jlab_phys_semin_dec05 k. egiyan today’s nucleonic picture of nuclei kim egiyan yerevan physics...

JLab_Phys_Semin_Dec05 K. Egiyan

Today’s Nucleonic Picture of Nuclei

Kim Egiyan Yerevan Physics Institute, Armenia

and

Jefferson Lab, USA


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 A1/3

This was strong evidence that nuclei are composed from the SP, in other words,

they are a bags with Fermi gas!!

Nucleus

e

e/

q (low)


Other possible components

HOWEVER

Strong NN (attractive and repulsive) interaction should result in Short Range Correlation (SRC)

1.7f

Nucleons

Nucleus

o= 0.17


Other possible components

HOWEVER


So, nuclear Hamiltonian should include

H = p2/2M + V2(r1,r2) + V3(r1,r2,r3) + ….

the correlation terms Vi

1.7f

Nucleons

Nucleus

o= 0.17


Main problems


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

4o


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

4o


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


1. Evidence for NON-single particle states - Spectroscopic factor

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

ee/

q

p

pi


1. Evidence for NON-single particle states - Spectroscopic factor



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(Ei,pi)dEidpi ≠ 1 (0.7)

ee/

q

p

εF,pFpi

Z


What is needed?



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(Ei,pi)dEidpi ≠ 1 (0.7)

ee/

qεF,pF

To measure SRC fraction 1. the direct interaction reactions

should be used,2. at higher energy and momentum

transfers (to resolve SRCs)


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/

q

p


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

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)

Nucleus

To resolve SRC, q ≥ 1 GeV/c

(D.Rohe et al., PRL 93:182501 (2004))

e

e/

q

p


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

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 the γ > 90o and

pn > pF cuts have been used

Nucleus

p

p1

q

p2n γ

pi

A. Tang, et al., PRL 90 ,042301 (2003)


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

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 the γ > 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)

Nucleus

p

p1

q

p2n γ

pi

N[(2pn(pn>pF)] N[2p]


4. 2N SRC momentum distribution measurement in 3He(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

3He

e

e1

q

p2

n

p1

R.Niazov, L. Weinstein, PRL;92:052303, 2004

(c.m.)

Q21 GeV2


4. 2N SRC momentum distribution measurement in 3He(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

3He

e

e1

q

p2

n

p1

R.Niazov, L. Weinstein, PRL;92:052303, 2004

(c.m.)

Q21 GeV2

Q23 GeV2

Cro

ss

se

c,

fb/M

eV

+ FSI + FSI

(c.m.)


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


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 Q2 and large xB=Q2/2Mν

Nucleus

e

e’

q

Back to Hofstadter! but with higher momentum transfer allowing to “look” Inside the nucleus


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 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

Nucleus

e

e’

q

Back to Hofstadter! but with higher momentum transfer allowing to “look” Inside the nucleus


Separation of (e,SRC) scattering reaction Selection of (e,SRC) scattering

from the large backgrounds:

Inelastic (eN) scattering (a)

Quasielastic scattering (b)

Nucleus

ee/

q

SRC

A-1A

ee/

A-2

ee/

SRC

q

q

A

pi

A

eq

pi

The reaction we are searching for is

a)b)

A-1

With backgrounds


Separation of (e,SRC) scattering reaction

Selection of (e,SRC) scattering from the large backgrounds:



Nucleus

ee/

q

SRC

A-1A

ee/

A-2

ee/

SRC

q

q

A

pi

A

eq

pi

a)b)

A-1

xB>1.2



Separation of (e,SRC) scattering reaction

Selection of (e,SRC) scattering from the large backgrounds:



Nucleus

ee/

q

SRC

A-1A

ee/

A-2

ee/

SRC

q

q

A

pi

A

eq

pi

a)b)

A-1

xB>1.2

pmin







Nucleus

ee/

q

SRC

A-1A

ee/

A-2

ee/

SRC

q

q

A

pi

A

eq

pi

The reaction we are using is

a)b)

A-1

xB>1.2

pmin

pi > pmin






Nucleus

ee/

q

SRC

A-1A

ee/

A-2

ee/

SRC

q

q

A

pi

A

eq

pi

a)b)

A-1

xB>1.2

pmin

pi > pminPmin should be found



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


Obtaining of SRC dominant momentum region


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


Obtain the SRC dominant region in corresponding (Q2, xB) space





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

pi

-pi

A-1

ee/

q


Obtain the SRC dominant region in corresponding (Q2, xB) space






Ratios of cross section from two nuclei should scale at corresponding (Q2, xB) combination

SRC region

pmin

Francfurt, Strikman, PR, ’81;’88


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 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

a2N(A1)a2N(A2)

SF

pmin

Francfurt, Strikman, PR, ’81;’88


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


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 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

Frankfurt,Strikman,Day, Sargsian, Phys.Rev. C ‘93


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-1N i

Nf

e e/

q

N i

e e/

q

SRC

FSIs


More localization of Final State Interaction in SRC

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 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!!

FSSD-Phys.Rev.C’93

AN i

e e/

q r

r max

(fm

)

Q2 (GeV2)

SRC

A A-1N i

Nf

e e/

q

N i

e e/

q

SRC

FSIs


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 A2 we choose 3He 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


Measured ratios of per-nucleon cross sections at Q2>1.4 GeV2 and xB<2

r(A/3He) = K(Q2)3A(Q2,xB)

AHe3(Q2,xB)

K(Q2) = A(2p+ n)3(Z p+N n)

where

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



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)



Scaling exist; Scaling factors (SF) are measured;

Observation 1

SF

Observation 2




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 3He


Measurement of 2-Nuclon SRC relative probabilities


Observation 1

SF

a2N(4He)a2N(3He)

=1.93±0.02±0.14

a2N(12C)a2N(3He)

=2.41±0.02±0.17

a2N(56Fe)a2N(3He)

=2.83±0.03±0.18

Observation 2




Observation 1

SF

a2N(4He)a2N(3He)

=1.93±0.02±0.14

a2N(12C)a2N(3He)

=2.41±0.02±0.17

a2N(56Fe)a2N(3He)

=2.83±0.03±0.18

Observation 2

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


Measurement of 2-Nuclon SRC absolute probabilities

Scaling exist; Scaling factors (SF) are measured; Scaling onsets (SO) are measured

Observation 1

SF

SO

a2N(4He)a2N(3He)

=1.93±0.02±0.14

a2N(12C)a2N(3He)

=2.41±0.02±0.17

a2N(56Fe)a2N(3He)

=2.83±0.03±0.18

Observation 2 Observation 3




Observation 1

SF

SO

a2N(4He)a2N(3He)

=1.93±0.02±0.14

a2N(12C)a2N(3He)

=2.41±0.02±0.17

a2N(56Fe)a2N(3He)

=2.83±0.03±0.18


SO measurement allows to find a2N(3He) using the wave functions of 3He and Deuterium


Calculation of a2N(3He) using 3He and 2H wave functions

a2N(3He) = x a2N(2H)

a2N(3He) a2N(2H)

SF



a2N(3He) = x a2N(2H)

From the calculated ratio r(3He/2H)

SF = = 2 ± 0.1

And a2N(3He) = (2 ± 0.1) x a2N(2H)

a2N(3He) a2N(2H)

a2N(3He) a2N(2H) SF



a2N(3He) = x a2N(2H) From the calculated ratio r(3He/2H)

SF = = 2 ± 0.1

And a2N(3He) = (2 ± 0.1) x a2N(2H)

To calculate a2N(2H) we use 2H Wave Function Measured pmin(Q2

onset,xBonset) =275±25 MeV

Integral over deuterium wave function in pi > pmin region is just 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

pmin

(4.+0.8)%

Deuterium Wave Function

a2N(3He) a2N(2H)

a2N(3He) a2N(2H) SF




Observation 1

SF

SO

a2N(4He)a2N(3He)

=1.93±0.02±0.14

a2N(12C)a2N(3He)

=2.41±0.02±0.17

a2N(56Fe)a2N(3He)

=2.83±0.03±0.18

= 0.080+0.016





Observation 1

SF

SO

a2N(4He) = 0.154±0.002±0.033

a2N(12C) = 0.193±0.002±0.041

a2N(56Fe) = 0.23±0.002±0.047





Observation 1

SF

SO

a2N(4He) = 0.154±0.002±0.033

a2N(12C) = 0.193±0.002±0.041

a2N(56Fe) = 0.23±0.002±0.047


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


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

56Fe

12C


We measure directly a 2-nucleon SRC numbers (probabilities)

Single particle (%) 2N SRC (%) 3N(and moreN) SRC (%)

56Fe ???? 23.0 ± 0.2 ± 4.7 ????

12C ???? 19.3 ± 0.2 ± 4.1 ????

4He ???? 15.4 ± 0.2 ± 3.3 ????

3He ???? 8.0 ± 1.6 -----

2H 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


Importance of measurements at xB > 2

Is not only to get the data on 3-nucleon SRC

But also to prove the interpretations of obtained data at xB< 2 by the SRC model

SRC model predicts: Existence of “positive” step in xB – dependence of cross section ratios at 2<xB<3, due

to the proportionality of aJN to the Jth power of nuclear density (J is order of SRC)

ajN ∫JA(r)dr

The step should increase with A

We measure the cross section ratios at 2 < xB < 3, for the first time


Ratios of per-nucleon cross sections at Q2>1.4 GeV2 and xxB B < 3< 3

Observation 1

2nd Scaling exist;

Existence of step (second scaling level) Is very strong argument for SRC model


Ratios of per-nucleon cross sections at Q2>1.4 GeV2 and xxB B < 3< 3


2nd 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 3He





SF

a3N(4He)a3N(3He)

a3N(12C)a3N(3He)

a3N(56Fe)a3N(3He)

= 2.33±0.12±0.19

= 3.05±0.14±0.22

= 4.38±0.18±0.33





SF

a3N(4He)a3N(3He)

a3N(12C)a3N(3He)

a3N(56Fe)a3N(3He)

= 2.33±0.12±0.19

= 3.05±0.14±0.22

= 4.38±0.18±0.33

Chances for every nucleon in 4He, 12C and 56Fe to be involved in 3N SRC are 2.33, 3.05 and 4.38 times larger than in 3He itself



Observation 1 Observation 2 Observation 3

2nd Scaling exist; 2nd Scaling factors (SF) are measured; 2nd Scaling onsets (SO) are measured

SF

a3N(4He)a3N(3He)

a3N(12C)a3N(3He)

a3N(56Fe)a3N(3He)

= 2.33±0.12±0.19

=3.05±0.14±0.22

= 4.38±0.18±0.33

SO





SF

a3N(4He)a3N(3He)

a3N(12C)a3N(3He)

a3N(56Fe)a3N(3He)

= 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 a3N(3He) using the 3He wave function





SF

a3N(4He)a3N(3He)

a3N(12C)a3N(3He)

a3N(56Fe)a3N(3He)

= 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)





SF

SO

a3N(4He)= 0.42±0.02±0.14

(%)

a3N(12C)= 0.55±0.03±0.18

a3N(56Fe)= 0.79±0.03±0.25





SF

SO

a3N(4He)= 0.42±0.02±0.14

(%)

a3N(12C)= 0.55±0.03±0.18

a3N(56Fe)= 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


Having these data, we know almost full (99%) nucleonic picture of nuclei with A 56

Single particle (%) 2N SRC (%) 3N SRC (%)

56Fe 76 ± 0.2 ± 4.7 23.0 ± 0.2 ± 4.7 0.79 ± 0.03 ± 0.25

12C 80 ± 02 ± 4.1 19.3 ± 0.2 ± 4.1 0.55 ± 0.03 ± 0.18

4He 86 ± 0.2 ± 3.3 15.4 ± 0.2 ± 3.3 0.42 ± 0.02 ± 0.14

3He 92 ± 1.6 8.0 ± 1.6 0.18 ± 0.06

2H 96 ± 0.7 4.0 ± 0.7 -----

Fractions

Nucleus


Comparisons with some theoretical predictions on SRC probabilities


56Fe 23.0 ± 4.7 25.5 0.79±0.25

12C 19.3 ± 4.1 20.3 0.55±0.18

4He 15.4 ± 3.3 16.2 0.42±0.14 -----

3He 8.0 ± 1.6 ---- 0.18±0.06 -----

2H 4.0 ± 0.7 ---- ----- -----

Fractions

Nucleus Exp SRC Exp SRC

Fe

/C=

1.4

3 ±0

.15

Fe

/C =

1.4

1. SRC model

SRC predictions are remarkably close to experiment


Comparisons with some theoretical predictions on SRC probabilities


56Fe 23.0 ± 4.7 25.5 14.6 0.79±0.25 3.6

12C 19.3 ± 4.1 20.3 12.5 0.55±0.18 2.6

4He 15.4 ± 3.3 16.2 16.6 0.42±0.14 ----- 4.7

3He 8.0 ± 1.6 ---- 13.4 0.18±0.06 ----- 2.2

2H 4.0 ± 0.7 ---- ---- ----- ----- -----

Fractions

Nucleus Exp SRC QCM Exp SRC QCM

Fe

/C=

1.4

3 ±0

.15

Fe

/C =

1.4

1. SRC model 2. QCM model

In QCM => Quark-Cluster-Model (unrealistic model in our Q2 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




56Fe 76 ± 0.2 ± 4.7 23.0 ± 0.2 ± 4.7 0.79 ± 0.03 ± 0.25

12C 80 ± 02 ± 4.1 19.3 ± 0.2 ± 4.1 0.55 ± 0.03 ± 0.18

4He 86 ± 0.2 ± 3.3 15.4 ± 0.2 ± 3.3 0.42 ± 0.02 ± 0.14

3He 92 ± 1.6 8.0 ± 1.6 0.18 ± 0.06

2H 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.,)


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 3He are measured in 1< xB < 3 region at Q2 >1.4 GeV2

Two scaling regions - at 1.5 < xB < 2 and xB > 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 3He are extracted

Using the measured onsets of scaling regions, combined with the known WF of 3He 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


Supporting Slides




56Fe 76 ± 0.2 ± 4.7 23.0 ± 0.2 ± 4.7 0.79 ± 0.03 ± 0.25

12C 80 ± 02 ± 4.1 19.3 ± 0.2 ± 4.1 0.55 ± 0.03 ± 0.18

4He 86 ± 0.2 ± 3.3 15.4 ± 0.2 ± 3.3 0.42 ± 0.02 ± 0.14

3He 92 ± 1.6 8.0 ± 1.6 0.18 ± 0.06

2H 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 12C

app(12C) 4 ± 2 %

a2N(12C) 20 ± 0.2 ± 4.1 % apn(12C) 12 ± 4 %

ann(12C) 4 ± 2 %


The Ratios at 1<xB<2; Observation of Scaling

Analyze the ratio

as a function of Q2 and xB

K takes into account differences between (e,p) and (e,n) elastic cross sections. In our Q2 region K=1.14 and 1.18 for 12C and 56Fe respectively

)He,e(A

)A,e()Q(K)He,A(r

3

23 3

• Ratios SCALE at Q2 > 1.4 GeV2

Onset of scaling is at xB ≥ 1.5

• Scaling vanishes at low Q2

Shown results are for 56Fe

Results for 12C and 4He are similar


Q2 scaling of relative probabilities a2 and a3 in Q2 = 1.4 – 2.6 GeV2 region



a2N(3He) = x a2N(2H) From the calculated ratio r(3He/2H)

SF = = 2 ± 0.1

And a2N(3He) = (2 ± 0.1) x a2N(2H)

a2N(3He) a2N(2H)

a2N(3He) a2N(2H) SF


Contributing diagrams in 2<xB<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 xB > 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 < xB < 2.25 region

p

-p 2N - SRC

p

p

p

p

-p2p

3N - SRC

“Star” “2- Body”


Contributing diagrams in 2<xB<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 xB > 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 < xB < 2.25 region only

At xB > 2.25 (pmin > 500 MeV/c) only “2 - Body” configuration is contributing

p

-p 2N - SRC

p

p

p

p

-p2p

3N - SRC

“Star” “2- Body”


Radiative Corrections

56Fe

12C

4He

56Fe12C

4He3He

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