Studying Short range Correlation in Nuclei at the Repulsive Core Limit via the triple Coincidence (e, e’ p N) Reaction PAC 31 / TJNAF Jan. 2007 Proposal.

Studying Short range Correlation in Nuclei at the Repulsive Core Limit via the triple Coincidence (e, e’ p N) Reaction

PAC 31 / TJNAF Jan. 2007

Proposal 07-006

(Next Generation of E01-015)

Hall A / TJNAF

e

e’

p

p or n

2N-Short Range Correlations )2N-SRC(

1.f

Nucleons

2N-SRC

1.7f

o = 0.17 GeV/fm3

5o

1.7 fm

~1 fm

SRC

in nuclei

Dynamics of neutron star formation and structure

Study of cold dense nuclear matter complementary to study of hot dense nuclear matter

Quark vs. hadronic degrees of freedom in nuclei

NN interaction: short range repulsive core and the role played by the tensor force

Why should we care about 2N-SRC ?

Coulomb sum rule

What do we want to know about 2N-SRC ?

•What fraction of the momentum distribution is due to 2N-SRC ?

•What is the relative momentum between the nucleons in the pair?

•What is the ratio of pp to pn pairs?

•Are these nucleons different from free nucleons )e.g size,shape, mass, etc.(?

·What is the pair CM momentum distribution ?

<1 fm

K 1 > KF ,

K 2 > KF

K 1

K 2

K 1 K 2

“Redefine” the problem in momentum space

A pair with “large” relative momentum between the nucleons and small CM

momentum.

Triple – coincidence measurements of large momentum transfer high energy reactions:

p

ppn

EVA / BNL

E01-015 / Jlab

p

e

e*

n

p

e

e*

p

Triple – coincidence measurements:

np-SRC pairs have been observed.

* 2N-SRC dominance

)74-100% are partners in 2N-SRC(.

* np-SRC dominance:

A. Tang Phys. Rev. Lett. 90 ,042301 )2003(

Piasetzky, Sargsian, Frankfurt, Strikman, Watson

PRL 162504(2006).

Removal of a proton with momentum above the Fermi sea level from 12C is 92±8

18 % accompanied by the emission of a neutron with momentum equal and opposite to the missing momentum.

Triple coincidence )p, p pn( measurements at EVA / BNL γ

p

n

Directional correlation

Did not observe pp-SRC. Upper limit of 13% for pp-SRC contribution to protons with momentum above 275 Mev/c in 12C.

Identify pp-SRC pairs in nuclei.

Determined the pp-SRC / np-SRC ratio.

Simultaneously measurements of the )e,e’ p( , )e, e’ p p( )e, e’ p n( reactions.

Determined the abundance of pp-SRC pairs.

E01-015

What did we want to achieve in E01-015 / Jlab ?

Verify the abundance of np-SRC pairs as deteremind by the EVA / BNL experiment.

)e, e’ p p(

)e, e’ p p( / )e, e’ p(

)e, e’ p n( / )e, e’ p(

)e, e’ p p( / )e, e’ p n(

It is important to identify pp-SRC pairs and to determined the pp-SRC/np-SRC ratio since they can tell us about the isospin dependence of the strong interaction at short distance scale.

Kinematics optimized to minimize the competing processes

High energy, Large Q2

MEC are reduced as 1/Q2 .

Large Q2 is required to probe high Pmiss with xB>1.

FSI can treated in Glauber approximation.

xB>1

Reduced contribution from isobar currents.

Large pmiss, and Emiss~p2miss/2M

Large Pmiss_z

E01-105: An Custom Experiment to study 2N-SRC

Q2 = 2 GeV/c , xB ~ 1.2 , Pm=250-650 MeV/c, E2m<140 MeV

Luminosity ~ 1037-38 cm-2s-1

The large Q2 is required to probe the small size SRC configuration.

Kinematics optimized to minimize the competing processes

FSI

Small )10-20%( .

Can treated in Glauber approximation.

Kinematics with a large component of pmiss in the virtual photon direction.

FSI with the A-2 system:

Pauli blocking for the recoil particle.

Geometry, )e, e’p( select periphery.

Canceled in some of the measured ratios.

FSI in the SRC pair:

Conserve the isospin structure of the pair .

Conserve the CM momentum of the pair.

These are not necessary small BUT:

p

e

e’

*n or p

p

Pm =

“30

0”,”

400”

,”50

0” M

eV/c

99 ±50

P =

300

-600

MeV

/c

Ee = 4.627 GeV

Ee’ = 3.724 GeV

Q2=2 (GeV/c)2

qv=1.65 GeV/c

50.40

19.50

40.1 ,35.8 ,32.00

p = 1.45,1.42,1.36 GeV/c

The selected kinematics for the measurement

X=1.245

Experimental setup

HRSHRS

p

e

e

p

Big Bite

n array

EXP 01-015 / Jlab

n

Lead wall

EXP 01-015 Jlab / Hall A Dec. 2004 – Apr. 2005

BigBite SpectrometerNeutron Detector

xB>1

12C(e,e’p)

12C)e,e’p(11B

“300 MeV/c”

“400 MeV/c”

“500 MeV/c”

missp

missp )e,e’∆()e,e’p(

“300 MeV/c”

“400 MeV/c”

“500 MeV/c”

TOF [ns]

Pmis=“300” MeV/c

)Signal : BG= 1.5:1(

Pmis=“400” MeV/c

)Signal : BG= 2.3:1(

Pmis=“500” MeV/c

Pmis=“500” MeV/c

)Signal : BG= 1:7(

)Signal : BG= 4:1(

TOF [ns]

)e,e’pp(

)e,e’pp(

)e,e’pp(

)e,e’pn(

12C(e,e’pp)

γ

Directional correlation

p

p

BG )off peak(

MCEEP Simulation with pair CM motion σCM=136 MeV/c

12C(e,e’pn)

γ

Directional correlation

p

n

MCEEP Simulation with pair CM motion σCM=136 MeV/c

BG )off peak(

CM motion of the pair:

)p,2pn( experiment at BNL : σCM=0.143±0.017 GeV/c

Theoretical prediction )Ciofi and Simula( : σCM=0.139 GeV/c

This experiment : σCM=0.136±0.015 GeV/c

Pc.mverical , “500 MeV/c “ setup

MCEEP with pair CM motion: σCM=50 MeV/c

σCM=100 MeV/c

σCM=136 MeV/c

2 components of and 3 kinematical setupsmcp .

Preliminary

9.5 ± 2 %

107 ±23 %

edextrapolat 12

12

)',(

)',(

peeC

pneeC

edextrapolat 12

12

)',(

)',(

peeC

ppeeC

R. Shneor et al., To be submitted

R. Subedi et al., To prepared

%.%)',(

)',(153

SRC-pp 27

SRCppSRCnppee

ppee

x

x

1-2x

Assuming in 12C nn-SRC = pp-SRC and 2N-SRC=100%

xxxpee

ppee2

221

x

/)()',(

)',(

A virtual photon with xB >1 “sees” all the pp pairs but only 50% of the np pairs.

For 275-600 MeV/c protons in 12C:

pn - SRC 74 – 93 %

4.75 ± 1 %

4.75 ± 1 %

Assuming for 12C nn-SRC = pp-SRC

np-SRC dominance

2N –SRC dominance Notice: 100% is the sum of all the nucleons in this momentum range

80 ± 4.5 % - single particle moving in an average potential.

20 ± 4.5 % - 2N SRC .

18.4 ± 4.5 % - SRC np pairs .

0.95±0.2% - SRC pp pairs.

0.95±0.2 % - SRC nn pairs.

Small ~1% - SRC of “more than 2 nucleons”.

60-70 % - independent particle in a shell model potential.

10-20 % - shell model

long range correlations

Thus, the deduced 12C structure is:

(e,e’)

(e,e’)

(e,e’p)

110070430

events (p,2p) of #

events n)(p,2p of # .

..

F

(p,2pn)

(e,e’pp)

? ~1% -non nucleonic degrees of freedom

or

TOF for the neutrons [ns]

179 ± 39

The (e, e’pn) / (e, e’pp) ratio

116±17

Corrected for detection efficiency:

2.2 8.2 12

12

)',(

)',(

ppeeC

pneeC

2.5 9.1 12

12

)',(

)',(

ppeeC

pneeC

Corrected for SCX )using Glauber(:

In Carbon:

5 18.2 SRCpp

SRCnp

The ratio of pp-SRC / pn-SRC pairs in 12C

)%()%()%.()(/)( 849374

17541212 CPCP pnpp

From the EVA / BNL 12C)p,ppn( data :

%)(/)( 131212 CPCP pnpp

From the combined EVA /BNL12C)p,ppn( and the E01-015 12C)e,e’pp( data:

From the E01-015 12C)e,e’pp( / 12C)e,e’pn( data:

Why ?

% 51551212 )..()(/)( CPCP pnpp

There are 18 ± 2 times more np-SRC than pp-SRC pairs in 12C.

Piasetzky, Sargsian, Frankfurt, Strikman, Watson PRL 162504(2006).

At 300-500 MeV/c there is an excess strength in the np momentum distribution due to the strong correlations induced by underline tensor NN potential.

3He3He

V18 Bonn

np np

pn

pp

pp pp

pp/np

3He

Schiavilla, Wiringa, Piere, Carson, nucl-th /0611037 )2006(.

Sargsian, Abrahamyan, Strikman, Frankfurt PR C71 044615 )2005(.

Proposal 07-006

Measurement of the 4He)e,e’pp( 4He)e,e’pn( reactions over the 4He)e,e’p( missing momentum range from 400 to 875 MeV/c.

)scaled to 4He(E01-105 12 C

This proposal - 4He

Sargsian

LagetPWIA

PWIA

+FSI

+FSI

)e,e’pN( calculations scaled to 4He

Density distribution

Sargsian et al.

Schiavilla et al.

3He

“d”

3He

Shield wall

2” lead+1” iron

Veto counters4 layers of neutron detectors

D)e,e’n(

D)e,e’pn(

The neutron-array

56 Scintillators: 350x25x2.5 mm3

24 3 mm ∆E counters24 30 mm E counters

E01-015

New for PR 07-006

56 350x25x2.5 mm3

scintillaor bars with one PM

56 counters

12 350x2.5x2.5 mm3

Fibers with 2 PMs

Auxilary plan

The Proposed Measurements:

Pmiss [Mev/c]

days )e,e’pp( events

)e,e’pn( events

400 5 110 200

750 5 280 150

500 5 110 200

625 5 235 160

875 5 320 140

Setup, calibrations, checks: 4 days

Total requested beam time: 29 days.

Total number of triple coincidence events ~ 2000

) E01-015 : Total number of triple coincidence events ~ 600 (

Summary

E01-015 Simultaneous measurement of the )e,e’pp(,)e,e’pn(, and )e,e’p( reactions on 12C over the )e,e’p( missing momentum range 300-500 MeV/c.

pp-SRC and np-SRC pairs were identified and their abundances were determined.

Data show sensitivity to the short-range NN tensor force.

PR 07-006 Simultaneous measurement of these reactions on 4He over )e,e’p( missing momentum range of 400-875 MeV/c.

The data is expected to be sensitive to the NN tensor force and the NN short range repulsive force.

The proposed experiment uses the Hall A cryotarget, the two HRSs, BigBite, and an array of neutron counters.

Total beam time request: 29 days

The experiment can be ready to run in 6 month from approval.

l

The end

,32

22

M

QxB

22 4.1 GeVQ

The observed “scaling” means that the electrons probe the high-momentum nucleons in the 2/3-nucleon phase, and the scaling factors determine the per-nucleon probability of the 2/3N-SRC phase in nuclei with A>3 relative to 3He.

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

The probabilities for 3-nucleon SRC are smaller by one order of magnitude relative to the 2N SRC.

New CLAS A)e,e'( Result:

3N-SRC Less than 1% of total

K. Sh. Egiyan et al. PRC 68, 014313.

cMeVM

QxB /,. 275P 51

2 in

2

2N-SRC(np,pp,nn) = 0.20 ± 0.045%

For 12 C:

Frankfurt, Sargsian, and StrikmanTheory:

Why FSI are predicted to be small in the chosen kinematics?

The FSI with the A-2 system

The FSI of the recoil proton with the rest of the nucleus

Suppressed due to Pauli blocking and the geometry of the (e,e’p) reaction.

Pandharipande and Pierper PR C45, 791 )1992(.

The FSI of the fast proton with the rest of the nucleus

The large anti-parallel component of pmiss (>kF) reduce the FSI.

Frankfurt, Sargsian, Strikman PR C56, 1124 )1997(.

The small reduction in the (e,e’pp)/(e,e’p) ratio due to the transparency of the low energy proton is partially compensated by a small increase in the ratio by single charge exchange that can turn pn-SRC pairs into (e,e’pp) events.

The absorptive (imaginary) part of the FSI amplitude does not modify the (e,e’pp)/(e,e’p) ratio.

p

2.4 fm

Simple estimates of the FSI effects, based on a Glauber approximation show that these are small compared to the large errors of the data.

Mardor,Mardor,Piasetzky,Alster, and Sargsian PR C 761 )1992(

The transparency of the low momentum protons is about 0.8. i.e the measured )e,e’pp(/)e,e’p( ratio should be increased by 20%

The same ratio should be decreased by 8-16% due to SCX.

These two, within the errors, compensate each other.

Simple estimates of the FSI effects, based on a Glauber approximation show that these are small compared to the large errors of the data.

Mardor,Mardor,Piasetzky,Alster, and Sargsian PR C 761 )1992(

The data itself indicate that FSI are small.

The extracted pair c.m distribution is a combination of c.m motion and FSI. The fact that we get :

a narrow width )σcm=136 MeV/c(,

similar in the transverse and longitudinal directions,

Same as in previous measurements of the )p,2pn( reaction,

Same as theoretical predications,

indicates that FSI contribution are not dominant.

The node in the pp / np ratio resulted from the NN-SRC

Is not filled by FSI.

dvdlzA

T eff )ˆexp( 1

mbcGeVeff 2651 )/.(

mbcMeVeff 14180 )/(

we adjust the effective cross section to obtain the measured Transparency:

We used the measured effective cross section at 180 MeV/c and the energy dependent of the mean free path as calculated by

Pandharipande and Pieper )Phys. Rev C45)1992(791.(.

dvdlnpdlzcGeVA

T recoileffeff ]ˆ)(exp[]ˆ)/.(exp[ 511

We calculated the conditioned transparency as:

The transparency of the recoil particle in the triple coincidence experiment is higher than that calculated for )e,e’p( since the )e,e’p( already selected an interaction point in the nucleus where the transparency of the )e,e’p( proton is high and therefore the transparency of the recoil proton is also high.

Single Charge Exchange (SCX)

TOTAL

SCXeff

SCXeff cGeV

)/.( 51 mb

mb

TOTAL

SCX

40

11.

Assuming the )e,e’pn( is 5-10 times the magnitude of the )e,e’pp(, the contamination of )e,e’pp( events with contribution from the np correlated pairs is 8-16%.Since the SCX is very forward peaked at these energies we assumed that each proton produced in a SCX process will be considered a correlated partner.

3He

PWIA

PWIA+FSI (only in the pair)

PWIA+FSI

Calculations by M. Sargsian

)unpublished(

The FSI between the two nucleons in the SRC pair

Notice: that the FSI in the SRC pair conserve the CM momentum of the pair and the isospin structure of the pair.

A B

2A Born

2B BA fsi

At the deep:

For pp A~0 2B fsi

For np 2B BA fsi

Since AB is negative FSI contribute more to pp

M. Sargsian )private communication (

Calculations by J. M. Laget

)unpublished(

Calculations by J. M. Laget)unpublished(

Calculations by J. M. Laget)unpublished(