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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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**Today’s Nucleonic Picture of Nuclei**Kim Egiyan Yerevan Physics Institute, Armenia and Jefferson Lab, USA K. Egiyan**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**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**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**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**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 4o K. Egiyan**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 4o K. Egiyan**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**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**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**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**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**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) = dexp(A)/dtheor(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**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**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**4. 2N SRC momentum distribution measurement in**3He(e,e’pp)n; Hall-B R.Niazov, L. Weinstein, PRL;92:052303, 2004 Q21 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**4. 2N SRC momentum distribution measurement in**3He(e,e’pp)n; Hall-B R.Niazov, L. Weinstein, PRL;92:052303, 2004 Q21 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 Q23 GeV2 Cross sec, fb/MeV (c.m.) 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 K. Egiyan**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**Measured ratios of per-nucleon cross sections at Q2>1.4 GeV2**and xB<2 3A(Q2,xB) AHe3(Q2,xB) r(A/3He) = K(Q2) where A(2p+ 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**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**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**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**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**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**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**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**Calculation of a2N(3He) using 3He and 2H wave functions**a2N(3He) a2N(2H) • a2N(3He) = xa2N(2H) SF K. Egiyan**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**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**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**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**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**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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