1. JLab_Phys_Semin_Dec05 K. Egiyan Today’s Nucleonic Picture of Nuclei Kim Egiyan Yerevan Physics Institute, Armenia and Jefferson Lab, USA

2. JLab_Phys_Semin_Dec05 K. Egiyan Hofstadter's nucleonic picture of nucleus  Single particles (SP) moving in an average field  Electron elastic scattering off nuclei have been measured and nuclear radii R were obtained  It was shown that R  A 1/3  This was strong evidence that nuclei are composed from the SP, in other words, they are a bags with Fermi gas!! Nucleus e e/e/ q (low)

3. JLab_Phys_Semin_Dec05 K. Egiyan Other possible components  HOWEVER  Strong NN (attractive and repulsive) interaction should result in Short Range Correlation (SRC) 1.7f Nucleons Nucleus   o = 0.17

4. JLab_Phys_Semin_Dec05 K. Egiyan Other possible components  HOWEVER  Strong NN (attractive and repulsive) interaction should result in Short Range Correlation (SRC) 1.7f Nucleons Nucleus   o = 0.17

5. JLab_Phys_Semin_Dec05 K. Egiyan Other possible components  HOWEVER  Strong NN (attractive and repulsive) interaction should result in Short Range Correlation (SRC)  So, nuclear Hamiltonian should include H = p 2 /2M + V 2 (r 1,r 2 ) + V 3 (r 1,r 2,r 3 ) + …. the correlation terms V i 1.7f Nucleons Nucleus   o = 0.17

6. JLab_Phys_Semin_Dec05 K. Egiyan Main problems  Strong NN (attractive and repulsive) interaction should result in Short Range Correlation (SRC)  Experimental problems should be addressed are:  Relative fractions of SP and SRC phases  Modification of nucleons in SRC  Properties of super-dens matter in SRC 1.7f Nucleons Nucleus   1f  o = 0.17   4  o

7. JLab_Phys_Semin_Dec05 K. Egiyan Main topic of talk  Strong NN (attractive and repulsive) interaction results in Short Range Correlation (SRC)  Problems should be addressed are:  Relative fractions of SP and SRC phases  Modification of nucleons in SRC  Properties of super-dens matter in SRC  In this talk the only first topic will be discussed : Fractions of SP and SRC phases in nuclei 1.7f Nucleons Nucleus   1f  o = 0.17   4  o

8. JLab_Phys_Semin_Dec05 K. Egiyan Main topic of talk  Strong NN (attractive and repulsive) interaction results in Short Range Correlation (SRC)  Problems should be addressed are:  Relative fractions of SP and SRC phases  Modification of nucleons in SRC  Properties of super-dens matter in SRC  In this talk the only first topic will be discussed : Fractions of SP and SRC phases in nuclei  What we know about SP and SRC? 1.7f Nucleus   1f

9. JLab_Phys_Semin_Dec05 K. Egiyan 1. Evidence for NON-single particle states - Spectroscopic factor  In first generation of A(e,e’p)A-1 measurements the S(E i,p i ) – spectral function – the probability a finding nucleon in nuclei with momentum p i and removal energy E i has been extracted Nucleus e e/e/ q p pipi

10. JLab_Phys_Semin_Dec05 K. Egiyan 1. Evidence for NON-single particle states - Spectroscopic factor  In first generation of A(e,e’p)A-1 measurements the S(E i,p i ) – spectral function – the probability a finding nucleon in nuclei with momentum p i and removal energy E i has been extracted  It was found that integral (Spectroscopic factor)  SP fractions is ≠ 1  Is SRC fraction  30%??  Measured results depend on integration limits  SRC contribution is not excluded (estimated)  FSI can affect on results  These results are impotent: they show the expected size of SRC contribution (10-20-30%) Nucleus Z ≡ 4  ∫ S(E i,p i )dE i dp i ≠ 1 (  0.7) e e/e/ q p ε F,p F pipi Z

11. JLab_Phys_Semin_Dec05 K. Egiyan What is needed?  In first generation of A(e,e’p)A-1 measurements the S(E i,p i ) – spectral function – the probability a finding nucleon in nuclei with momentum p i and removal energy E i has been extracted  It was found that integral (Spectroscopic factor)  SP fractions is ≠ 1  Is SRC fraction  30%??  Measured results depend on integration limits  SRC contribution is not excluded (estimated)  FSI can affect on results  These results are impotent: they show the expected size of SRC contribution (10-20-30%) Nucleus Z ≡ 4  ∫ S(E i,p i )dE i dp i ≠ 1 (  0.7) e e/e/ q ε F,p F To measure SRC fraction 1.the direct interaction reactions should be used, 2.at higher energy and momentum transfers (to resolve SRCs)

12. JLab_Phys_Semin_Dec05 K. Egiyan 2. Hall C attempt for direct SRC measurement with (e,e’p)  To suppress SP contributions the parallel kinematics was used Nucleus To resolve SRC, q ≥ 1 GeV/c (D.Rohe et al., PRL 93:182501 (2004)) e e/e/ q p

13. JLab_Phys_Semin_Dec05 K. Egiyan 2. Hall C attempt for direct SRC measurement with (e,e’p)  To suppress SP contributions the parallel kinematics was used  S(p m,E m ) – spectral function was constricted as  S(p m,E m ) = d  exp (A)/d  theor (eN / )  Certain domain in (p m,E m ) plain was chosen, where SP impact expected to be small  In that particular region and for only 12 C nucleus the 10% SRC involvement for protons has been obtained  However, the total number (probability) of SRC have not been found  Many unclear corrections-assumptions have been made (FSI, transparency, off-shell (eN / ) cross section, SP impact, p m =p i, etc) Nucleus To resolve SRC, q ≥ 1 GeV/c (D.Rohe et al., PRL 93:182501 (2004)) e e/e/ q p

14. JLab_Phys_Semin_Dec05 K. Egiyan 3. Measurement of 2N SRC relative strength in (p,2p+n) reaction (EVA/BNL)  In final state the p 1, p 2 and n were detected  p i and γ were calculated  SP contribution was suppressed using the scaling behavior of NN interaction cross section  As a signature of 2N SRC the γ > 90 o and p n > p F cuts have been used Nucleus p p1p1 q p2p2 n γ pipi A. Tang, et al., PRL 90,042301 (2003)

15. JLab_Phys_Semin_Dec05 K. Egiyan 3. Measurement of 2N SRC relative strength in (p,2p+n) reaction (EVA/BNL)  In final state the p 1, p 2 and n were detected  p i and γ were calculated  SP contribution was suppressed using the scaling behavior of NN interaction cross section  As a signature of 2N SRC the γ > 90 o and p n > p F cuts have been used  Was found that for cosγ < 0  F(pn/NN) = = 0.49 ±0.12  Main conclusions are: For 12 C nucleus  SRCs were directly “seen”  The ratio of isotopic configurations (pn)/[(pn)+(pp)] is measured (if correct for neutron transparency) Nucleus p p1p1 q p2p2 n γ pipi N[(2pn(p n >p F )] N[2p]

16. JLab_Phys_Semin_Dec05 K. Egiyan 4. 2N SRC momentum distribution measurement in 3 He(e,e’pp)n; Hall-B  Detection of 2 protons in final state provides a full kinematics  By certain kinematical cuts the 2N SRCs [(np) and (pp)] have been separated 3 He e e1e1 q p2p2 n p1p1 R.Niazov, L. Weinstein, PRL;92:052303, 2004 (c.m.) Q 2  1 GeV 2

17. JLab_Phys_Semin_Dec05 K. Egiyan 4. 2N SRC momentum distribution measurement in 3 He(e,e’pp)n; Hall-B  Detection of 2 protons in final state provides a full kinematics  By certain kinematical cuts the 2N SRCs [(np) and (pp)] have been separated  Two type important information was extracted:  Momentum distributions of nucleons in SRC  Momentum distribution of SRC (c.m.) itself  New data at are in analyzing  No information on strength (probabilities) of SRC are available 3 He e e1e1 q p2p2 n p1p1 R.Niazov, L. Weinstein, PRL;92:052303, 2004 (c.m.) Q 2  1 GeV 2 Q 2  3 GeV 2 Cross sec, fb/MeV + FSI (c.m.)

18. JLab_Phys_Semin_Dec05 K. Egiyan These are, up to date, the published experimental data on SRC  We know about at least two experiments, ready to present a new data  From FermiLab by J. Peterson, who is planning to visit us and present data obtained with very high proton beam energies, and nuclei up to Pb  Hall A (e,e’p+n) experiment (D. Higinbotham, E. Piasetzky), measurements are finished, data are in an analyzing stage  However, probably, best way to measure the strengths of SRC is an inclusive electron scattering

19. JLab_Phys_Semin_Dec05 K. Egiyan Measuring the SRC probabilities with inclusive A(e,e’) scattering  There is good opportunity to measure the strengths of SRCs,  Using the electron inclusive scattering on nuclei at high Q 2 and large x B =Q 2 /2Mν Nucleus e e’ q Back to Hofstadter! but with higher momentum transfer allowing to “look” Inside the nucleus

20. JLab_Phys_Semin_Dec05 K. Egiyan Measuring the SRC probabilities with inclusive A(e,e’) scattering  There is good opportunity to measure the strengths of SRCs,  Using the electron inclusive scattering on nuclei at high Q 2 and large x B =Q 2 /2Mν  Inclusive scattering has a great advantage:  FSI can be excluded (see below)  However there is a big problem  Separation of (e,SRC) interaction from scattering off single nucleons Nucleus e e’ q Back to Hofstadter! but with higher momentum transfer allowing to “look” Inside the nucleus

21. JLab_Phys_Semin_Dec05 K. Egiyan Separation of (e,SRC) scattering reaction Nucleus e e/e/ q SRC A-2 e e/e/ SRC q A The reaction we are searching for is

22. JLab_Phys_Semin_Dec05 K. Egiyan Separation of (e,SRC) scattering reaction  Selection of (e,SRC) scattering from the large backgrounds:  Inelastic (eN) scattering (a)  Quasielastic scattering (b) Nucleus e e/e/ q SRC A-1 A e e/e/ A-2 e e/e/ SRC q q A pipi A e q pipi The reaction we are searching for is a) b) A-1 With backgrounds

23. JLab_Phys_Semin_Dec05 K. Egiyan Separation of (e,SRC) scattering reaction  Selection of (e,SRC) scattering from the large backgrounds:  Inelastic (eN) scattering (a)  Quasielastic scattering (b) Nucleus e e/e/ q SRC A-1 A e e/e/ A-2 e e/e/ SRC q q A pipi A e q pipi a) b) A-1 x B >1.2 The reaction we are searching for is

24. JLab_Phys_Semin_Dec05 K. Egiyan Separation of (e,SRC) scattering reaction  Selection of (e,SRC) scattering from the large backgrounds:  Inelastic (eN) scattering (a)  Quasielastic scattering (b) Nucleus e e/e/ q SRC A-1 A e e/e/ A-2 e e/e/ SRC q q A pipi A e q pipi a) b) A-1 x B >1.2 p min The reaction we are searching for is

25. JLab_Phys_Semin_Dec05 K. Egiyan Separation of (e,SRC) scattering reaction  Selection of (e,SRC) scattering from the large backgrounds:  Inelastic (eN) scattering (a)  Quasielastic scattering (b) Nucleus e e/e/ q SRC A-1 A e e/e/ A-2 e e/e/ SRC q q A pipi A e q pipi The reaction we are using is a) b) A-1 x B >1.2 p min p i > p min

26. JLab_Phys_Semin_Dec05 K. Egiyan Separation of (e,SRC) scattering reaction  Selection of (e,SRC) scattering from the large backgrounds:  Inelastic (eN) scattering (a)  Quasielastic scattering (b) Nucleus e e/e/ q SRC A-1 A e e/e/ A-2 e e/e/ SRC q q A pipi A e q pipi a) b) A-1 x B >1.2 p min p i > p min P min should be found The reaction we are searching for is

27. JLab_Phys_Semin_Dec05 K. Egiyan Obtaining of SRC dominant momentum region  Use the high momentum WF similarity for all nuclei to obtain the onset value of p min starting from which SRCs dominate

28. JLab_Phys_Semin_Dec05 K. Egiyan Obtaining of SRC dominant momentum region  Use the high momentum WF similarity for all nuclei to obtain the onset value of p min starting from which SRCs dominate  Ratios of cross section from two nuclei should scale starting from p min, where SP contribution in WF is negligible and SRC component dominates SRC region p min

29. JLab_Phys_Semin_Dec05 K. Egiyan Obtain the SRC dominant region in corresponding (Q 2, x B ) space  Use the high momentum WF similarity for all nuclei to obtain the onset value of p min starting from which SRCs dominate  Ratios of cross section from two nuclei should scale starting from p min, where SP contribution in WF is negligible and SRC component dominates  For A(e,e’) scattering off SP any combination of measured Q 2 and x B allows to calculate the p min = p min (Q 2, x B ) SRC region p min pipi -p i A-1 e e/e/ q

30. JLab_Phys_Semin_Dec05 K. Egiyan Obtain the SRC dominant region in corresponding (Q 2, x B ) space  Use the high momentum WF similarity for all nuclei to obtain the onset value of p min starting from which SRCs dominate  Ratios of cross section from two nuclei should scale starting from p min, where SP contribution in WF is negligible and SRC component dominates  For A(e,e’) scattering off SP any combination of measured Q 2 and x B allows to calculate the p min = p min (Q 2, x B )  Ratios of cross section from two nuclei should scale at corresponding (Q 2, x B ) combination SRC region p min Francfurt, Strikman, PR, ’81;’88

31. JLab_Phys_Semin_Dec05 K. Egiyan Use A(e,e’) cross section ratios to measure SRC probabilities  Use the high momentum WF similarity for all nuclei to obtain the onset value of p min starting from which SRCs dominate,  Ratios of cross section from two nuclei should scale starting from p min, where SP contribution in WF is negligible and SRC component dominates  For A(e,e’) scattering off SP any combination of measured Q 2 and x B allows to calculate the p min = p min (Q 2, x B )  Ratios of cross section from two nuclei should scale at corresponding (Q 2, x B ) combination  In SRC model the scaling factor (SF) indicate the ratio of SRC probabilities a 2N (A 1 ) and a 2N (A 2 ) in nuclei A 1 and A 2 : SF = a 2 (A 1 /A 2 ) = SRC region a 2N (A 1 ) a 2N (A 2 ) SF p min Francfurt, Strikman, PR, ’81;’88

32. JLab_Phys_Semin_Dec05 K. Egiyan To check this idea SLAC existing data were reanalyzed  The old SLAC data were analyzed  A/D ratios were extracted for A=4,12, 27, 56  Evidence for scaling is obvious  Scaling factors were used to estimate 2-nucleon SRC probabilities in nuclei A relative to D Frankfurt,Strikman,Day, Sargsian, Phys.Rev. C ‘93

33. JLab_Phys_Semin_Dec05 K. Egiyan To check this idea SLAC existing data were reanalyzed  The old SLAC data were analyzed  A/D ratios were extracted for A=4,12, 27, 56  Evidence for scaling is obvious  Scaling factors were used to estimate 2-nucleon SRC probabilities in nuclei A relative to D However  Data for nuclei A and for D were measured in large difference of kinematics, the theoretical calculation were used to obtain data at the same Q 2 and x B for heavy nuclei and D  Absolute probabilities were no able to obtain  x B interval used was limited (<1.6)  Systematic and dedicated measurements are needed Frankfurt,Strikman,Day, Sargsian, Phys.Rev. C ‘93

34. JLab_Phys_Semin_Dec05 K. Egiyan Final State Interaction in (e,SRC) Scattering  Struck nucleon interacts with other nucleon(s) from the same SRC  This interaction is much stronger since relative momenta are smaller and they are spatially closer  Interaction of nucleons with nucleons from the A-2 residual  This interaction is much weaker since relative momenta are larger and they are spatially more separated  FSI is primarily localized in SRC A A-1 NiNi NfNf e e/e/ q NiNi e e/e/ q SRC FSIs

35. JLab_Phys_Semin_Dec05 K. Egiyan More localization of Final State Interaction in SRC  In QM there is some distance (r) where FSI still can affect on (e,N i ) interaction.  At Q 2 > 1.5 GeV 2 and x B > 1.3 the maximum value r is < 1fm.  Since R SRC  r, the FSI of nucleons from the same SRC only can affect on cross section in (q,N i ) vertex!  Great advantage of ratio technique we are using is that, due to the this localization of FSI in SRC, it’s effect will cancel!! FSSD-Phys.Rev.C’93 A NiNi e e/e/ q r r max (fm) Q 2 (GeV 2 ) SRC A A-1 NiNi NfNf e e/e/ q NiNi e e/e/ q SRC FSIs

36. JLab_Phys_Semin_Dec05 K. Egiyan Our experiment  Experiment has been performed at JLab with CLAS detector at beam energy 4.46 and 4.7 GeV at E2 Run  As a nucleus A 2 we choose 3 He with well known wave function, as a nucleus A 1 - 4 He, 12 C, 56 Fe  A(e,e’) inclusive reaction was measured  Standard fiducial cuts and momentum corrections were applied  x B – dependences of per-nucleon cross section ratios for nuclei 4 He, 12 C, 56 Fe and 3 He were constructed in Q 2 =0.6-2.6 GeV 2 range, at x B at > 0.8  Obtained ratios (or cross sections) were corrected on  Acceptances  Radiative effects  Energy small difference   - contamination

37. JLab_Phys_Semin_Dec05 K. Egiyan Measured ratios of per-nucleon cross sections at Q 2 >1.4 GeV 2 and x B <2

38. JLab_Phys_Semin_Dec05 K. Egiyan Measured ratios of per-nucleon cross sections at Q 2 >1.4 GeV 2 and x B <2 r(A/ 3 He) = K(Q 2 ) 3  A (Q 2,x B ) A  He3 (Q 2,x B ) K(Q 2 ) = A(2  p +  n ) 3(Z  p +N  n ) where and takes into account the difference between (ep) and (en) cross sections For our Q 2 range K(Q 2 ) = 1.14 for 4 He and 12 C and = 1.18 for 56 Fe

39. JLab_Phys_Semin_Dec05 K. Egiyan Measured ratios of per-nucleon cross sections at Q 2 >1.4 GeV 2 and x B <2 Scaling exist; Observation 1 Hypotheses of Wave Function similarity in high momentum region for all nuclei Is correct see also (Francfurt, Strikman, Day, Sargsyan, PRC, 1993) (Egiyan et al., PRC, 2003)

40. JLab_Phys_Semin_Dec05 K. Egiyan Measured ratios of per-nucleon cross sections at Q 2 >1.4 GeV 2 and x B <2 Scaling exist; Scaling factors (SF) are measured; Observation 1 SF Observation 2

41. JLab_Phys_Semin_Dec05 K. Egiyan Measured ratios of per-nucleon cross sections at Q 2 >1.4 GeV 2 and x B <2 Scaling exist; Scaling factors (SF) are measured; Observation 1 SF Observation 2 In SRC model the measured scaling factors are just a ratios of 2-nucleon SRC probabilities in nucleus A and 3 He

42. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 2-Nuclon SRC relative probabilities Scaling exist; Scaling factors (SF) are measured; Observation 1 SF a 2N ( 4 He) a 2N ( 3 He) =1.93 ±0.02±0.14 a 2N ( 12 C) a 2N ( 3 He) =2.41 ±0.02±0.17 a 2N ( 56 Fe) a 2N ( 3 He) =2.83 ±0.03±0.18 Observation 2

43. JLab_Phys_Semin_Dec05 K. Egiyan Comparison with SRC model calculations  Comparison of the experimental x B – dependences of per-nucleon cross section ratios with theoretical once calculated at several values of Q 2 in Q 2 >1.4 GeV 2 region (M. Sargsian’s code)  The agreement is very well, if take into account  10% systematic uncertainties both in theory and in experiment,

44. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 2-Nuclon SRC relative probabilities Scaling exist; Scaling factors (SF) are measured; Observation 1 SF a 2N ( 4 He) a 2N ( 3 He) =1.93 ±0.02±0.14 a 2N ( 12 C) a 2N ( 3 He) =2.41 ±0.02±0.17 a 2N ( 56 Fe) a 2N ( 3 He) =2.83 ±0.03±0.18 Observation 2 Theoretical expectations 2.03 0.16 1.76 2.53 0.13 ---- 3.13 1.46 ---- SRC QCM Den/ratio (F-S) (Vary) (Forest)

45. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 2-Nuclon SRC relative probabilities Scaling exist; Scaling factors (SF) are measured; Observation 1 SF a 2N ( 4 He) a 2N ( 3 He) =1.93 ±0.02±0.14 a 2N ( 12 C) a 2N ( 3 He) =2.41 ±0.02±0.17 a 2N ( 56 Fe) a 2N ( 3 He) =2.83 ±0.03±0.18 Observation 2 Thus, Chances for every nucleon in 4 He, 12 C and 56 Fe to be involved in 2N SRC are 1.93, 2.41 and 2.83 times larger than in 3 He

46. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 2-Nuclon SRC absolute probabilities Scaling exist; Scaling factors (SF) are measured; Scaling onsets (SO) are measured Observation 1 SF SO a 2N ( 4 He) a 2N ( 3 He) =1.93 ±0.02±0.14 a 2N ( 12 C) a 2N ( 3 He) =2.41 ±0.02±0.17 a 2N ( 56 Fe) a 2N ( 3 He) =2.83 ±0.03±0.18 Observation 2 Observation 3

47. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 2-Nuclon SRC absolute probabilities Scaling exist; Scaling factors (SF) are measured; Scaling onsets (SO) are measured Observation 1 SF SO a 2N ( 4 He) a 2N ( 3 He) =1.93 ±0.02±0.14 a 2N ( 12 C) a 2N ( 3 He) =2.41 ±0.02±0.17 a 2N ( 56 Fe) a 2N ( 3 He) =2.83 ±0.03±0.18 Observation 2 Observation 3 SO measurement allows to find a 2N ( 3 He) using the wave functions of 3 He and Deuterium

48. JLab_Phys_Semin_Dec05 K. Egiyan Calculation of a 2N ( 3 He) using 3 He and 2 H wave functions  a 2N ( 3 He) = x a 2N ( 2 H) a 2N ( 3 He) a 2N ( 2 H) SF

49. JLab_Phys_Semin_Dec05 K. Egiyan Calculation of a 2N ( 3 He) using 3 He and 2 H wave functions  a 2N ( 3 He) = x a 2N ( 2 H)  From the calculated ratio r( 3 He/ 2 H) SF = = 2 ± 0.1  And a 2N ( 3 He) = (2 ± 0.1) x a 2N ( 2 H) a 2N ( 3 He) a 2N ( 2 H) a 2N ( 3 He) a 2N ( 2 H) SF

50. JLab_Phys_Semin_Dec05 K. Egiyan Calculation of a 2N ( 3 He) using 3 He and 2 H wave functions  a 2N ( 3 He) = x a 2N ( 2 H)  From the calculated ratio r( 3 He/ 2 H) SF = = 2 ± 0.1  And a 2N ( 3 He) = (2 ± 0.1) x a 2N ( 2 H)  To calculate a 2N ( 2 H) we use  2 H Wave Function  Measured p min (Q 2 onset,x B onset ) =275±25 MeV  Integral over deuterium wave function in p i > p min region is just a 2N ( 2 H)  Thus, definition of SRC is - the relative momentum of nucleons in SRC > 275 MeV/c  a 2N ( 2 H) = 0.040 ± 0.007  a 2N ( 3 He) = 0.080 ± 0.016 p min (4.+0.8)% Deuterium Wave Function a 2N ( 3 He) a 2N ( 2 H) a 2N ( 3 He) a 2N ( 2 H) SF

51. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 2-Nuclon SRC absolute probabilities Scaling exist; Scaling factors (SF) are measured; Scaling onsets (SO) are measured Observation 1 SF SO a 2N ( 4 He) a 2N ( 3 He) =1.93 ±0.02±0.14 a 2N ( 12 C) a 2N ( 3 He) =2.41 ±0.02±0.17 a 2N ( 56 Fe) a 2N ( 3 He) =2.83 ±0.03±0.18 = 0.080+0.016 Observation 2 Observation 3

52. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 2-Nuclon SRC absolute probabilities Scaling exist; Scaling factors (SF) are measured; Scaling onsets (SO) are measured Observation 1 SF SO a 2N ( 4 He) = 0.154± 0.002±0.033 a 2N ( 12 C) = 0.193 ±0.002±0.041 a 2N ( 56 Fe) = 0.23 ±0.002±0.047 Observation 2 Observation 3

53. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 2-Nuclon SRC absolute probabilities Scaling exist; Scaling factors (SF) are measured; Scaling onsets (SO) are measured Observation 1 SF SO a 2N ( 4 He) = 0.154± 0.002±0.033 a 2N ( 12 C) = 0.193 ±0.002±0.041 a 2N ( 56 Fe) = 0.23 ±0.002±0.047 Observation 2 Observation 3 Every nucleon in nuclei 3 He, 4 He, 12 C and 56 Fe 8%, 15.4%, 19.3% and 23% of its life-time is “living” In SRC state with other nucleon

54. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 2-Nuclon SRC absolute probabilities Scaling exist; Scaling factors (SF) are measured; Scaling onsets (SO) are measured Observation 1 SF SO a 2N ( 4 He) = 0.154± 0.002±0.033 a 2N ( 12 C) = 0.193 ±0.002±0.041 a 2N ( 56 Fe) = 0.23 ±0.002±0.047 Observation 2 Observation 3 In other words At any moment, in nuclei 3 He, 4 He, 12 C and 56 Fe can be obtained, respectively, 0.12, 0.30, 1.14 and 6.44 2-nucleon SRCs

55. JLab_Phys_Semin_Dec05 K. Egiyan In other words  In any moment in 12 C one can be seen one 2N SRC  While in any moment in 56 Fe one can exist six 2N SRC 56 Fe 12 C

56. JLab_Phys_Semin_Dec05 K. Egiyan We measure directly a 2-nucleon SRC numbers (probabilities) Single particle (%) 2N SRC (%)3N(and moreN) SRC (%) 56 Fe ???? 23.0 ± 0.2 ± 4.7 ???? 12 C ???? 19.3 ± 0.2 ± 4.1 ???? 4 He ???? 15.4 ± 0.2 ± 3.3 ???? 3 He ???? 8.0 ± 1.6 ----- 2 H 95.9 ± 0.7 4.1 ± 0.7 ----- But it is still not enough to know a full nucleonic picture of nuclei Fractions Nucleus We need to measure 3-and-more-nucleonic SRC fraction

57. JLab_Phys_Semin_Dec05 K. Egiyan Importance of measurements at x B > 2  Is not only to get the data on 3-nucleon SRC  But also to prove the interpretations of obtained data at x B < 2 by the SRC model  SRC model predicts:  Existence of “positive” step in x B – dependence of cross section ratios at 2<x B <3, due to the proportionality of a JN to the J th power of nuclear density (J is order of SRC) a jN  ∫  J A (r)dr  The step should increase with A  We measure the cross section ratios at 2 < x B < 3, for the first time

58. JLab_Phys_Semin_Dec05 K. Egiyan x B 1.4 GeV 2 and x B <3

59. JLab_Phys_Semin_Dec05 K. Egiyan x B 1.4 GeV 2 and x B < 3 Observation 1 2 nd Scaling exist; Existence of step (second scaling level) Is very strong argument for SRC model

60. JLab_Phys_Semin_Dec05 K. Egiyan x B 1.4 GeV 2 and x B < 3 Observation 1Observation 2 2 nd Scaling exist; 2nd Scaling factors (SF) are measured; SF

61. JLab_Phys_Semin_Dec05 K. Egiyan x B 1.4 GeV 2 and x B < 3 Observation 1Observation 2 2 nd Scaling exist; 2nd Scaling factors (SF) are measured; SF In SRC model the measured scaling factors are just a ratios of 3-nucleon SRC probabilities in nucleus A and 3 He

62. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 3-Nuclon SRC relative probabilities Observation 1Observation 2 2 nd Scaling exist; 2nd Scaling factors (SF) are measured; SF a 3N ( 4 He) a 3N ( 3 He) a 3N ( 12 C) a 3N ( 3 He) a 3N ( 56 Fe) a 3N ( 3 He) = 2.33 ±0.12±0.19 = 3.05±0.14±0.22 = 4.38±0.18±0.33

63. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 3-Nuclon SRC relative probabilities Observation 1Observation 2 2 nd Scaling exist; 2nd Scaling factors (SF) are measured; SF a 3N ( 4 He) a 3N ( 3 He) a 3N ( 12 C) a 3N ( 3 He) a 3N ( 56 Fe) a 3N ( 3 He) = 2.33 ±0.12±0.19 = 3.05±0.14±0.22 = 4.38±0.18±0.33 Chances for every nucleon in 4 He, 12 C and 56 Fe to be involved in 3N SRC are 2.33, 3.05 and 4.38 times larger than in 3 He itself

64. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 3-Nuclon SRC absolute probabilities Observation 1Observation 2 Observation 3 2 nd Scaling exist; 2nd Scaling factors (SF) are measured; 2nd Scaling onsets (SO) are measured SF a 3N ( 4 He) a 3N ( 3 He) a 3N ( 12 C) a 3N ( 3 He) a 3N ( 56 Fe) a 3N ( 3 He) = 2.33 ±0.12±0.19 =3.05±0.14±0.22 = 4.38±0.18±0.33 SO

65. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 3-Nuclon SRC absolute probabilities Observation 1Observation 2 Observation 3 2 nd Scaling exist; 2nd Scaling factors (SF) are measured; 2nd Scaling onsets (SO) are measured SF a 3N ( 4 He) a 3N ( 3 He) a 3N ( 12 C) a 3N ( 3 He) a 3N ( 56 Fe) a 3N ( 3 He) = 2.33 ±0.12±0.19 =3.05±0.14±0.22 = 4.38±0.18±0.33 SO Measurement of SO allows to calculate the a 3N ( 3 He) using the 3 He wave function

66. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 3-Nuclon SRC absolute probabilities Observation 1Observation 2 Observation 3 2 nd Scaling exist; 2nd Scaling factors (SF) are measured; 2nd Scaling onsets (SO) are measured SF a 3N ( 4 He) a 3N ( 3 He) a 3N ( 12 C) a 3N ( 3 He) a 3N ( 56 Fe) a 3N ( 3 He) = 2.33 ±0.12±0.19 =3.05±0.14±0.22 = 4.38±0.18±0.33 SO = 0.0018 ±0.0006 (M. Sargsyan’s calculations)

67. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 3-Nuclon SRC absolute probabilities Observation 1Observation 2 Observation 3 2 nd Scaling exist; 2nd Scaling factors (SF) are measured; 2nd Scaling onsets (SO) are measured SF SO a 3N ( 4 He)= 0.42 ±0.02±0.14 (%) a 3N ( 12 C)= 0.55 ±0.03±0.18 a 3N ( 56 Fe)= 0.79 ±0.03±0.25

68. JLab_Phys_Semin_Dec05 K. Egiyan Measurement of 3-Nuclon SRC absolute probabilities Observation 1Observation 2 Observation 3 2 nd Scaling exist; 2nd Scaling factors (SF) are measured; 2nd Scaling onsets (SO) are measured SF SO a 3N ( 4 He)= 0.42 ±0.02±0.14 (%) a 3N ( 12 C)= 0.55 ±0.03±0.18 a 3N ( 56 Fe)= 0.79 ±0.03±0.25 Per-nucleon probabilities of 3N SRC are smaller then the same probabilities of 2N SRC more the one order of magnitude

69. JLab_Phys_Semin_Dec05 K. Egiyan Having these data, we know almost full (  99%) nucleonic picture of nuclei with A  56 Single particle (%) 2N SRC (%) 3N SRC (%) 56 Fe 76 ± 0.2 ± 4.7 23.0 ± 0.2 ± 4.7 0.79 ± 0.03 ± 0.25 12 C 80 ± 02 ± 4.1 19.3 ± 0.2 ± 4.1 0.55 ± 0.03 ± 0.18 4 He 86 ± 0.2 ± 3.3 15.4 ± 0.2 ± 3.3 0.42 ± 0.02 ± 0.14 3 He 92 ± 1.6 8.0 ± 1.6 0.18 ± 0.06 2 H 96 ± 0.7 4.0 ± 0.7 ----- Fractions Nucleus

70. JLab_Phys_Semin_Dec05 K. Egiyan Comparisons with some theoretical predictions on SRC probabilities Single particle (%) 2N SRC (%) 3N SRC (%) 56 Fe 23.0 ± 4.7 25.50.79 ±0.25 12 C 19.3 ± 4.1 20.30.55 ±0.18 4 He 15.4 ± 3.3 16.20.42 ±0.14 ----- 3 He 8.0 ± 1.6 ----0.18 ±0.06 ----- 2 H 4.0 ± 0.7 ---- ----- ----- Fractions Nucleus Exp SRC Fe/C= 1.43 ±0.15 Fe/C = 1.4 1. SRC model SRC predictions are remarkably close to experiment

71. JLab_Phys_Semin_Dec05 K. Egiyan Comparisons with some theoretical predictions on SRC probabilities Single particle (%) 2N SRC (%) 3N SRC (%) 56 Fe 23.0 ± 4.7 25.5 14.60.79 ±0.25 3.6 12 C 19.3 ± 4.1 20.3 12.50.55 ±0.18 2.6 4 He 15.4 ± 3.3 16.2 16.60.42 ±0.14 ----- 4.7 3 He 8.0 ± 1.6 ---- 13.40.18 ±0.06 ----- 2.2 2 H 4.0 ± 0.7 ---- ---- ----- ----- ----- Fractions Nucleus Exp SRC QCM Fe/C= 1.43 ±0.15 Fe/C = 1.4 1. SRC model 2. QCM model In QCM => Quark-Cluster-Model (unrealistic model in our Q 2 range) 2N SRC ===> 6q Bag; 3N SRC ===> 9q Bag QCM predictions for 2N SRC are close to experiment, while for 3N SRC almost 10 times are higher

72. JLab_Phys_Semin_Dec05 K. Egiyan Having these data, we know almost full (  99%) nucleonic picture of nuclei with A  56 Single particle (%) 2N SRC (%) 3N SRC (%) 56 Fe 76 ± 0.2 ± 4.7 23.0 ± 0.2 ± 4.7 0.79 ± 0.03 ± 0.25 12 C 80 ± 02 ± 4.1 19.3 ± 0.2 ± 4.1 0.55 ± 0.03 ± 0.18 4 He 86 ± 0.2 ± 3.3 15.4 ± 0.2 ± 3.3 0.42 ± 0.02 ± 0.14 3 He 92 ± 1.6 8.0 ± 1.6 0.18 ± 0.06 2 H 96 ± 0.7 4.0 ± 0.7 ----- Fractions Nucleus The similar data for heavier (A>56) nuclei is important, Hall C data will be available soon (J.Arrington et al.,)

73. JLab_Phys_Semin_Dec05 K. Egiyan SUMMARY  Existing experimental date indicate the presence of SRCs in nuclei, however, there are no “exact” measurements of their probabilities  Inclusive A(e,e’) scattering is effective tool for these type measurements  The ratios of per-nucleon cross sections of A(e,e’) reaction for nuclei with A = 4,12, 56 and 3 He are measured in 1 1.4 GeV 2  Two scaling regions - at 1.5 2.25 - are observed  Using the measured scaling factors, in the framework of SRC model, the 2- and 3- nucleon SRC per-nucleon probabilities in nuclei with A=4,12, 56 relative to 3 He are extracted  Using the measured onsets of scaling regions, combined with the known WF of 3 He and Deuterium, the absolute per-nucleon probabilities of 2- and 3- nucleon SRC are estimated  In the framework of SRC model the nucleonic picture of nuclei with A  56 is established

74. JLab_Phys_Semin_Dec05 K. Egiyan Supporting Slides

75. JLab_Phys_Semin_Dec05 K. Egiyan Having these data, we know almost full (  99%) nucleonic picture of nuclei with A  56 Single particle (%) 2N SRC (%) 3N SRC (%) 56 Fe 76 ± 0.2 ± 4.7 23.0 ± 0.2 ± 4.7 0.79 ± 0.03 ± 0.25 12 C 80 ± 02 ± 4.1 19.3 ± 0.2 ± 4.1 0.55 ± 0.03 ± 0.18 4 He 86 ± 0.2 ± 3.3 15.4 ± 0.2 ± 3.3 0.42 ± 0.02 ± 0.14 3 He 92 ± 1.6 8.0 ± 1.6 0.18 ± 0.06 2 H 96 ± 0.8 4.0 ± 0.8 ----- Fractions Nucleus Using the published data on (p,2p+n) [PRL,90 (2003) 042301] estimate the isotopic composition of 2N SRC in 12 C a pp ( 12 C)  4 ± 2 % a 2N ( 12 C)  20 ± 0.2 ± 4.1 % a pn ( 12 C)  12 ± 4 % a nn ( 12 C)  4 ± 2 %

76. JLab_Phys_Semin_Dec05 K. Egiyan The Ratios at 1<x B <2; Observation of Scaling  Analyze the ratio as a function of Q 2 and x B 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 GeV 2  Onset of scaling is at x B ≥ 1.5 Scaling vanishes at low Q 2  Shown results are for 56 Fe  Results for 12 C and 4 He are similar

77. JLab_Phys_Semin_Dec05 K. Egiyan Q 2 scaling of relative probabilities a 2 and a 3 in Q 2 = 1.4 – 2.6 GeV 2 region

78. JLab_Phys_Semin_Dec05 K. Egiyan Calculation of a 2N ( 3 He) using 3 He and 2 H wave functions  a 2N ( 3 He) = x a 2N ( 2 H)  From the calculated ratio r( 3 He/ 2 H) SF = = 2 ± 0.1  And a 2N ( 3 He) = (2 ± 0.1) x a 2N ( 2 H) a 2N ( 3 He) a 2N ( 2 H) a 2N ( 3 He) a 2N ( 2 H) SF

79. JLab_Phys_Semin_Dec05 K. Egiyan Contributing diagrams in 2<x B <3 region Three states can contribute:  3-nucleon SRCs in “2-body” and “Star” configurations,  2-nucleon SRC, due to the c.m. motion  In x B > 2 region “2 - Body” configuration of 3-nucleon SRC dominates ( M.Sargsian et al., PRC 71, 044615 (2005) )  Experiment shows that 2-nucleon SRC contribution is significant in 2 < x B < 2.25 region p -p 2N - SRC p p p p -p 2p 3N - SRC “Star”“2- Body”

80. JLab_Phys_Semin_Dec05 K. Egiyan Contributing diagrams in 2<x B <3 region Three states can contribute:  3-nucleon SRCs in “2-body” and “Star” configurations,  2-nucleon SRC, due to the c.m. motion  In x B > 2 region “2 - Body” configuration of 3-nucleon SRC dominates ( M.Sargsian et al., PRC 71, 044615 (2005) )  Experiment shows that 2-nucleon SRC contribution is significant in 2 < x B < 2.25 region only  At x B > 2.25 (p min > 500 MeV/c) only “2 - Body” configuration is contributing p -p 2N - SRC p p p p -p 2p 3N - SRC “Star”“2- Body”

81. JLab_Phys_Semin_Dec05 K. Egiyan Radiative Corrections 56 Fe 12 C 4 He 56 Fe 12 C 4 He 3 He