L. Weinstein, Gordon 2004 1

The Nucleons Went Two By Two: Short Range

Correlations in NucleiLarry WeinsteinOld 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 > kF Calculable for few-body nuclei, nuclear matter. Dominated by two-nucleon short range correlationsPoorly understood part of nuclear structureNN potential models not applicable at p > 350 MeV/c

Uncertainty in SR interaction leads to uncertainty at k>>kf, 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/c25% of nucleons60% of KE

k < 250 MeV/c75% of nucleons40% of KE

p (GeV/c)

n(p

) (G

eV/c

)-3

0.80.2

Two nucleon short range correlations (NN-SRC)

1.7 fm~1.0 fm

0 = 0.16 fm-3

NN-SRC ~ 50

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 StateResponsible for the high momentum part of of the Nuclear WF

Two-body currents are not Correlations

Cor

rela

tion

sC

urre

nts 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) Momentum (1/fm)

Ciofi degli Atti, PRC 53 (1996) 1689

Correlations

p-15Nbreakup

ContinuumContinuum

p-dbreakup CorrM

omen

tum

Den

sity

Correlations are Universal: A(e,e’)

Frankfurt et al, PRC48 2451 (1993)

Egiyan et al., PRL 96, 082501 (2006)

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 SRCx > 2.3: dominated by 3N SRC

Rat

io o

f (e

,e’)

C

ross

sec

tion

s

12C/3He

56Fe/3He

4He/3He

Ratios to 3He (3/A)

21

Q2 > 1.4 GeV2

xB

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

cos

Large neutron momentum p opposite nSmall neutron momentum p isotropicHigh momentum nucleons are paired Tang et al, PRL 90, 042301 (2003)

p

pp

n

12C

Jefferson Lab Site

Hall C

Hall B

Hall A

south linacnorth linac

injector

CLAS

Pmiss = 300, 400, 500 MeV/c

e

e’

*n or p p

P =

300

-600

MeV

/c

Ee = 4.627 GeV

Ee’ = 3.724 GeV

50.40

19.50

40.1 ,35.8 ,32.00p

p ~ 1.4 GeV/c

Knockout the proton, look for its partner nucleon

JLab Hall A C(e,e’pN)Q2 = 2 GeV2

xB = Q2/2m = 1.2Pmiss = 300-600 MeV/c

R. Subedi et al., Science, 2008

9.5 ± 2 % R. Shneor et al.,

PRL 99, 072501 (2007)

Missing momentum [MeV/c]

edextrapolat )',(

)',(12

12

peeC

ppeeC

BNL Experiment

measurement was 92%

+8-18

edextrapolat )',(

)',(12

12

peeC

pneeC96 ± 23 %

Yie

ld R

ati

o [

%]

Yie

ld R

ati

o [

%]

pp/pN = 5%Since the electroncan hit eitherproton

High momentum protons have partners

pn

pp

(proton initial momentum)

3He(e,eX) in JLab CLAS

2.2 and 4.7 GeV electronsInclusive triggerAlmost 4 detector

CLAS Event Display

Sectors 1 and 4

TOFCER

CAL

DC1DC2

DC3

Beamline

CLAS in Maintenance Position

CLAS3He(e,e’p

p)Detect 2 protons,reconstruct the neutron

Huge electron acceptance

<Q2> ~ 0.8

<Q2> ~ 1.8

Select peaksin 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 GeVleading ppn pair

Isotropic!Smallforwardmomentum(describedby theory)

2 GeV

cos(neutron q angle)

2 GeV

pn pair2 GeV

pn pair4.7 GeV

Similar momentum distributions•Relative•Totalpn:pp ratio ~ 4

Results: 2.2 GeV (Q2≈0.8 GeV2)4.7 GeV (Q2≈1.5 GeV2)4.7 GeV scaled by 5.3 4.7 GeV

5.3

2 GeV

Golak 2.2

Golak 4.7 5.3

pn pairs pn pairs

pp pairspp pairs+ =1-Body

Theory (Golak)•Describes 2 GeV OK

•Prel too low•Too low at 4.7 GeV

pp to pn compariso

n

<Q2>(GeV2)

pn to pp ratio

Hall A / BNL

2 / ?? 18

CLAS 1-2 4

Contradiction???

Subedi et al, Science (2008)

Relative

np/2N

pp/2N

12C

BNL Hall A

HALL A Hall A

The s-wave momentum distribution has a minimumThe np minimum is filled in by strong tensor correlations

pn

pp

Ciofi degli Atti, Alvioli;

Schiavilla, Wiringa, Pieper, Carlson

Sargsian, Abrahamyan, Strikman, Frankfurt

3He3He

V18 Bonn

np np

pp pp

Pair relative momentum

3He8Be

Why is np/pp so dominant at prel=300-500 MeV/c?

4000 1000

pp to pn resolution:pp/pn ratio increases with pair total

momentum Ptot

Hall A: small Ptot less ppCLAS: large Ptot more pp

Larger Ptot pp pair wave fn minimum fills in

300 < Prelative < 500 MeV/cTensorCorrelations!

Hall A / BNL

CLAS

Correlations and Neutron Stars

‘Classical’ neutron star: fermi gases of e, p and nLow temperature almost filled fermi spheres limited ability of pn 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 results1. 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 < prel < 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 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??