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

1
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.

2
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 lt ro, creating a
• new state of nuclear matter, the Short
• Range Correlations (SRC).

Nucleus
1.7f
?
Nucleons
SRC
Nucleus
?1.f
Nucleons
3
SRCs are High Density Matter

• Nuclear medium is characterized by
• the average density - ?o0.17 GeV/fermi3.
• Since typical distances in 2-nucleon
• SRC are 1.0 fermi their density can
• increase by a factor 4 times comparable
• density of the neutron stars.
• SRCs in nuclei allow us to study the
• properties of cold dense matter in the
• laboratories.

Neutron
Proton
? ? 4?o
?o 0.17 GeV/fermi3
Nucleus
4
SRC are the High-momentum Component of Nuclear
Wave Function

• Because of the short distance nature
• of SRCs (r?1f) , 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.

Neutron
Proton
r

Nucleus
5
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.

Neutron
Proton

Nucleus
6
Experimental Program

• The first step must be measurement of
  probabilities to find SRCs in nuclei.
• This information can be obtained in inclusive
  electron scattering from
• light 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 1ltxBlt3 and 0.65ltQ2lt2.6
  GeV2
• Extract the probabilities of 2- and 3- nucleon
  SRCs.
• Measurements at JLab using CLAS.

7
Why A(e,e), not A(e,eN) or A(e,eNN)?
e/
e

• Advantages
• Simplicity of measurements,
• No FSI effect of nucleons.
• Disadvantage
• Hard to select SRCs,
• But still possible!

Nucleons
q
N1
Nucleus
N2
8
The CLAS Detector
Beam Energy 2.6 and 4.4 GeV
9
Main Characteristics of CLAS Detectorfor
Electron Registration

• Polar angle
• Coverage . 8o lt ?e lt 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).

10
Experimental Data for Reaction A(e,e/) in 1ltxBlt3
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 1ltxBlt2 range.

11
The XB - Spectra at 1ltxBlt2
We should find the domain where SRC contributions
are dominant.
12
Kinematics for SRC in A(e,e/) Reaction

• The reaction we are
• investigating is.
• In xB gt 1 region there is only
• one background process with
• larger cross section the
• quasielastic scattering off low-
• momentum and uncorrelated
• nucleons.
• Choose the kinematics where
• this process is suppressed.

e/
e/
e
e
q
q
SRC
A-2
A
Nucleus
SRC

e/
e
q
pi
A-1
A
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Kinematics for SRC in A(e,e/) Reaction (continue)

• For all nuclei the single particle
• configuration in nuclear wave function
• vanishes 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?

14
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 xBgt1
• 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.

15
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.

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Normalized ratios at 1ltxBlt2

• Analyze the ratio
• K takes into account differences between
• (e,p) and (e,n) elastic cross sections. In our
• Q2 region K1.14 and 1.18 for 12C and 56Fe
• respectively.

• Results for 56Fe

• Ratios SCALE at Q2 gt 1.4 GeV2
• - Scaling vanishes at low Q2.
• -Onset of scaling observed at xBgt1.5
• Similar results are obtained for 12C and 4He

17
Relation between nucleon initial momentum piand
xB for (e,Ni) interaction

• In A(e,e/) at xB gt1 the pi is unknown.
• Measuring Q2 and xB, the minimum value
• of pi can be obtained
• (qpA-pA-1)2pf2mN2
• Q2-(Q2/mNxB)(MA-Emin)2qvpmin2MAEmin-?0
• ?MA2MA-12-mN2 Emin(mN2pmin2)1/2
• Events with pi gtpmin can be rejected by selecting
  specific xB ranges at fixed Q2.

Deuterium
Q22 GeV2
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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.C93
19
Ratios at 1.4ltQ2lt2.6 for 3 Nuclei

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3 Main Observations From These Data

• Ratios scale at large xB for Q2gt1.4 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.

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Previous data

• The first experimental results on
• ratios of A(e,e/) cross sections at
• xBgt1 were shown by D. Day at the
• PANIC Conference, 1987 (Kyoto).
• Scaling behavior in 1.4ltxBlt2 range for Q2gt1.2
  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)
22
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.

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

• Advantages
• 3He was chosen as a base target in CLAS E2 run.
• Against Deuterium
• No complications in xB2 region from elastic
  (e,D) scattering.
• Allows us to investigate 3-nucleon correlations.
• Statistics are at least 2 times higher.
• Against 4He
• The wave function is known to extract SRC
  probabilities.
• Disadvantages
• Against Deuterium
• No direct measurements of 2-nucleon correlations.
• Measured scaling factor is 2 times smaller.
• Against 4He
• Statistics are at least 2 times lower.
• No studies of 4-nucleon SRCs.
• Complications in xB3 from elastic (e,3He)
  scattering.

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Ratios of probabilities for 2-nucleon SRCs

• Scaling factors are the ratios of
• probabilities 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 is
• 1.97, 2.51 and 3.0 times higher than
• in 3He.
• This is what we measured directly.

25
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)0.080.004

Measured
Calculated
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Calculation of a2(3He) parameter

• Calculations of the ratio of 3He and Deuterium
  cross sections in 1ltxBlt2 region show that
• a2N(3He)/ a2N(D) 20.1.
• From Deuterium WF we have
• a2N(D)0.04.
• Therefore,
• a2N(3He)0.080.004

0.04
27
Conclusions on 2-nucleon SRC

• 1. Cross sections of A(e,e/) scattering have
  been measured at xBgt1 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 gt 1.5
  for Q2 gt 1.4 GeV2.
• 3. The scaling indicates that for nucleon with
  high initial momenta, which
• corresponds to the kinematics of xBgt1.5
  Q2gt1.4 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).

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Conclusions on 2-nucleon SRC

• 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!!

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SRC gt 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
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Conclusions on 2-nucleon SRC

• 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

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Conclusions on 2-nucleon SRC

• 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

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