1. BigBite 05.2004K.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.

2. BigBite 05.2004K.Egiyan Short Range Correlations - what are they? A typical scale in nuclei is the inter- nucleon distance – r o 1.7fermi. At r r o 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 < r o, creating a new state of nuclear matter, the Short Range Correlations (SRC). 1.7f Nucleons 1.f Nucleus Nucleons Nucleus SRC

3. BigBite 05.2004K.Egiyan SRCs are High Density Matter Nuclear medium is characterized by the average density - ρ o =0.17 GeV/fermi 3. 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. Nucleus Neutron Proton o = 0.17 GeV/fermi 3 4 o

4. BigBite 05.2004K.Egiyan 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. Nucleus Neutron Proton r

5. BigBite 05.2004K.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 Neutron Proton

6. BigBite 05.2004K.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 from light and heavy nuclei, using the unique scaling behavior of the ratios of heavy-to-light nucleus cross sections. Measure yields for 3 He, 4 He, 12 C and 56 Fe targets, and determine the Ratios A(e,e / )/ 3 He for 1<x B <3 and 0.65<Q 2 <2.6 GeV 2 Extract the probabilities of 2- and 3- nucleon SRCs. Measurements at JLab using CLAS.

7. BigBite 05.2004K.Egiyan Why A(e,e), not A(e,eN) or A(e,eNN)? Advantages: Simplicity of measurements, No FSI effect of nucleons. Disadvantage: Hard to select SRCs, But still possible! e e/e/ q Nucleus Nucleons N1N1 N2N2

8. BigBite 05.2004K.Egiyan The CLAS Detector Beam Energy: 2.6 and 4.4 GeV

9. BigBite 05.2004K.Egiyan Main Characteristics of CLAS Detector for Electron Registration Polar angle: Coverage …. 8 o < e < 50 o, 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 …. 10 34 (for hydrogen target).

10. BigBite 05.2004K.Egiyan Experimental Data for Reaction A(e,e / ) in 1<x B <3 Region Cross sections were measured as a function of x B at fixed four momentum transfer Q 2. Shown are spectra for lightest ( 3 He) and heaviest ( 56 Fe) nuclei used. Similar data for 4 He and 12 C. Need to find the domain where SRC contributions are dominant. First focus on 2-nucleon SRC expected in 1<x B <2 range.

11. BigBite 05.2004K.Egiyan The X B - Spectra at 1<x B <2 We should find the domain where SRC contributions are dominant.

12. BigBite 05.2004K.Egiyan Kinematics for SRC in A(e,e / ) Reaction The reaction we are investigating is. In x B > 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. Nucleus e e/e/ q SRC A-1 A e e/e/ A-2 e e/e/ SRC q q A pipi

13. BigBite 05.2004K.Egiyan 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. BigBite 05.2004K.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 x B >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.

15. BigBite 05.2004K.Egiyan Searching of SRC Kinematics in A(e,e / ) Reaction (continue) Frankfurt and Strikman showed that the same ratios should also scale at large x B for fixed Q 2. SRC are expected to be dominant for large x B where the cross section ratios for heavy and light nuclei are Scaled.

16. BigBite 05.2004K.Egiyan Normalized ratios at 1<x B <2 Analyze the ratio K takes into account differences between (e,p) and (e,n) elastic cross sections. In our Q 2 region K=1.14 and 1.18 for 12 C and 56 Fe respectively. Ratios SCALE at Q 2 > 1.4 GeV2 - Scaling vanishes at low Q 2. -Onset of scaling observed at x B >1.5 Similar results are obtained for 12 C and 4 He Results for 56 Fe

17. BigBite 05.2004K.Egiyan Relation between nucleon initial momentum p i and x B for (e,N i ) interaction In A(e,e / ) at x B >1 the p i is unknown. Measuring Q 2 and x B, the minimum value of p i can be obtained (q+p A -p A-1 ) 2 =p f 2 =m N 2 Q 2 -(Q 2 /m N x B )(M A -E min )+2q v p min +2M A E min - =0 =M A 2 +M A-1 2 -m N 2 ; E min =(m N 2 +p min 2 ) 1/2 Events with p i >p min can be rejected by selecting specific x B ranges at fixed Q 2. Deuterium Q 2 =2 GeV 2 pipi -p i A-1 e e/e/ q NfNf NiNi

18. BigBite 05.2004K.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.C93

19. BigBite 05.2004K.Egiyan Ratios at 1.4<Q2<2.6 for 3 Nuclei

20. BigBite 05.2004K.Egiyan 3 Main Observations From These Data Ratios scale at large x B for Q 2 >1.4 GeV 2 and for all nuclei. Onset of scaling is at x B 1.5, which corresponds to p min 0.25 GeV/c. Scaling factors increase with A.

21. BigBite 05.2004K.Egiyan Previous data The first experimental results on ratios of A(e,e / ) cross sections at x B >1 were shown by D. Day at the PANIC Conference, 1987 (Kyoto). Scaling behavior in 1.4 1.2 GeV 2 was observed for 56 Fe/ 4 He. Comparison of the cross section of e-Fe and e- 4 He scattering reported by D.Day (NE-2 SLAC at PANIC 1987 (Kioto)

22. BigBite 05.2004K.Egiyan Previous data New analysis of SLAC data was performed in Phys.Rev. C93. The probabilities of 2-nucleon SRC in 4 He, 27 Al and 56 Fe were estimated from the A(e,e / )/D(e,e / ) ratios. Theoretical calculation were used to obtain data at the same Q 2 and x B for heavy nuclei and D. x B interval limited. New data are needed.

23. BigBite 05.2004K.Egiyan Why A(e,e / )/ 3 He(e,e / ) Ratios Advantages: 3 He was chosen as a base target in CLAS E2 run. Against Deuterium: oNo complications in x B =2 region from elastic (e,D) scattering. oAllows us to investigate 3-nucleon correlations. oStatistics are at least 2 times higher. Against 4 He : oThe wave function is known to extract SRC probabilities. Disadvantages Against Deuterium: oNo direct measurements of 2-nucleon correlations. oMeasured scaling factor is 2 times smaller. Against 4 He : oStatistics are at least 2 times lower. oNo studies of 4-nucleon SRCs. oComplications in x B =3 from elastic (e, 3 He) scattering.

24. BigBite 05.2004K.Egiyan Ratios of probabilities for 2-nucleon SRCs Scaling factors are the ratios of probabilities of 2-nucleon SRC in nucleus A and in 3 He, a 2N (A)/a 2N ( 3 He) = 1.97 ± 0.02 - 4 He 2.51 ± 0.02 - 12 C 3.00 ± 0.03 - 56 Fe The chance for every nucleon in nuclei 4 He; 12 C and 56 Fe to be involved in 2-nucleon SRC is 1.97, 2.51 and 3.0 times higher than in 3 He. This is what we measured directly.

25. BigBite 05.2004K.Egiyan Per-nucleon Probabilities of 2-Nucleon SRCs From measured ratios we can estimate the absolute values of a 2N (A) (=per nucleon probabilities for 2-nucleon SRC in heavy nuclei) if a 2N ( 3 He) is known. The a 2N ( 3 He) can be calculated using the well known wave functions of 3 He and Deuterium. We obtain a 2N ( 3 He)=0.08+0.004 MeasuredCalculated

26. BigBite 05.2004K.Egiyan Calculation of a 2 ( 3 He) parameter Calculations of the ratio of 3 He and Deuterium cross sections in 1<x B <2 region show that a 2N ( 3 He)/ a 2N (D) = 2+0.1. From Deuterium WF we have a 2N (D)=0.04. Therefore, a 2N ( 3 He)=0.08+0.004 0.04

27. BigBite 05.2004K.Egiyan Conclusions on 2-nucleon SRC 1. Cross sections of A(e,e / ) scattering have been measured at x B >1 in identical kinematical conditions for all nuclei. 2. Ratios of cross sections of heavy nuclei to 3 He were analyzed, and it was found that they scale at x B > 1.5 for Q 2 > 1.4 GeV 2. 3. The scaling indicates that for nucleon with high initial momenta, which corresponds to the kinematics of x B >1.5; Q 2 >1.4 GeV 2 : - 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 3 He were obtained. 1.97 ± 0.023 ± 0.01 - 4 He 2.51 ± 0.025 ± 0.14 - 12 C 3.00 ± 0.032 ± 0.17 - 56 Fe 6. These data are published in Phys.Rev. C 68, 014313 (2003).

28. BigBite 05.2004K.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 3 He and Deuterium. 0.15 - 4 He 0.20 - 12 C 0.24 - 56 Fe P.S. At any moment, in 56 Fe nucleus 6-7 2-nucleon SRCs can be found!!

29. BigBite 05.2004K.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

30. BigBite 05.2004K.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 3 He and Deuterium. 0.15 - 4 He - 0.166 NN Config. 0.20 - 12 C - 0.125 6q-Claster (J. Vary et al.) 0.24 - 56 Fe - 0.146

31. BigBite 05.2004K.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 3 He and Deuterium. 0.15 - 4 He - 0.166 NN Config. 0.20 - 12 C - 0.125 6q-Claster (J. Vary et al.) 0.24 - 56 Fe - 0.146 Our Experiment 3 He - 0.134 6q-Claster (J. Vary et al.) 1.97 - 4 He - 1.23 {a 2N (A)/a 2N ( 3 He)} ex 2.51 - 12 C - 0.93 6q-Claster (J. Vary et al.) 3.00 - 56 Fe - 1.09 Big discrepancy, although {a 2N ( 3 He)/a 2N (D)} 6q = 1.94 2.19

32. BigBite 05.2004K.Egiyan