not describe data 1. Little FSI or MEC XB<1 o predicted θ>100 3. Backward (x<1) data matches calculation better data No obvious sensitivity to the bound state wf 3He(e,e’pp)n: pN > 250 MeV/c Spectator pairs
Pair has back-to-back peak!
Select peaks pn pair in Dalitz plot
Cut on leading nucleon perpendicular momentum I don’t want to get involved: spectator correlated pairs Small Isotropic! forward pn pair momentum 2 GeVGeV (described by theory)
2 GeV pn pair 4.7 GeV
leading p 4.7 GeV pn pair
cos(neutron q angle) Results: 2.2 GeV (Q2≈0.8 GeV2) pn pairs pn pairs 2 2 4.7 GeV (Q ≈1.5 GeV ) 2 GeV
4.7 GeV scaled by 5.3 4.7 GeV ×5.3 Golak 2.2 Similar momentum distributions •Relative Golak 4.7 •Total ×5.3 pn:pp ratio ~ 4
pp pairs pp pairs + =1-Body
Theory (Golak) •Describes 2 GeV OK
•Prel too low •Too low at 4.7 GeV BNL Hall A np/2N pp to pn comparison
pp/2N Subedi et al, Science (2008)
HALL A Hall A 12 C 2 Relative pp to pn (GeV2) ratio Hall A / 2 / ?? 1/18 BNL CLAS 1-2 1/4
Contradiction??? Why is pp/np so small at prel=300-500 MeV/c?
3He→8Be pn The s-wave momentum distribution has a minimum The np minimum is filled in by pp strong tensor correlations
0 400 1000
3 3He He np np pp pp Ciofi degli Atti, Alvioli; V18 Bonn Schiavilla, Wiringa, Pieper, Carlson Sargsian, Abrahamyan, Strikman, Frankfurt Pair relative momentum pp to pn resolution:
pp/pn ratio increases with pair total momentum Ptot
300 < Prelative < 500 MeV/c Tensor 3 He mom dist Correlations! Golak 1-body
data
Hall A / BNL
Small Ptot ⇒ pp pair in s-wave (no tensor) ⇒ wave fn minimum at prel=400 MeV/c
Hall A: small Ptot ⇒ less pp Hall B: large Ptot ⇒ more pp Summary • NN Correlations are universal in nuclei • Dominate the nuclear wave function for p > 0.25 GeV/c • 25% in heavy nuclei • SRC and new EMC Ratios agree • High momentum nucleons are emitted opposite their knocked-out correlated partner • Momentum distributions from two-forward and forward-backward pp pairs strongly disagree • other processes? • which one is sensitive to the initial state? • Two-nucleon correlated pairs are predominantly pn
• The pp/pn ratio increases with increasing ptot • Tensor correlations dominant at 0.3 < prel < 0.5 GeV/c • Measurements at higher relative momentum coming soon … 2N currents enhance correlations Central correlations only Central + tensor corr
12 80 σ σ
1250 σ
360
Em 90 30 0 θpq Corr + MEC O(e,e’p) Ryckebusch kinematics