bigbite 05.2004k.egiyan probabilities of src in nuclei measured with a(e,e / ) reactions k. egiyan...

BigBite 05.2004 K.Egiyan

Probabilities of SRC in Nuclei Measured with A(e,e/) Reactions

K. Egiyan

(Yerevan Physics Institute, Yerevan, Armenia and Jefferson Lab, Newport News VA, USA)

For the CLAS Collaboration

1. Introduction Short Range Correlations and Nuclear Scaling:

2. Experimental Data on: - 2-Nucleon Short Range Correlations, - 3-Nucleon Short Range Correlations.

4. Summary.


Short Range Correlations - what are they?

A typical scale in nuclei is the inter-nucleon distance – ro 1.7fermi.

At r ≥ ro the nuclear processes can be approximately presented as sums of processes on single nucleons.

Due to the quantum fluctuations, 2 or more nucleons may overlap at the smaller distances r < ro, creating a new state of nuclear matter, the Short Range Correlations (SRC).

1.7f

Nucleons

1.f

Nucleus

Nucleons

Nucleus

SRC


SRCs are High Density Matter

Nuclear medium is characterized by the average density - ρo=0.17 GeV/fermi3.

Since typical distances in 2-nucleonSRC are ~1.0 fermi their density can increase by a factor ~4 times comparabledensity of the neutron stars.

SRCs in nuclei allow us to study the properties of cold dense matter in thelaboratories.

Nucleus

NeutronProton

o = 0.17 GeV/fermi3

4o


SRC are the High-momentum Component of Nuclear Wave Function

Because of the short distance nature

of SRCs (r1f) , they contribute to the high

momentum component of the nuclear

Wave Function.

The study of SRCs allows us to probe

the short range properties of Nuclear

Matter.

Nucleus

NeutronProton

r


Are Nucleons Modified in SRC?

Because nucleons in SRC are deeply bounded, they should be modified, e.g., in shape, in quark distributions.

Electron scattering from the nucleons in SRC will probe these modifications. This contributes towards better understanding of nucleon structure.

These studies are one of the main direction of electro-nuclear program at JLab.

Nucleus

NeutronProton


Experimental Program

The first step must be measurement of probabilities to find SRCs in nuclei.

This information can be obtained in inclusive electron scattering fromlight and heavy nuclei, using the unique scaling behavior of the ratios of heavy-to-light nucleus cross sections.

Measure yields for 3He, 4He, 12C and 56Fe targets, and determine the

Ratios A(e,e/)/3He for 1<xB<3 and 0.65<Q2<2.6 GeV2

Extract the probabilities of 2- and 3- nucleon SRCs.

Measurements at JLab using CLAS.


Why A(e,e’), not A(e,e’N) or A(e,e’NN)?

Advantages: Simplicity of measurements,

No FSI effect of nucleons.

Disadvantage: Hard to select SRCs, But still possible!

ee/

q

Nucleus

Nucleons

N1

N2


The CLAS Detector

Beam Energy:2.6 and 4.4 GeV


Main Characteristics of CLAS Detectorfor Electron Registration

Polar angle:

Coverage …. 8o < e < 50o,

Resolution .. 1 mrad.

Azimuthal angle: Coverage ….... 2 (with coil shadows). Resolution .. 4 mrad.

Momentum: Coverage …. ≥ 0.5 GeV/c, Resolution .. p/p 5.10-3.

/e - separation factor: 10-3.

Typical luminosity …. 1034 (for hydrogen target).


Experimental Data for Reaction A(e,e/) in 1<xB<3 Region

Cross sections were measured as a function of xB at fixed four momentum transfer Q2.

Shown are spectra for lightest (3He) and heaviest (56Fe) nuclei used.

Similar data for 4He and 12C.

Need to find the domain where SRC contributions are dominant.

First focus on 2-nucleon SRC expected in 1<xB<2 range.


The XB - Spectra at 1<xB<2

We should find the domain where SRC contributions are dominant.


Kinematics for SRC in A(e,e/) Reaction

The reaction we areinvestigating is.

In xB > 1 region there is only one background process with larger cross section – thequasielastic scattering off low-momentum and uncorrelated nucleons.

Choose the kinematics where this process is suppressed.

Nucleus

ee/

q

SRC

A-1A

ee/

A-2

ee/

SRC

q

q

A

pi


Kinematics for SRC in A(e,e/) Reaction (continue)

For all nuclei the single particle configuration in nuclear wave functionvanishes at high nucleon momentum.

Quasielastic scattering on a single nucleon will not be dominant at high

momenta.

The problem is, how we can identify the high momenum regime in inclusive reaction?


Kinematics for SRC in A(e,e/) Reaction(continue)

At high momenta nucleon momentum distributions are similar in shape for light and heavy nuclei.

The cross sections of A(e,e/) at xB>1 depend primarily on the nuclear wave function, i.e., they should have similar shapes at high momenta for all nuclei.

The cross section ratios for heavy-to-light nuclei should scale at high momenta, where SRC contribution dominate.


Searching of SRC Kinematics in A(e,e/) Reaction(continue)

Frankfurt and Strikman showed that

the same ratios should also scale at

large xB for fixed Q2.

SRC are expected to be dominant

for large xB where the cross section

ratios for heavy and light nuclei are

Scaled.


Normalized ratios at 1<xB<2

Analyze the ratio

K takes into account differences between (e,p) and (e,n) elastic cross sections. In our Q2 region K=1.14 and 1.18 for 12C and 56Fe respectively.

)He,e(A

)A,e()Q(K)He,A(r

3

23 3

Ratios SCALE at Q2 > 1.4 GeV2 - Scaling vanishes at low Q2. -Onset of scaling observed at xB>1.5

Similar results are obtained for 12C and 4He

Results for 56Fe


Relation between nucleon initial momentum pi

and xB for (e,Ni) interaction

In A(e,e/) at xB >1 the pi is unknown. Measuring Q2 and xB, the minimum valueof pi can be obtained

(q+pA-pA-1)2=pf2=mN

2

Q2-(Q2/mNxB)(MA-Emin)+2qvpmin+2MAEmin-=0

=MA2+MA-1

2-mN2 ; Emin=(mN

2+pmin2)1/2

Events with pi >pmin can be rejected by selecting specific xB ranges at fixed Q2.

Deuterium

Q2=2 GeV2

pi

-pi

A-1

ee/

q

Nf

Ni


Final State Interaction in (e,SRC) Scattering

Two FSI in (e,SRC) scattering: NN scattering in SRC, N(A-1) interactions.

FSI are localized in SRC: Lower NN relative momentum in SRC.

Maximum distance, at which the FSI can contribute to the electron

scattering cross section, is small.

Due to the localization in SRC the FSI-effect in the ratio of two nuclei cross sections will cancel!!

FSSD-Phys.Rev.C’93


Ratios at 1.4<Q2<2.6 for 3 Nuclei


3 Main Observations From These Data

Ratios scale at large xB for Q2>1.4 GeV2 and for all nuclei.

Onset of scaling is at xB 1.5, which corresponds to pmin 0.25 GeV/c.

Scaling factors increase with A.


Previous data

The first experimental results on

ratios of A(e,e/) cross sections at

xB>1 were shown by D. Day at the

PANIC Conference, 1987 (Kyoto).

Scaling behavior in 1.4<xB<2 range for Q2>1.2 GeV2 was observed for 56Fe/4He.

Comparison of the cross section of e-Fe and e-4He scattering reported by D.Day (NE-2 SLAC at PANIC 1987 (Kioto)


Previous data

New analysis of SLAC data was performed in Phys.Rev. C93. The probabilities of 2-nucleon SRC in 4He, 27Al and 56Fe were estimated from the A(e,e/)/D(e,e/) ratios.

Theoretical calculation were used to obtain data at the same Q2 and xB for heavy nuclei and D.

xB interval limited.

New data are needed.


Why A(e,e/)/3He(e,e/) Ratios

Advantages: 3He was chosen as a base target in CLAS E2 run.

Against Deuterium:o No complications in xB=2 region from elastic (e,D) scattering.o Allows us to investigate 3-nucleon correlations.o Statistics are at least 2 times higher.

Against 4He : o The wave function is known to extract SRC probabilities.

Disadvantages Against Deuterium:

o No direct measurements of 2-nucleon correlations.o Measured scaling factor is 2 times smaller.

Against 4He : o Statistics are at least 2 times lower.o No studies of 4-nucleon SRCs.o Complications in xB=3 from elastic (e,3He) scattering.


Ratios of probabilities for 2-nucleon SRCs Scaling factors are the ratios ofprobabilities of 2-nucleon SRC in nucleus A and in 3He,

a2N(A)/a2N(3He) = 1.97 ± 0.02 -4He 2.51 ± 0.02 -12C 3.00 ± 0.03 -56Fe

The chance for every nucleon in nuclei 4He; 12C and 56Fe to be involved in 2-nucleon SRC is1.97, 2.51 and 3.0 times higher thanin 3He.

This is what we measured directly.


Per-nucleon Probabilities of 2-Nucleon SRCs

From measured ratios we can estimate the absolute values of a2N(A) (=per nucleon probabilities for 2-nucleon SRC in heavy nuclei) if a2N(3He) is known.

The a2N(3He) can be calculated using the well known wave functions of 3He and Deuterium. We obtain

a2N(3He)=0.08+0.004 Measured Calculated


Calculation of a2(3He) parameter

Calculations of the ratio of 3He and Deuterium cross sections in 1<xB<2 region show that

a2N(3He)/ a2N(D) = 2+0.1.

From Deuterium WF we have

a2N(D)=0.04.

Therefore,

a2N(3He)=0.08+0.004 0.04


Conclusions on 2-nucleon SRC

1. Cross sections of A(e,e/) scattering have been measured at xB>1 in identical kinematical conditions for all nuclei.

2. Ratios of cross sections of heavy nuclei to 3He were analyzed, and it was found that they scale at xB > 1.5 for Q2 > 1.4 GeV2.

3. The scaling indicates that for nucleon with high initial momenta, which corresponds to the kinematics of xB>1.5; Q2>1.4 GeV2: - The momentum distributions in all nuclei are identical in shape, - The (e,SRC) interaction dominate in A(e,e/) scattering.

4. Using the scaling factors the per nucleon probabilities of 2-nucleon SRC in heavy nuclei relative to 3He were obtained.

1.97 ± 0.023 ± 0.01 - 4He 2.51 ± 0.025 ± 0.14 - 12C 3.00 ± 0.032 ± 0.17 - 56Fe

6. These data are published in Phys.Rev. C 68, 014313 (2003).



6. The absolute values of per nucleon probabilities of 2-nucleon SRC

were extracted using the wave functions of 3He and Deuterium.

0.15 - 4He

0.20 - 12C

0.24 - 56Fe

P.S. At any moment, in 56Fe nucleus 6-7 2-nucleon SRCs can be found!!


SRC => NN Configurations or Quark Clusters?

NN Configuration (we used).

Quark Clusters (J. Vary et al.), Theoretical calculations for

almost all nuclei,

(Phys.Rev C. 33, 1062 (1986)).

Nucleus



6. The absolute values of per nucleon probabilities of 2-nucleon SRC were extracted using the wave functions of 3He and Deuterium.

0.15 - 4He - 0.166

NN Config. 0.20 - 12C - 0.125 6q-Claster (J. Vary et al.)

0.24 - 56Fe - 0.146



6. The absolute values of per nucleon probabilities of 2-nucleon SRC were extracted using the wave functions of 3He and Deuterium.

0.15 - 4He - 0.166 NN Config. 0.20 - 12C - 0.125 6q-Claster (J. Vary et al.)

0.24 - 56Fe - 0.146 Our Experiment 3He - 0.134 6q-Claster (J. Vary et al.)

1.97 - 4He - 1.23{a2N(A)/a2N(3He)}ex 2.51 - 12C - 0.93 6q-Claster (J. Vary et al.)

3.00 - 56Fe - 1.09

Big discrepancy, although {a2N(3He)/a2N(D)}6q = 1.94 2.19

bigbite 05.2004k.egiyan probabilities of src in nuclei measured with a(e,e / ) reactions k. egiyan...

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