bigbite 05.2004k.egiyan probabilities of src in nuclei measured with a(e,e / ) reactions k. egiyan...
TRANSCRIPT
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.
BigBite 05.2004 K.Egiyan
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
BigBite 05.2004 K.Egiyan
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
BigBite 05.2004 K.Egiyan
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
BigBite 05.2004 K.Egiyan
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
BigBite 05.2004 K.Egiyan
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.
BigBite 05.2004 K.Egiyan
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
BigBite 05.2004 K.Egiyan
The CLAS Detector
Beam Energy:2.6 and 4.4 GeV
BigBite 05.2004 K.Egiyan
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).
BigBite 05.2004 K.Egiyan
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.
BigBite 05.2004 K.Egiyan
The XB - Spectra at 1<xB<2
We should find the domain where SRC contributions are dominant.
BigBite 05.2004 K.Egiyan
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
BigBite 05.2004 K.Egiyan
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?
BigBite 05.2004 K.Egiyan
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.
BigBite 05.2004 K.Egiyan
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.
BigBite 05.2004 K.Egiyan
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
BigBite 05.2004 K.Egiyan
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
BigBite 05.2004 K.Egiyan
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
BigBite 05.2004 K.Egiyan
Ratios at 1.4<Q2<2.6 for 3 Nuclei
BigBite 05.2004 K.Egiyan
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.
BigBite 05.2004 K.Egiyan
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)
BigBite 05.2004 K.Egiyan
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.
BigBite 05.2004 K.Egiyan
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.
BigBite 05.2004 K.Egiyan
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.
BigBite 05.2004 K.Egiyan
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
BigBite 05.2004 K.Egiyan
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
BigBite 05.2004 K.Egiyan
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).
BigBite 05.2004 K.Egiyan
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!!
BigBite 05.2004 K.Egiyan
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
BigBite 05.2004 K.Egiyan
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
BigBite 05.2004 K.Egiyan
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
BigBite 05.2004 K.Egiyan