Todays Nucleonic Picture of Nuclei Kim Egiyan Yerevan

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

Today’s Nucleonic Picture of Nuclei Kim Egiyan Yerevan Physics Institute, Armenia and Jefferson Lab, USA JLab_Phys_Semin_Dec 05 K. Egiyan

Hofstadter's nucleonic picture of nucleus Ø Single particles (SP) moving in an average field

Hofstadter's nucleonic picture of nucleus Ø Single particles (SP) moving in an average field Nucleus Ø Electron elastic scattering off nuclei have been measured and nuclear radii R were obtained Ø It was shown that R A 1/3 q (low) e Ø This was strong evidence that nuclei are composed from the SP, in other words, they are a bags with Fermi gas!! JLab_Phys_Semin_Dec 05 e/ K. Egiyan

Other possible components Ø HOWEVER Nucleus 1 Ø Strong NN (attractive and repulsive) interaction

Other possible components Ø HOWEVER Nucleus 1 Ø Strong NN (attractive and repulsive) interaction should result in Short Range Correlation (SRC) . 7 f o= 0. 17 Nucleons JLab_Phys_Semin_Dec 05 K. Egiyan

Other possible components Ø HOWEVER Nucleus 1 Ø Strong NN (attractive and repulsive) interaction

Other possible components Ø HOWEVER Nucleus 1 Ø Strong NN (attractive and repulsive) interaction should result in Short Range Correlation (SRC) . 7 f o= 0. 17 Nucleons JLab_Phys_Semin_Dec 05 K. Egiyan

Other possible components Ø HOWEVER Nucleus 1 Ø Strong NN (attractive and repulsive) interaction

Other possible components Ø HOWEVER Nucleus 1 Ø Strong NN (attractive and repulsive) interaction should result in Short Range Correlation (SRC) . 7 f o= 0. 17 Ø So, nuclear Hamiltonian should include Nucleons H = p 2/2 M + V 2(r 1, r 2) + V 3(r 1, r 2, r 3) + …. the correlation terms Vi JLab_Phys_Semin_Dec 05 K. Egiyan

Main problems Nucleus Ø Strong NN (attractive and repulsive) interaction should result in Short

Main problems Nucleus Ø Strong NN (attractive and repulsive) interaction should result in Short Range Correlation (SRC) 1 . 7 f o= 0. 17 Ø 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 Nucleons 1 f 4 o JLab_Phys_Semin_Dec 05 K. Egiyan

Main topic of talk Nucleus Ø Strong NN (attractive and repulsive) interaction results in

Main topic of talk Nucleus Ø Strong NN (attractive and repulsive) interaction results in Short Range Correlation (SRC) 1 . 7 f o= 0. 17 Ø Problems should be addressed are: § § § Relative fractions of SP and SRC phases Modification of nucleons in SRC Properties of super-dens matter in SRC Ø In this talk the only first topic will be discussed : Fractions of SP and SRC phases in nuclei JLab_Phys_Semin_Dec 05 Nucleons 1 f K. Egiyan 4 o

Main topic of talk Nucleus Ø Strong NN (attractive and repulsive) interaction results in

Main topic of talk Nucleus Ø Strong NN (attractive and repulsive) interaction results in Short Range Correlation (SRC) 1 . 7 f Ø 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 f Ø In this talk the only first topic will be discussed : Fractions of SP and SRC phases in nuclei Ø What we know about SP and SRC? JLab_Phys_Semin_Dec 05 K. Egiyan

1. Evidence for NON-single particle states - Spectroscopic factor Ø In first generation of

1. Evidence for NON-single particle states - Spectroscopic factor Ø 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 Nucleus p q pi e e/ JLab_Phys_Semin_Dec 05 K. Egiyan

1. Evidence for NON-single particle states - Spectroscopic factor Ø In first generation of

1. Evidence for NON-single particle states - Spectroscopic factor Ø 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 Nucleus p Ø It was found that integral (Spectroscopic factor) ∫ Z ≡ 4 S(Ei, pi)d. Eidpi ≠ 1 ( 0. 7) q εF, p. F pi e Ø SP fractions is ≠ 1 e/ Ø Is SRC fraction 30%? ? § § § Measured results depend on integration limits SRC contribution is not excluded (estimated) FSI can affect on results Z Ø These results are impotent: they show the expected size of SRC contribution (10 -20 -30%) JLab_Phys_Semin_Dec 05 K. Egiyan

What is needed? Ø In first generation of A(e, e’p)A-1 measurements the S(Ei, pi)

What is needed? Ø 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 Nucleus Ø It was found that integral (Spectroscopic factor) ∫ Z ≡ 4 S(Ei, pi)d. Eidpi ≠ 1 ( 0. 7) q εF, p. F e Ø SP fractions is ≠ 1 e/ Ø Is SRC fraction 30%? ? § § § Measured results depend on integration limits SRC contribution is not excluded (estimated) FSI can affect on results To measure SRC fraction 1. the direct interaction reactions should be used, 2. at higher energy and momentum transfers (to resolve SRCs) Ø These results are impotent: they show the expected size of SRC contribution (10 -20 -30%) JLab_Phys_Semin_Dec 05 K. Egiyan

2. Hall C attempt for direct SRC measurement with (e, e’p) Nucleus Ø To

2. Hall C attempt for direct SRC measurement with (e, e’p) Nucleus Ø To suppress SP contributions the parallel kinematics was used p e q e/ To resolve SRC, q ≥ 1 Ge. V/c (D. Rohe et al. , PRL 93: 182501 (2004)) JLab_Phys_Semin_Dec 05 K. Egiyan

2. Hall C attempt for direct SRC measurement with (e, e’p) Nucleus Ø To

2. Hall C attempt for direct SRC measurement with (e, e’p) Nucleus Ø To suppress SP contributions the parallel kinematics was used Ø S(pm, Em) – spectral function was constricted as p Ø S(pm, Em) = d exp(A)/d theor(e. N/) Ø Certain domain in (pm, Em) plain was chosen, where SP impact expected to be small e Ø In that particular region and for only 12 C nucleus the 10% SRC involvement for protons has been obtained e/ Ø However, the total number (probability) of SRC have not been found Ø Many unclear corrections-assumptions have been made (FSI, transparency, off-shell (e. N/) cross section, SP impact, pm=pi, etc) JLab_Phys_Semin_Dec 05 q To resolve SRC, q ≥ 1 Ge. V/c (D. Rohe et al. , PRL 93: 182501 (2004)) K. Egiyan

3. Measurement of 2 N SRC relative strength in (p, 2 p+n) reaction (EVA/BNL)

3. Measurement of 2 N SRC relative strength in (p, 2 p+n) reaction (EVA/BNL) Nucleus Ø In final state the p 1, p 2 and n were detected Ø pi and γ were calculated pi Ø SP contribution was suppressed using the scaling behavior of NN interaction cross section Ø As a signature of 2 N SRC the γ > 90 o and pn > p. F cuts have been used n p p 2 γ q p 1 A. Tang, et al. , PRL 90 , 042301 (2003) JLab_Phys_Semin_Dec 05 K. Egiyan

3. Measurement of 2 N SRC relative strength in (p, 2 p+n) reaction (EVA/BNL)

3. Measurement of 2 N SRC relative strength in (p, 2 p+n) reaction (EVA/BNL) Nucleus Ø In final state the p 1, p 2 and n were detected Ø pi and γ were calculated pi Ø SP contribution was suppressed using the scaling behavior of NN interaction cross section Ø As a signature of 2 N SRC the γ > 90 o and pn > p. F cuts have been used n p p 2 γ q p 1 Ø Was found that for cosγ < 0 Ø F(pn/NN) = N[(2 pn(pn>p. F)] N[2 p] = 0. 49 ± 0. 12 Ø 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) JLab_Phys_Semin_Dec 05 K. Egiyan

4. 2 N SRC momentum distribution measurement in 3 He(e, e’pp)n; Hall-B R. Niazov,

4. 2 N SRC momentum distribution measurement in 3 He(e, e’pp)n; Hall-B R. Niazov, L. Weinstein, PRL; 92: 052303, 2004 Q 2 1 Ge. V 2 3 He Ø Detection of 2 protons in final state provides a full kinematics (c. m. ) Ø By certain kinematical cuts the 2 N SRCs [(np) and (pp)] have been separated p 2 n e p 1 q e 1 JLab_Phys_Semin_Dec 05 K. Egiyan

4. 2 N SRC momentum distribution measurement in 3 He(e, e’pp)n; Hall-B R. Niazov,

4. 2 N SRC momentum distribution measurement in 3 He(e, e’pp)n; Hall-B R. Niazov, L. Weinstein, PRL; 92: 052303, 2004 Q 2 1 Ge. V 2 3 He Ø Detection of 2 protons in final state provides a full kinematics (c. m. ) Ø By certain kinematical cuts the 2 N SRCs [(np) and (pp)] have been separated n p 1 q e e 1 Ø Two type important information was extracted: § § p 2 Momentum distributions of nucleons in SRC Momentum distribution of SRC (c. m. ) itself Ø New data at Q 2 3 Ge. V 2 are in analyzing Ø No information on strength (probabilities) of SRC are available + FSI Cross sec, fb/Me. V + FSI (c. m. ) JLab_Phys_Semin_Dec 05 K. Egiyan

These are, up to date, the published experimental data on SRC Ø We know

These are, up to date, the published experimental data on SRC Ø We know about at least two experiments, ready to present a new data § From Fermi. Lab 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 q However, probably, best way to measure the strengths of SRC is an inclusive electron scattering JLab_Phys_Semin_Dec 05 K. Egiyan

Measuring the SRC probabilities with inclusive A(e, e’) scattering Nucleus Ø There is good

Measuring the SRC probabilities with inclusive A(e, e’) scattering Nucleus Ø There is good opportunity to measure the strengths of SRCs, Ø Using the electron inclusive scattering on nuclei at high Q 2 and large x. B=Q 2/2 Mν e q e’ Back to Hofstadter! but with higher momentum transfer allowing to “look” Inside the nucleus JLab_Phys_Semin_Dec 05 K. Egiyan

Measuring the SRC probabilities with inclusive A(e, e’) scattering Nucleus Ø There is good

Measuring the SRC probabilities with inclusive A(e, e’) scattering Nucleus Ø There is good opportunity to measure the strengths of SRCs, Ø Using the electron inclusive scattering on nuclei at high Q 2 and large x. B=Q 2/2 Mν Ø Inclusive scattering has a great advantage: § FSI can be excluded (see below) e Ø However there is a big problem e’ Back to Hofstadter! but with higher momentum transfer allowing to “look” Inside the nucleus Ø Separation of (e, SRC) interaction from scattering off single nucleons JLab_Phys_Semin_Dec 05 q K. Egiyan

Separation of (e, SRC) scattering reaction Ø Selection of (e, SRC) scattering from the

Separation of (e, SRC) scattering reaction Ø Selection of (e, SRC) scattering from the large backgrounds: § § The reaction we are searching for is Inelastic (e. N) scattering (a) e/ e/ e e q Quasielastic scattering (b) q SRC A Nucleus A-2 SRC With backgrounds a) b) e e q q pi pi A JLab_Phys_Semin_Dec 05 K. Egiyan e/ A-1 A A-1

Separation of (e, SRC) scattering reaction Ø Selection of (e, SRC) scattering from the

Separation of (e, SRC) scattering reaction Ø Selection of (e, SRC) scattering from the large backgrounds: § § The reaction we are searching for is Inelastic (e. N) scattering (a) e/ e/ e e q Quasielastic scattering (b) q SRC A Nucleus A-2 SRC a) b) e e q q pi pi A e/ A-1 A x. B>1. 2 JLab_Phys_Semin_Dec 05 K. Egiyan

Separation of (e, SRC) scattering reaction Ø Selection of (e, SRC) scattering from the

Separation of (e, SRC) scattering reaction Ø Selection of (e, SRC) scattering from the large backgrounds: § § The reaction we are searching for is Inelastic (e. N) scattering (a) e/ e/ e e q Quasielastic scattering (b) q SRC A Nucleus pmin A-2 SRC a) b) e e q q pi pi A e/ A-1 A x. B>1. 2 JLab_Phys_Semin_Dec 05 K. Egiyan

Separation of (e, SRC) scattering reaction Ø Selection of (e, SRC) scattering from the

Separation of (e, SRC) scattering reaction Ø Selection of (e, SRC) scattering from the large backgrounds: § § The reaction we are using is Inelastic (e. N) scattering (a) e/ e/ e e q Quasielastic scattering (b) q SRC A Nucleus pmin A-2 SRC a) b) e e q q pi pi A A-1 pi > pmin JLab_Phys_Semin_Dec 05 K. Egiyan e/ A-1 A x. B>1. 2

Separation of (e, SRC) scattering reaction Ø Selection of (e, SRC) scattering from the

Separation of (e, SRC) scattering reaction Ø Selection of (e, SRC) scattering from the large backgrounds: § § The reaction we are searching for is Inelastic (e. N) scattering (a) e/ e/ e e q Quasielastic scattering (b) q SRC A Nucleus pmin A-2 SRC a) b) e e q q pi pi A Pmin should be found JLab_Phys_Semin_Dec 05 A-1 pi > pmin K. Egiyan e/ A-1 A x. B>1. 2

Obtaining of SRC dominant momentum region Ø Use the high momentum WF similarity for

Obtaining of SRC dominant momentum region Ø Use the high momentum WF similarity for all nuclei to obtain the onset value of pmin starting from which SRCs dominate JLab_Phys_Semin_Dec 05 K. Egiyan

Obtaining of SRC dominant momentum region Ø Use the high momentum WF similarity for

Obtaining of SRC dominant momentum region Ø Use the high momentum WF similarity for all nuclei to obtain the onset value of pmin starting from which SRCs dominate Ø Ratios of cross section from two nuclei should scale starting from pmin, where SP contribution in WF is negligible and SRC component dominates SRC region pmin JLab_Phys_Semin_Dec 05 K. Egiyan

Obtain the SRC dominant region in corresponding (Q 2, x. B) space Ø Use

Obtain the SRC dominant region in corresponding (Q 2, x. B) space Ø Use the high momentum WF similarity for all nuclei to obtain the onset value of pmin starting from which SRCs dominate Ø Ratios of cross section from two nuclei should scale starting from pmin, where SP contribution in WF is negligible and SRC component dominates Ø SRC region For A(e, e’) scattering off SP any combination of measured Q 2 and x. B allows to calculate the pmin = pmin(Q 2, x. B) e/ e q pi JLab_Phys_Semin_Dec 05 -pi A-1 K. Egiyan pmin

Obtain the SRC dominant region in corresponding (Q 2, x. B) space Ø Use

Obtain the SRC dominant region in corresponding (Q 2, x. B) space Ø Use the high momentum WF similarity for all nuclei to obtain the onset value of pmin starting from which SRCs dominate Ø Ratios of cross section from two nuclei should scale starting from pmin, where SP contribution in WF is negligible and SRC component dominates SRC region Ø For A(e, e’) scattering off SP any combination of measured Q 2 and x. B allows to calculate the pmin = pmin(Q 2, x. B) Ø Ratios of cross section from two nuclei should scale at corresponding (Q 2, x. B) combination pmin Francfurt, Strikman, PR, ’ 81; ’ 88 JLab_Phys_Semin_Dec 05 K. Egiyan

Use A(e, e’) cross section ratios to measure SRC probabilities Ø Use the high

Use A(e, e’) cross section ratios to measure SRC probabilities Ø Use the high momentum WF similarity for all nuclei to obtain the onset value of pmin starting from which SRCs dominate, Ø Ratios of cross section from two nuclei should scale starting from pmin, where SP contribution in WF is negligible and SRC component dominates SRC region Ø For A(e, e’) scattering off SP any combination of measured Q 2 and x. B allows to calculate the pmin = pmin(Q 2, x. B) Ø Ratios of cross section from two nuclei should scale at corresponding (Q 2, x. B) combination Ø In SRC model the scaling factor (SF) indicate the ratio of SRC probabilities a 2 N(A 1) and a 2 N(A 2) in nuclei A 1 and A 2: SF = a 2(A 1/A 2) = a (A ) 2 N 1 a 2 N(A 2) pmin SF Francfurt, Strikman, PR, ’ 81; ’ 88 JLab_Phys_Semin_Dec 05 K. Egiyan

To check this idea SLAC existing data were reanalyzed Ø The old SLAC data

To check this idea SLAC existing data were reanalyzed Ø 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 JLab_Phys_Semin_Dec 05 Frankfurt, Strikman, Day, Sargsian, Phys. Rev. C ‘ 93 K. Egiyan

To check this idea SLAC existing data were reanalyzed Ø The old SLAC data

To check this idea SLAC existing data were reanalyzed Ø 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 However Ø Data for nuclei A and for D were measured in large difference of kinematics, theoretical calculation were used to obtain data at the same Q 2 and x. B for heavy nuclei and D Ø Absolute probabilities were no able to obtain Ø x. B interval used was limited (<1. 6) Ø Systematic and dedicated measurements are needed JLab_Phys_Semin_Dec 05 K. Egiyan

Final State Interaction in (e, SRC) Scattering q Struck nucleon interacts with other nucleon(s)

Final State Interaction in (e, SRC) Scattering q Struck nucleon interacts with other nucleon(s) from the same SRC § q q SRC A This interaction is much weaker since relative momenta are larger and they are spatially more separated FSI is primarily localized in SRC JLab_Phys_Semin_Dec 05 Nf Ni A-1 FSIs Interaction of nucleons with nucleons from the A-2 residual § q This interaction is much stronger since relative momenta are smaller and they are spatially closer e/ e K. Egiyan

More localization of Final State Interaction in SRC q q q In QM there

More localization of Final State Interaction in SRC q q q In QM there is some distance (r) where FSI still can affect on (e, Ni ) interaction. Q 2 Ge. V 2 At > 1. 5 and x. B > 1. 3 the maximum value r is < 1 fm. Since RSRC r, the FSI of nucleons from the same SRC only can 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!! q SRC A r Nf Ni A-1 FSIs FSSD-Phys. Rev. C’ 93 rmax (fm) q e/ e Q 2 (Ge. V 2) JLab_Phys_Semin_Dec 05 K. Egiyan

Our experiment Ø Experiment has been performed at JLab with CLAS detector at beam

Our experiment Ø Experiment has been performed at JLab with CLAS detector at beam energy 4. 46 and 4. 7 Ge. V at E 2 Run Ø 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 Ø A(e, e’) inclusive reaction was measured Ø Standard fiducial cuts and momentum corrections were applied Ø 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 Ge. V 2 range, at x. B at > 0. 8 Ø Obtained ratios (or cross sections) were corrected on § § Acceptances Radiative effects Energy small difference - contamination JLab_Phys_Semin_Dec 05 K. Egiyan

Measured ratios of per-nucleon cross sections at Q 2>1. 4 Ge. V 2 and

Measured ratios of per-nucleon cross sections at Q 2>1. 4 Ge. V 2 and x. B<2 r(A/3 He) = K(Q 2) 3 A(Q 2, x. B) A He 3(Q 2, x. B) where K(Q 2) = A(2 p+ n) 3(Z p+N n) 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 JLab_Phys_Semin_Dec 05 K. Egiyan

Measured ratios of per-nucleon cross sections at Q 2>1. 4 Ge. V 2 and

Measured ratios of per-nucleon cross sections at Q 2>1. 4 Ge. V 2 and x. B<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) JLab_Phys_Semin_Dec 05 K. Egiyan

Measured ratios of per-nucleon cross sections at Q 2>1. 4 Ge. V 2 and

Measured ratios of per-nucleon cross sections at Q 2>1. 4 Ge. V 2 and x. B<2 Observation 1 Scaling exist; Observation 2 Scaling factors (SF) are measured; SF JLab_Phys_Semin_Dec 05 K. Egiyan

Measured ratios of per-nucleon cross sections at Q 2>1. 4 Ge. V 2 and

Measured ratios of per-nucleon cross sections at Q 2>1. 4 Ge. V 2 and x. B<2 Observation 1 Scaling exist; Observation 2 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 3 He SF JLab_Phys_Semin_Dec 05 K. Egiyan

Measurement of 2 -Nuclon SRC relative probabilities Observation 1 Scaling exist; Observation 2 Scaling

Measurement of 2 -Nuclon SRC relative probabilities Observation 1 Scaling exist; Observation 2 Scaling factors (SF) are measured; a 2 N(4 He) a 2 N(3 He) =1. 93± 0. 02± 0. 14 a 2 N(12 C) a 2 N(3 He) =2. 41± 0. 02± 0. 17 SF a 2 N(56 Fe) =2. 83± 0. 03± 0. 18 a 2 N(3 He) JLab_Phys_Semin_Dec 05 K. Egiyan

Measurement of 2 -Nuclon SRC relative probabilities Observation 1 Scaling exist; Observation 2 Scaling

Measurement of 2 -Nuclon SRC relative probabilities Observation 1 Scaling exist; Observation 2 Scaling factors (SF) are measured; a 2 N(4 He) a 2 N(3 He) =1. 93± 0. 02± 0. 14 a 2 N(12 C) a 2 N(3 He) =2. 41± 0. 02± 0. 17 SF a 2 N(56 Fe) =2. 83± 0. 03± 0. 18 a 2 N(3 He) Thus, Chances for every nucleon in 4 He, 12 C and 56 Fe to be involved in 2 N SRC are 1. 93, 2. 41 and 2. 83 times larger than in 3 He JLab_Phys_Semin_Dec 05 K. Egiyan

Measurement of 2 -Nuclon SRC absolute probabilities Observation 1 Scaling exist; Observation 2 Observation

Measurement of 2 -Nuclon SRC absolute probabilities Observation 1 Scaling exist; Observation 2 Observation 3 Scaling factors (SF) are measured; Scaling onsets (SO) are measured a 2 N(4 He) a 2 N(3 He) =1. 93± 0. 02± 0. 14 a 2 N(12 C) a 2 N(3 He) =2. 41± 0. 02± 0. 17 SF a 2 N(56 Fe) =2. 83± 0. 03± 0. 18 a 2 N(3 He) SO JLab_Phys_Semin_Dec 05 K. Egiyan

Measurement of 2 -Nuclon SRC absolute probabilities Observation 1 Scaling exist; Observation 2 Observation

Measurement of 2 -Nuclon SRC absolute probabilities Observation 1 Scaling exist; Observation 2 Observation 3 Scaling factors (SF) are measured; Scaling onsets (SO) are measured a 2 N(4 He) a 2 N(3 He) =1. 93± 0. 02± 0. 14 SO measurement allows to find a 2 N(3 He) using the wave functions of 3 He and Deuterium a 2 N(12 C) a 2 N(3 He) =2. 41± 0. 02± 0. 17 SF a 2 N(56 Fe) =2. 83± 0. 03± 0. 18 a 2 N(3 He) SO JLab_Phys_Semin_Dec 05 K. Egiyan

Calculation of a 2 N(3 He) using 3 He and 2 H wave functions

Calculation of a 2 N(3 He) using 3 He and 2 H wave functions Ø a 2 N (3 He) = a 2 N(3 He) 2 H) x a ( 2 2 N a 2 N( H) SF JLab_Phys_Semin_Dec 05 K. Egiyan

Calculation of a 2 N(3 He) using 3 He and 2 H wave functions

Calculation of a 2 N(3 He) using 3 He and 2 H wave functions Ø Ø a 2 N (3 He) a 2 N(3 He) = a (2 H) x a 2 N(2 H) 2 N From the calculated ratio r(3 He/2 H) a 2 N(3 He) SF = a (2 H) = 2 ± 0. 1 2 N Ø SF And a 2 N(3 He) = (2 ± 0. 1) x a 2 N(2 H) JLab_Phys_Semin_Dec 05 K. Egiyan

Calculation of a 2 N(3 He) using 3 He and 2 H wave functions

Calculation of a 2 N(3 He) using 3 He and 2 H wave functions Ø Ø a 2 N (3 He) = a 2 N(3 He) x a 2 N(2 H) From the calculated ratio r(3 He/2 H) a 2 N(3 He) SF = = 2 ± 0. 1 a 2 N(2 H) Ø SF And a 2 N(3 He) = (2 ± 0. 1) x a 2 N(2 H) Ø To calculate a 2 N(2 H) we use § § 2 H Wave Function Measured pmin(Q 2 onset, x. Bonset) =275± 25 Me. V Deuterium Wave Function pmin Ø Integral over deuterium wave function in pi > pmin region is just a 2 N(2 H) Ø Thus, definition of SRC is - the relative momentum of nucleons in SRC > 275 Me. V/c § § a 2 N(2 H) = 0. 040 ± 0. 007 a 2 N(3 He) = 0. 080 ± 0. 016 JLab_Phys_Semin_Dec 05 (4. +0. 8)% K. Egiyan

Measurement of 2 -Nuclon SRC absolute probabilities Observation 1 Scaling exist; Observation 2 Observation

Measurement of 2 -Nuclon SRC absolute probabilities Observation 1 Scaling exist; Observation 2 Observation 3 Scaling factors (SF) are measured; Scaling onsets (SO) are measured a 2 N(4 He) a 2 N(3 He) =1. 93± 0. 02± 0. 14 = 0. 080+0. 016 a 2 N(12 C) a 2 N(3 He) =2. 41± 0. 02± 0. 17 SF a 2 N(56 Fe) =2. 83± 0. 03± 0. 18 a 2 N(3 He) SO JLab_Phys_Semin_Dec 05 K. Egiyan

Measurement of 2 -Nuclon SRC absolute probabilities Observation 1 Scaling exist; Observation 2 Observation

Measurement of 2 -Nuclon SRC absolute probabilities Observation 1 Scaling exist; Observation 2 Observation 3 Scaling factors (SF) are measured; Scaling onsets (SO) are measured a 2 N(4 He) = 0. 154± 0. 002± 0. 033 a 2 N(12 C) = 0. 193± 0. 002± 0. 041 SF a 2 N(56 Fe) = 0. 23± 0. 002± 0. 047 SO JLab_Phys_Semin_Dec 05 K. Egiyan

Measurement of 2 -Nuclon SRC absolute probabilities Observation 1 Scaling exist; Observation 2 Observation

Measurement of 2 -Nuclon SRC absolute probabilities Observation 1 Scaling exist; Observation 2 Observation 3 Scaling factors (SF) are measured; Scaling onsets (SO) are measured a 2 N(4 He) = 0. 154± 0. 002± 0. 033 a 2 N(12 C) = 0. 193± 0. 002± 0. 041 SF a 2 N(56 Fe) = 0. 23± 0. 002± 0. 047 SO JLab_Phys_Semin_Dec 05 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 K. Egiyan

In other words Ø In any moment in 12 C one can be seen

In other words Ø In any moment in 12 C one can be seen one 2 N SRC 12 C Ø While in any moment in 56 Fe one can exist six 2 N SRC JLab_Phys_Semin_Dec 05 56 Fe K. Egiyan

We measure directly a 2 -nucleon SRC numbers (probabilities) But it is still not

We measure directly a 2 -nucleon SRC numbers (probabilities) But it is still not enough to know a full nucleonic picture of nuclei Fractions Nucleus Single particle (%) 2 N SRC (%) 3 N(and more. N) 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 ----- We need to measure 3 -and-more-nucleonic SRC fraction JLab_Phys_Semin_Dec 05 K. Egiyan

Importance of measurements at x. B > 2 Ø Is not only to get

Importance of measurements at x. B > 2 Ø Is not only to get the data on 3 -nucleon SRC Ø But also to prove the interpretations of obtained data at x. B< 2 by the SRC model Ø 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 Jth power of nuclear density (J is order of SRC) aj. N ∫ JA(r)dr The step should increase with A Ø We measure the cross section ratios at 2 < x. B < 3, for the first time JLab_Phys_Semin_Dec 05 K. Egiyan

Ratios of per-nucleon cross sections at Q 2>1. 4 Ge. V 2 and x.

Ratios of per-nucleon cross sections at Q 2>1. 4 Ge. V 2 and x. B < 3 Observation 1 2 nd Scaling exist; Existence of step (second scaling level) Is very strong argument for SRC model JLab_Phys_Semin_Dec 05 K. Egiyan

Ratios of per-nucleon cross sections at Q 2>1. 4 Ge. V 2 and x.

Ratios of per-nucleon cross sections at Q 2>1. 4 Ge. V 2 and x. B < 3 Observation 1 2 nd Scaling exist; Observation 2 2 nd Scaling factors (SF) are measured; In SRC model the measured scaling factors are just a ratios of 3 -nucleon SRC probabilities in nucleus A and 3 He SF JLab_Phys_Semin_Dec 05 K. Egiyan

Measurement of 3 -Nuclon SRC relative probabilities Observation 1 2 nd Scaling exist; Observation

Measurement of 3 -Nuclon SRC relative probabilities Observation 1 2 nd Scaling exist; Observation 2 2 nd Scaling factors (SF) are measured; a 3 N(4 He) a 3 N(3 He) = 2. 33± 0. 12± 0. 19 a 3 N(12 C) a 3 N(3 He) = 3. 05± 0. 14± 0. 22 SF a 3 N(56 Fe) a 3 N(3 He) = 4. 38± 0. 18± 0. 33 JLab_Phys_Semin_Dec 05 K. Egiyan

Measurement of 3 -Nuclon SRC relative probabilities Observation 1 2 nd Scaling exist; Observation

Measurement of 3 -Nuclon SRC relative probabilities Observation 1 2 nd Scaling exist; Observation 2 2 nd Scaling factors (SF) are measured; a 3 N(4 He) a 3 N(3 He) = 2. 33± 0. 12± 0. 19 a 3 N(12 C) a 3 N(3 He) = 3. 05± 0. 14± 0. 22 SF a 3 N(56 Fe) a 3 N(3 He) = 4. 38± 0. 18± 0. 33 Chances for every nucleon in 4 He, 12 C and 56 Fe to be involved in 3 N SRC are 2. 33, 3. 05 and 4. 38 times larger than in 3 He itself JLab_Phys_Semin_Dec 05 K. Egiyan

Measurement of 3 -Nuclon SRC absolute probabilities Observation 1 2 nd Scaling exist; Observation

Measurement of 3 -Nuclon SRC absolute probabilities Observation 1 2 nd Scaling exist; Observation 2 Observation 3 2 nd Scaling factors (SF) are measured; 2 nd Scaling onsets (SO) are measured a 3 N(4 He) a 3 N(3 He) = 2. 33± 0. 12± 0. 19 a 3 N(12 C) a 3 N(3 He) =3. 05± 0. 14± 0. 22 SF a 3 N(56 Fe) a 3 N(3 He) = 4. 38± 0. 18± 0. 33 SO JLab_Phys_Semin_Dec 05 K. Egiyan

Measurement of 3 -Nuclon SRC absolute probabilities Observation 1 2 nd Scaling exist; Observation

Measurement of 3 -Nuclon SRC absolute probabilities Observation 1 2 nd Scaling exist; Observation 2 Observation 3 2 nd Scaling factors (SF) are measured; 2 nd Scaling onsets (SO) are measured a 3 N(4 He) a 3 N(3 He) = 2. 33± 0. 12± 0. 19 Measurement of SO allows to calculate the a 3 N(3 He) using the 3 He wave function a 3 N(12 C) a 3 N(3 He) =3. 05± 0. 14± 0. 22 SF a 3 N(56 Fe) a 3 N(3 He) = 4. 38± 0. 18± 0. 33 SO JLab_Phys_Semin_Dec 05 K. Egiyan

Measurement of 3 -Nuclon SRC absolute probabilities Observation 1 2 nd Scaling exist; Observation

Measurement of 3 -Nuclon SRC absolute probabilities Observation 1 2 nd Scaling exist; Observation 2 Observation 3 2 nd Scaling factors (SF) are measured; 2 nd Scaling onsets (SO) are measured a 3 N(4 He) a 3 N(3 He) = 2. 33± 0. 12± 0. 19 = 0. 0018± 0. 0006 (M. Sargsyan’s calculations) a 3 N(12 C) a 3 N(3 He) =3. 05± 0. 14± 0. 22 SF a 3 N(56 Fe) a 3 N(3 He) = 4. 38± 0. 18± 0. 33 SO JLab_Phys_Semin_Dec 05 K. Egiyan

Measurement of 3 -Nuclon SRC absolute probabilities Observation 1 2 nd Scaling exist; Observation

Measurement of 3 -Nuclon SRC absolute probabilities Observation 1 2 nd Scaling exist; Observation 2 Observation 3 2 nd Scaling factors (SF) are measured; 2 nd Scaling onsets (SO) are measured (%) a 3 N(4 He)= 0. 42± 0. 02± 0. 14 a 3 N(12 C)= 0. 55± 0. 03± 0. 18 SF a 3 N(56 Fe)= 0. 79± 0. 03± 0. 25 SO JLab_Phys_Semin_Dec 05 K. Egiyan

Measurement of 3 -Nuclon SRC absolute probabilities Observation 1 2 nd Scaling exist; Observation

Measurement of 3 -Nuclon SRC absolute probabilities Observation 1 2 nd Scaling exist; Observation 2 Observation 3 2 nd Scaling factors (SF) are measured; 2 nd Scaling onsets (SO) are measured (%) a 3 N(4 He)= 0. 42± 0. 02± 0. 14 a 3 N(12 C)= 0. 55± 0. 03± 0. 18 SF a 3 N(56 Fe)= 0. 79± 0. 03± 0. 25 SO JLab_Phys_Semin_Dec 05 Per-nucleon probabilities of 3 N SRC are smaller then the same probabilities of 2 N SRC more the one order of magnitude K. Egiyan

Having these data, we know almost full ( 99%) nucleonic picture of nuclei with

Having these data, we know almost full ( 99%) nucleonic picture of nuclei with A 56 Fractions Nucleus Single particle (%) 2 N 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 2 H 96 ± 0. 7 4. 0 ± 0. 7 ----- JLab_Phys_Semin_Dec 05 K. Egiyan 3 N SRC (%) ± 0. 06

Comparisons with some theoretical predictions on SRC probabilities 1. SRC model Fractions Single particle

Comparisons with some theoretical predictions on SRC probabilities 1. SRC model Fractions Single particle (%) 2 N SRC (%) Exp SRC 3 N SRC (%) Exp SRC Nucleus Fe/C= 1. 43 ± 0. 15 23. 0 ± 4. 7 25. 5 0. 79± 0. 25 12 C 19. 3 ± 4. 1 20. 3 0. 55± 0. 18 4 He 15. 4 ± 3. 3 16. 2 0. 42± 0. 14 ----- Fe/C = 1. 4 56 Fe 3 He 8. 0 ± 1. 6 ---- 0. 18± 0. 06 ----- 2 H 4. 0 ± 0. 7 ----- SRC predictions are remarkably close to experiment JLab_Phys_Semin_Dec 05 K. Egiyan

Comparisons with some theoretical predictions on SRC probabilities 2. QCM model 1. SRC model

Comparisons with some theoretical predictions on SRC probabilities 2. QCM model 1. SRC model Fractions Single particle (%) 2 N SRC (%) Exp SRC 3 N SRC (%) QCM Exp SRC QCM Nucleus 23. 0 ± 4. 7 25. 5 14. 6 0. 79± 0. 25 3. 6 12 C 19. 3 ± 4. 1 20. 3 12. 5 0. 55± 0. 18 Fe/C = 1. 4 Fe/C= 1. 43 ± 0. 15 56 Fe 4 He 15. 4 ± 3. 3 16. 2 16. 6 0. 42± 0. 14 ----- 4. 7 2. 6 3 He 8. 0 ± 1. 6 ---- 13. 4 0. 18± 0. 06 ----- 2. 2 2 H 4. 0 ± 0. 7 ----- ----- In QCM => Quark-Cluster-Model (unrealistic model in our Q 2 range) 2 N SRC ===> 6 q Bag; 3 N SRC ===> 9 q Bag QCM predictions for 2 N SRC are close to experiment, while for 3 N SRC almost 10 times are higher JLab_Phys_Semin_Dec 05 K. Egiyan

Having these data, we know almost full ( 99%) nucleonic picture of nuclei with

Having these data, we know almost full ( 99%) nucleonic picture of nuclei with A 56 Fractions Nucleus Single particle (%) 2 N SRC (%) 3 N 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 2 H 96 ± 0. 7 4. 0 ± 0. 7 ----- The similar data for heavier (A>56) nuclei is important, Hall C data will be available soon (J. Arrington et al. , ) JLab_Phys_Semin_Dec 05 K. Egiyan ± 0. 06

SUMMARY Ø Existing experimental date indicate the presence of SRCs in nuclei, however, there

SUMMARY Ø Existing experimental date indicate the presence of SRCs in nuclei, however, there are no “exact” measurements of their probabilities Ø Inclusive A(e, e’) scattering is effective tool for these type measurements Ø 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< x. B < 3 region at Q 2 >1. 4 Ge. V 2 Ø Two scaling regions - at 1. 5 < x. B < 2 and x. B > 2. 25 - are observed Ø 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 Ø 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 Ø In the framework of SRC model the nucleonic picture of nuclei with A 56 is established JLab_Phys_Semin_Dec 05 K. Egiyan

Supporting Slides JLab_Phys_Semin_Dec 05 K. Egiyan

Supporting Slides JLab_Phys_Semin_Dec 05 K. Egiyan

Having these data, we know almost full ( 99%) nucleonic picture of nuclei with

Having these data, we know almost full ( 99%) nucleonic picture of nuclei with A 56 Fractions Nucleus Single particle (%) 2 N SRC (%) 3 N 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 2 H 96 ± 0. 8 4. 0 ± 0. 8 ----- ± 0. 06 Using the published data on (p, 2 p+n) [PRL, 90 (2003) 042301] estimate the isotopic composition of 2 N SRC in 12 C a pp(12 C) a 2 N(12 C) 20 ± 0. 2 ± 4. 1 % JLab_Phys_Semin_Dec 05 4± 2% 12 ± 4 % ann(12 C) 4 ± 2 % apn(12 C) K. Egiyan

The Ratios at 1<x. B<2; Observation of Scaling § Analyze the ratio as a

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 § Shown results are for 56 Fe § Results for 12 C and 4 He are similar • • Ratios SCALE at Q 2 > 1. 4 Ge. V 2 Ø Onset of scaling is at x. B ≥ 1. 5 Scaling vanishes at low Q 2 JLab_Phys_Semin_Dec 05 K. Egiyan

Q 2 scaling of relative probabilities a 2 and a 3 in Q 2

Q 2 scaling of relative probabilities a 2 and a 3 in Q 2 = 1. 4 – 2. 6 Ge. V 2 region JLab_Phys_Semin_Dec 05 K. Egiyan

Calculation of a 2 N(3 He) using 3 He and 2 H wave functions

Calculation of a 2 N(3 He) using 3 He and 2 H wave functions Ø Ø a 2 N (3 He) a 2 N(3 He) = x a 2 N(2 H) From the calculated ratio r(3 He/2 H) a 2 N(3 He) SF = = 2 ± 0. 1 a 2 N(2 H) Ø SF And a 2 N(3 He) = (2 ± 0. 1) x a 2 N(2 H) JLab_Phys_Semin_Dec 05 K. Egiyan

Contributing diagrams in 2<x. B<3 region Three states can contribute: q p 3 -nucleon

Contributing diagrams in 2<x. B<3 region Three states can contribute: q p 3 -nucleon SRCs in “ 2 -body” and “Star” configurations, 2 N - SRC -p p -p q 2 p 2 -nucleon SRC, due to the c. m. motion p § In x. B > 2 region “ 2 - Body” configurationp 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 JLab_Phys_Semin_Dec 05 p “Star” K. Egiyan “ 2 - Body” 3 N - SRC

Contributing diagrams in 2<x. B<3 region Three states can contribute: q p 3 -nucleon

Contributing diagrams in 2<x. B<3 region Three states can contribute: q p 3 -nucleon SRCs in “ 2 -body” and “Star” configurations, 2 N - SRC -p p -p q 2 p 2 -nucleon SRC, due to the c. m. motion p § In x. B > 2 region “ 2 - Body” configurationp 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 (pmin > 500 Me. V/c) only “ 2 Body” configuration is contributing JLab_Phys_Semin_Dec 05 p “Star” K. Egiyan “ 2 - Body” 3 N - SRC

Radiative Corrections 3 He 4 He 12 C 56 Fe JLab_Phys_Semin_Dec 05 K. Egiyan

Radiative Corrections 3 He 4 He 12 C 56 Fe JLab_Phys_Semin_Dec 05 K. Egiyan