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Today’s Nucleonic Picture of Nuclei

Today’s Nucleonic Picture of Nuclei. Kim Egiyan Yerevan Physics Institute, Armenia and Jefferson Lab, USA. Hofstadter's nucleonic picture of nucleus. Nucleus. Single particles ( SP ) moving in an average field

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Today’s Nucleonic Picture of Nuclei

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

  2. Hofstadter's nucleonic picture of nucleus 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  A1/3 • This was strong evidence that nuclei are composed from the SP, in other words, they are a bags with Fermi gas!! q (low) e e/ K. Egiyan

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

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

  5. Other possible components Nucleus  1.7f • HOWEVER • Strong NN (attractive and repulsive) interaction should result in Short Range Correlation (SRC) • So, nuclear Hamiltonian should include H = p2/2M + V2(r1,r2) + V3(r1,r2,r3) + …. the correlation terms Vi o= 0.17 Nucleons K. Egiyan

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

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

  8. Main topic of talk Nucleus  1.7f • 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-densmatter in SRC • In this talk the only first topic will be discussed : Fractions of SP and SRC phases in nuclei • What we know about SPand SRC?  1f K. Egiyan

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

  10. 1.Evidence for NON-single particle states - Spectroscopic factor Nucleus • In first generation of A(e,e’p)A-1 measurements the S(Ei,pi) – spectral function – the probability a finding nucleon in nuclei with momentum pi and removal energy Ei has been extracted • It was found that integral (Spectroscopic factor) • SPfractions is ≠ 1 • Is SRCfraction 30%?? • Measured results depend on integration limits • SRCcontribution is not excluded (estimated) • FSI can affect on results • These results are impotent: they show the expected size of SRCcontribution (10-20-30%) p Z ≡ 4∫S(Ei,pi)dEidpi ≠ 1 (0.7) q pi εF,pF e e/ Z K. Egiyan

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

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

  13. 2. Hall C attempt for direct SRC measurement with (e,e’p) Nucleus • To suppress SP contributions the parallel kinematics was used • S(pm,Em) – spectral function was constricted as • S(pm,Em) = dexp(A)/dtheor(eN/) • Certain domain in (pm,Em) plain was chosen, where SP impact expected to be small • In that particular region and for only 12C 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, pm=pi, etc) p q e e/ To resolve SRC, q ≥ 1 GeV/c (D.Rohe et al., PRL 93:182501 (2004)) K. Egiyan

  14. 3. Measurement of 2N SRC relative strength in (p,2p+n) reaction (EVA/BNL) Nucleus • In final state the p1, p2 and n were detected • pi and γ were calculated • SP contribution was suppressed using the scaling behavior of NN interaction cross section • As a signature of 2NSRCtheγ > 90o and pn > pF cuts have been used pi n p2 γ q p p1 A. Tang, et al., PRL 90 ,042301 (2003) K. Egiyan

  15. 3. Measurement of 2N SRC relative strength in (p,2p+n) reaction (EVA/BNL) Nucleus • In final state the p1, p2 and n were detected • pi and γ were calculated • SP contribution was suppressed using the scaling behavior of NN interaction cross section • As a signature of 2N SRC theγ > 90o and pn > pF cuts have been used • Was found that for cosγ< 0 • F(pn/NN) = = 0.49 ±0.12 • Main conclusions are: For 12C nucleus • SRCs were directly “seen” • The ratio of isotopic configurations (pn)/[(pn)+(pp)] is measured (if correct for neutron transparency) pi n p2 γ q p p1 N[(2pn(pn>pF)] N[2p] K. Egiyan

  16. 4. 2N SRC momentum distribution measurement in 3He(e,e’pp)n; Hall-B R.Niazov, L. Weinstein, PRL;92:052303, 2004 Q21 GeV2 3He • Detection of 2 protons in final state provides a full kinematics • By certain kinematical cuts the 2N SRCs [(np) and (pp)] have been separated (c.m.) p2 n p1 q e e1 K. Egiyan

  17. 4. 2N SRC momentum distribution measurement in 3He(e,e’pp)n; Hall-B R.Niazov, L. Weinstein, PRL;92:052303, 2004 Q21 GeV2 3He • 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 (c.m.) p2 n p1 q e e1 + FSI + FSI Q23 GeV2 Cross sec, fb/MeV (c.m.) K. Egiyan

  18. 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 K. Egiyan

  19. Measuring the SRC probabilities with inclusive A(e,e’) scattering Nucleus • There is good opportunity to measure the strengths of SRCs, • Using the electron inclusive scattering on nuclei at high Q2 and large xB=Q2/2Mν q e e’ Back to Hofstadter! but with higher momentum transfer allowing to “look” Inside the nucleus K. Egiyan

  20. Measuring the SRC probabilities with inclusive A(e,e’) scattering Nucleus • There is good opportunity to measure the strengths of SRCs, • Using the electron inclusive scattering on nuclei at high Q2 and large xB=Q2/2Mν • 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 q e e’ Back to Hofstadter! but with higher momentum transfer allowing to “look” Inside the nucleus K. Egiyan

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

  22. Separation of (e,SRC) scattering reaction The reaction we are searching for is • Selection of (e,SRC) scattering from the large backgrounds: • Inelastic (eN) scattering (a) • Quasielastic scattering (b) e/ e/ e e q q SRC A A-2 Nucleus SRC a) b) e/ e e q q pi pi A-1 A A A-1 xB>1.2 K. Egiyan

  23. Separation of (e,SRC) scattering reaction The reaction we are searching for is • Selection of (e,SRC) scattering from the large backgrounds: • Inelastic (eN) scattering (a) • Quasielastic scattering (b) e/ e/ e e q q SRC A A-2 Nucleus SRC pmin a) b) e/ e e q q pi pi A-1 A A A-1 xB>1.2 K. Egiyan

  24. Separation of (e,SRC) scattering reaction The reaction we are using is • Selection of (e,SRC) scattering from the large backgrounds: • Inelastic (eN) scattering (a) • Quasielastic scattering (b) e/ e/ e e q q SRC A A-2 Nucleus SRC pmin a) b) e/ e e q q pi pi A-1 A A A-1 xB>1.2 pi > pmin K. Egiyan

  25. Separation of (e,SRC) scattering reaction The reaction we are searching for is • Selection of (e,SRC) scattering from the large backgrounds: • Inelastic (eN) scattering (a) • Quasielastic scattering (b) e/ e/ e e q q SRC A A-2 Nucleus SRC pmin a) b) e/ e e q q pi pi A-1 A A A-1 xB>1.2 Pmin should be found pi > pmin K. Egiyan

  26. Obtaining of SRC dominant momentum region • Use the high momentum WF similarity for all nuclei to obtain the onset value of pmin starting from which SRCs dominate K. Egiyan

  27. Obtaining of SRC dominant momentum region • Use the high momentum WF similarity for all nuclei to obtain the onset value of pmin starting from which SRCs dominate • Ratios of cross section from two nuclei should scale starting from pmin, whereSPcontribution in WF is negligible and SRCcomponent dominates SRC region pmin K. Egiyan

  28. e/ e -pi q A-1 pi Obtain the SRC dominant region in corresponding (Q2, xB) space • Use the high momentum WF similarity for all nuclei to obtain the onset value of pmin starting from which SRCs dominate • Ratios of cross section from two nuclei should scale starting from pmin, whereSPcontribution in WF is negligible and SRCcomponent dominates • For A(e,e’) scattering off SP any combination of measured Q2 and xB allows to calculate the pmin = pmin(Q2, xB) SRC region pmin K. Egiyan

  29. Obtain the SRC dominant region in corresponding (Q2, xB) space • Use the high momentum WF similarity for all nuclei to obtain the onset value of pmin starting from which SRCs dominate • Ratios of cross section from two nuclei should scale starting from pmin, whereSPcontribution in WF is negligible and SRCcomponent dominates • For A(e,e’) scattering offSP any combination of measured Q2 and xB allows to calculate the pmin = pmin(Q2, xB) • Ratios of cross section from two nuclei should scale at corresponding (Q2, xB) combination SRC region pmin Francfurt, Strikman, PR, ’81;’88 K. Egiyan

  30. 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 pmin starting from which SRCs dominate, • Ratios of cross section from two nuclei should scale starting from pmin, whereSPcontribution in WF is negligible and SRCcomponent dominates • For A(e,e’) scattering offSP any combination of measured Q2 and xB allows to calculate the pmin = pmin(Q2, xB) • Ratios of cross section from two nuclei should scale at corresponding (Q2, xB) combination • In SRC model the scaling factor (SF) indicate the ratio of SRC probabilities a2N(A1) and a2N(A2) in nuclei A1 and A2: SF = a2(A1/A2) = SRC region pmin a2N(A1) a2N(A2) SF Francfurt, Strikman, PR, ’81;’88 K. Egiyan

  31. To check this idea SLAC existing data were reanalyzed Frankfurt,Strikman,Day, Sargsian, Phys.Rev. C ‘93 • The old SLAC data were analyzed • A/D ratios were extractedfor 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 K. Egiyan

  32. To check this idea SLAC existing data were reanalyzed Frankfurt,Strikman,Day, Sargsian, Phys.Rev. C ‘93 • The old SLAC data were analyzed • A/D ratios were extractedfor 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 Q2 and xB for heavy nuclei and D • Absolute probabilities were no able to obtain • xB interval used was limited (<1.6) • Systematic and dedicated measurements are needed K. Egiyan

  33. Final State Interaction in (e,SRC) Scattering e/ e/ e e q q • Struck nucleon interacts withother 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 Nf Ni Ni SRC A A-1 FSIs K. Egiyan

  34. More localization of Final State Interaction in SRC e/ e/ e/ e e e r q q q • In QM there is some distance (r) where FSI still can affect on (e,Ni ) interaction. • At Q2 > 1.5 GeV2 and xB > 1.3 the maximum value r is < 1fm. • Since RSRC r, the FSI of nucleons from the same SRC onlycan affect on cross section in (q,Ni ) 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!! Nf Ni Ni Ni SRC SRC A A A-1 FSIs FSSD-Phys.Rev.C’93 rmax (fm) Q2 (GeV2) K. Egiyan

  35. 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 A2we choose3He with well known wave function, as a nucleus A1 - 4He, 12C, 56Fe • A(e,e’) inclusive reaction was measured • Standard fiducial cuts and momentum corrections were applied • xB – dependences of per-nucleon cross section ratios for nuclei 4He, 12C, 56Fe and 3He were constructed in Q2 =0.6-2.6 GeV2 range, at xB at > 0.8 • Obtained ratios (or cross sections) were corrected on • Acceptances • Radiative effects • Energy small difference • - contamination K. Egiyan

  36. Measured ratios of per-nucleon cross sections at Q2>1.4 GeV2 and xB<2 3A(Q2,xB) AHe3(Q2,xB) r(A/3He) = K(Q2) where A(2p+ n) 3(Z p+N n) K(Q2) = and takes into account the difference between (ep) and (en) cross sections For our Q2 range K(Q2) = 1.14 for 4He and 12C and = 1.18 for 56Fe K. Egiyan

  37. Measured ratios of per-nucleon cross sections at Q2>1.4 GeV2 and xB<2 Observation 1 Scaling exist; 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) K. Egiyan

  38. Measured ratios of per-nucleon cross sections at Q2>1.4 GeV2 and xB<2 Observation 1 Observation 2 Scaling exist;Scaling factors (SF)are measured; SF K. Egiyan

  39. Measured ratios of per-nucleon cross sections at Q2>1.4 GeV2 and xB<2 Observation 1 Observation 2 Scaling exist;Scaling factors (SF)are measured; In SRC model the measured scaling factors are just a ratios of 2-nucleon SRC probabilities in nucleus A and 3He SF K. Egiyan

  40. Measurement of 2-Nuclon SRC relative probabilities Observation 1 Observation 2 Scaling exist;Scaling factors (SF)are measured; a2N(4He) a2N(3He) =1.93±0.02±0.14 a2N(12C) a2N(3He) =2.41±0.02±0.17 SF a2N(56Fe) a2N(3He) =2.83±0.03±0.18 K. Egiyan

  41. Measurement of 2-Nuclon SRC relative probabilities Observation 1 Observation 2 Scaling exist;Scaling factors (SF)are measured; a2N(4He) a2N(3He) =1.93±0.02±0.14 a2N(12C) a2N(3He) =2.41±0.02±0.17 SF a2N(56Fe) a2N(3He) =2.83±0.03±0.18 Thus, Chances for every nucleon in 4He, 12C and 56Fe to be involved in 2N SRC are 1.93, 2.41 and 2.83 times larger than in 3He K. Egiyan

  42. Measurement of 2-Nuclon SRC absolute probabilities Observation 1 Observation 2 Observation 3 Scaling exist;Scaling factors (SF)are measured;Scaling onsets (SO) are measured a2N(4He) a2N(3He) =1.93±0.02±0.14 a2N(12C) a2N(3He) =2.41±0.02±0.17 SF a2N(56Fe) a2N(3He) =2.83±0.03±0.18 SO K. Egiyan

  43. Measurement of 2-Nuclon SRC absoluteprobabilities Observation 1 Observation 2 Observation 3 Scaling exist;Scaling factors (SF)are measured;Scaling onsets (SO) are measured a2N(4He) a2N(3He) =1.93±0.02±0.14 SO measurement allows to find a2N(3He) using the wave functions of 3He and Deuterium a2N(12C) a2N(3He) =2.41±0.02±0.17 SF a2N(56Fe) a2N(3He) =2.83±0.03±0.18 SO K. Egiyan

  44. Calculation of a2N(3He) using 3He and 2H wave functions a2N(3He) a2N(2H) • a2N(3He) = xa2N(2H) SF K. Egiyan

  45. Calculation of a2N(3He) using 3He and 2H wave functions a2N(3He) a2N(2H) • a2N(3He) = xa2N(2H) • From the calculatedratio r(3He/2H) SF ==2 ± 0.1 • And a2N(3He) = (2 ± 0.1)xa2N(2H) a2N(3He) a2N(2H) SF K. Egiyan

  46. Calculation of a2N(3He) using 3He and 2H wave functions a2N(3He) a2N(2H) • a2N(3He) = xa2N(2H) • From the calculatedratio r(3He/2H) SF ==2 ± 0.1 • And a2N(3He) = (2 ± 0.1)xa2N(2H) • To calculate a2N(2H) weuse • 2H Wave Function • Measured pmin(Q2onset,xBonset) =275±25 MeV • Integral over deuterium wave function in pi > pmin regionisjust a2N(2H) • Thus, definition of SRC is - the relative momentum of nucleons in SRC > 275 MeV/c • a2N(2H) = 0.040 ± 0.007 • a2N(3He) = 0.080 ± 0.016 a2N(3He) a2N(2H) SF Deuterium Wave Function pmin (4.+0.8)% K. Egiyan

  47. Measurement of 2-Nuclon SRC absoluteprobabilities Observation 1 Observation 2 Observation 3 Scaling exist;Scaling factors (SF)are measured;Scaling onsets (SO) are measured a2N(4He) a2N(3He) =1.93±0.02±0.14 = 0.080+0.016 a2N(12C) a2N(3He) =2.41±0.02±0.17 SF a2N(56Fe) a2N(3He) =2.83±0.03±0.18 SO K. Egiyan

  48. Measurement of 2-Nuclon SRC absoluteprobabilities Observation 1 Observation 2 Observation 3 Scaling exist;Scaling factors (SF)are measured;Scaling onsets (SO) are measured a2N(4He) = 0.154±0.002±0.033 a2N(12C) = 0.193±0.002±0.041 SF a2N(56Fe) = 0.23±0.002±0.047 SO K. Egiyan

  49. Measurement of 2-Nuclon SRC absoluteprobabilities Observation 1 Observation 2 Observation 3 Scaling exist;Scaling factors (SF)are measured;Scaling onsets (SO) are measured a2N(4He) = 0.154±0.002±0.033 a2N(12C) = 0.193±0.002±0.041 SF a2N(56Fe) = 0.23±0.002±0.047 SO Every nucleon in nuclei 3He, 4He, 12C and 56Fe 8%, 15.4%, 19.3% and 23% of its life-time is “living” In SRC state with other nucleon K. Egiyan

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

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