Detailed Study of the 4He Nuclei through Response Function Separations at High

Momentum Transfers

Spokespersons

Fatiha Benmokhtar U. Maryland, College Park, MD

Konrad Aniol CSULA, Los Angeles, CA

Shalev Gilad M.I.T., Cambridge, MA

Doug Higinbotham Jefferson Lab, Newport News, VA

Arun Saha* Jefferson Lab, Newport News, VA*Contact person saha@jlab.org

4He(e,e’p)3H and 4He(e,e’p)X

)2cos()cos()2(

'3

'

'''

5

TTTTTLTLLLTT

rec

Mottp

epe

RVRVRVRVf

pE

dEdd

d

= Ee – Ee’

q = pe - pe’

Response functions RX depend on q, , p’, and

VX and frec are known kinematical factors.

)180()0(

)180()0(

TLA

One photon exchange cross section for two body breakup

2

ee’ q

p’

z

x

y

φ

θ

Kinematics

Perpendicular Kinematics, xB ~ 1E = 4.8 GeV and 1.25 GeV, q = 1.5 GeV/c, = 0.84 GeV

Cross Sections pmiss: from 0 to 1.2 GeV/c

ATL,RTL pmiss: from 0 to 0.5 GeV/c

RT, RL+TT pmiss: 0, 0.4, 0.5 GeV/c

Parallel Kinematics

E = 0.85 to 4.8 GeV

xB ~1, pmiss=0

q = 1.0, 1.5,2.0, 3.0 GeV/c

Cross Sections, RT, RL, RL/RT

E = 1.25 and 4.8 GeV

xB=1.86, pmiss = 0.4 GeV/c

q = 1.5 GeV/c3

Perpendicular Kinematics, xB = 1.2

E = 4.8 GeV, q = 1.6 GeV/c, = 0.85 GeV

Cross Sections: pmiss = 0.1 to 0.3 GeV/c

Definition of perpendicular kinematics,

4

Quasielastic peak and the Bjorken variable xB

3,4He(e,e’)X

3He4He

RL

RT

5

Physics MotivationProvide a large and precise data set for testing and constraining theoretical models in few-body nuclei Microscopic wave functions + relativistic kinematics Relativistic mean-field models

Study short range structure of 4He (and other nuclei)

Is RL quenched in 4He(e,e’p)3H? RL seems to be quenched in 4He(e,e’). Measure the q dependence.

Look for NN correlations at high pmiss and emiss cross sections and Response function separations

Find the limits of hadronic degrees of freedom in the nucleus

We need to understand the impact of reaction dynamics, relativity, and final state interaction effects on the observables.

6

Why Study 4He ?

It is a tightly bound system so NN correlations should be more important here than in a lighter nucleus.

It is a bridge between 2/3 body systems and heavier nuclei. Its density is similar to that of a heavier nucleus.

Microscopic calculations are possible, which may help establish the baseline for looking for exotic effects.

Study the A dependence, A = 2,3,4 and density dependence of the high pmiss region as a measure of final state interactions plus initial state correlations.

High quality data exist for 2H and 3He. 4He data are needed to complete the systematic survey of the few body nuclei.

7

Perpendicular Kinematics

Measurements in quasielastic kinematics ( xB ~1) emphasize the electron-single nucleon interaction aspect of the reaction.

Low pmiss allows both relativistic mean field models and microscopic models to be compared to the data.

High pmiss allows investigation of short range structure.

Extreme pmiss and q may reveal non-hadronic degrees of freedom in nuclear structure. Example 3He ?

E97111 looked for the dip in the cross section at 425 MeV/c. Theory Ryckebusch and Laget. However, RL+TT from pmiss = 0.4 to 0.5 GeV/c may show effects due to the minimum in the 4He wave function.

The asymmetry ATL is predicted to be sensitive to dynamical relativistic effects in the 4He wave function.

8

Parallel Kinematics

At low pmiss (~ 0 MeV/c) both relativistic mean field theory and microscopic theory should be able to predict the nuclear w.f. 4He(e,e’p) data show a reduction in RL at lower q.

Polarization transfer data show a reduction in GEp/GMp in 4He compared to the free proton .

Study q dependence of RL and RT.

Only RL and RT contribute to the cross section. FSI are minimized but not negligible. High quality parallel Kinematics data were measured for 3He(e,e’p)3H.

For pmiss = 0.4 GeV/c and xB = 1.86 we expect minimal effects from MEC and pion production for NN correlations. Experience from e89044 at xB=1 shows strong FSI effects.

9

Beam Time RequestPerpendicular Kinematics

(i) Response function separations (0-0.5 GeV/c) 227 hours

(ii) High pmiss(0.6 – 1.2 GeV/c) 128 hours

Parallel Kinematics ( xB ~ 1) 12 hours

Parallel Kinematics (xB = 1.86) 57 hours

Setup and Calibrations(i) Spectrometer changes (fields and angles) 16 hours(ii) Energy measurements (Arc and ep) 12 hours(iii) Optics studies 16 hours(iv) Elastic scattering measurements 12 hours

Total time requested 492 hours = 20.5 days

10

xB = 1.2, 12 hours

Summary

In perpendicular kinematics (xB ~ 1 and 1.2)

(i) Cross sections will be measured over an unprecedented Range of pmiss, up to 1.2 GeV/c

(ii) Response functions will be extracted to 0.5 GeV/c

Parallel kinematics (xB ~1) measure RL/RT vs. q

Parallel kinematics (xB = 1.86) look for NN correlations

This will produce high quality data to be compared to

(i) 3He(e,e’p) over the same kinematical conditions

(ii) Modern theoretical interpretations

11

Experiment is Ready to Run

There is a strong collaboration of experimentalists and theorists on the proposal. 59 physicists have signed on as collaborators.

The standard Hall A equipment was designed for high resolution experiments.

Sister experiment, E89044 has educated three PhD students : 3 theses (MIT), (Grenoble) and (Rutgers) completed.

Two Physical Review Letters have been published by the collaboration.

12

Some Recent Theoretical Calculations for 4He at JLab energies

Fully relativistic models

Microscopic 4He wave function generated from modern nucleon-nucleon potentials, e.g., R. Schiavilla + others.Madrid Ghent

Mean field wave function

Optical potential

Relativistic multiple scattering Glauber approximation

J. –M. Laget

Diagrammatic approach allows incorporation of MEC, FSI = rescattering

U. Perugia, INFN, Dubna, St. Petersburg, Sapporo Gakuin U., U. Trieste, Heidelberg, others

Non-relativistic models

Glauber approximation, Finite Formation Time effects,

Rome INFN, Juelich, Landau Institute

Glauber/eikonal approx. color transparency

Effect of lower component of w. f. on ATL

Generally improved spectroscopic factors for A>4

Medium modifications of nucleon EM form factors

13Goto 6

A = 3

3He(e,e’p)2H, E89044 dataM. Rvachev et al., Phys. Rev. Lett. 94 (2005) 192302

Data exceed calculation by a factor of 26 at pmiss = 1 GeV/c

This region must be studied in 4He.

14

Goto 8

PRL 69 (1992) 41 Z.-E. Meziani et al.,

Is there a q dependence to the quenching of the longitudinal vs transverse response?

15Goto 6

4He(e,e’p)3H Response function

The minimum in the pt spectral function should produce an observable break in the slope of RL+TT.

16

Goto 8

Relativistic calculations for 4He(e,e’p)

Nucl. Phys. A278 (2003) 226

J. Ryckebusch et al.

ATL

Response functions at proposed kinematics

17

Goto 8

New response function calculations by J. M. Laget

Perpendicular kinematics

A = 4

18

Goto 8

ATL

4He(e,e’p)3H

Ee=4.8 GeV

q=1.5 GeV/c

= 0.84 GeV

The enhancement of the lower component of the bound state wave function is evident in the relativistic calculation. See the result for 3He(e,e’p)2H.

In 4He the RPWIA produces significant oscillation in ATL. In 3He the RPWIA gives a monotonic dependence of ATL on pm.

For 4He ATL depends both on FSI and on the lower component of the wave function.

19

Goto 8

Expand 3He

Preliminary E97111 data from Bodo Reitz, calculation by J. –M. Laget, private communication. Modern calculations fill in the dip in cross section.

4He(e,e’p)3H

A=4

20Goto 8

pm = 30 MeV/c

pm = 90 MeV/c

pm = 190 MeV/c

0.

0.5

1.0

0.

0.5

1.0

300 600 9000

q MeV/c

0 300 600 900

4He(e,e’p)3H

Is the longitudinal response quenched?

R

R

R = ratio of theoretically corrected longitudinal to corrected transverse spectral function, SL(corr)/ST(corr)

A

B

A – ratio calculated by J.-M. Laget

B – ratio calculated by R. Schiavilla

Data - J. E. Ducret et al., NP A556 (1993) 373

However, at q=685 MeV/c R. Florizone et al. did not observe a quenching of the longitudinal response. (MIT thesis 1999)

21

Goto 9

Preliminary JLab data, 4He(e,e’p)3H, Bodo Reitz

Calculation by C. Ciofi degli Atti and H. Morita, private communication

Distorted spectral function from JLab experiment E97-111, in parallel (Py2) and perpendicular (cq2) kinematics

A = 4

cq2, (,q)=(0.53,1.70)GeV/c; py2, 0.59<Q2<.89 (GeV/c)2

22

New cross section calculation by J. M. Laget

Perpendicular kinematics

A = 423

Calculations: M. Avioli et al., arXiv:nucl-th/03123123v1 29Dec, 2003

A = 3

24Note: Calculations by J.-M. Laget show a similar strong FSI effect

Goto 30

A = 3

25

26

a b c

aa+ba+b+c+meca+b+c, see effect in pm=620 MeV/c

EmissGoto 8

Also in triple coincidence JLab exp

F. Benmokhtar et al. Phys. Rv. Lett 94 (2005) 082305

A = 3

3He(e,e’p)2H, E89044Marat Rvachev, MIT thesis, 2003

Calculations, Madrid group, private communication

27

A = 3

3He(e,e’p)2H, E89044 data

Marat Rvachev, MIT thesis, 2003

Calculations: Madrid group, private communications

28

The oscillation in the calculated ATL is caused by FSI.

Goto 19

P. E. Ulmer, et al., PRL 89 (2002) 062301

JLab data, P. E. Ulmer et al., calculations M. Avioli et al., arXiv:nucl-th/0312123v1 29 Dec 2003

2H(e,e’p)n, JLab data and recent theoretical fits

A = 2

29

Also E01-020 finished data taking. Q2 survey to study short range structure, FSI, and to obtain RLT . Data analysis in progress

E89044, Parallel kinematics

A = 3

Theoretical curves by J.-M. Laget

30

Goto 9

J.J. van Leeuwe et al., Phys. Lett. 523B(2001)6

= 215 MeV

q = 401(MeV/c)

xB = 0.28

Q2 = 0.11 (GeV/c)2

31

4He(e,e’p)X

Calculation – Laget

Variational Monte Carlo wf, Urbanna NN potential

dashed – 1 body+FSI

solid – includes MEC and IC

MEC&IC more important for large pq.goto 32

Effects of Short Range Correlations in 4He(e,e’p)X at high pmiss and Emiss

From 4He(e,e’p)X of van Leeuwe et al and calculations by Laget

Minimize pq to minimize MEC and IC; do response function separations

Q2 = 0.11 (GeV/c)2 , xB = 0.28

From 3He(e,e’p)X of E89044 and calculations by Laget

Large Q2 suppresses MEC ; even at small pq FSI dominate the cross section

Q2 = 1.55 (GeV/c)2 , xB = 0.96, perpendicular kinematics

From 4He(e,e’)X of K. Egiyan et al. Phys. Rev. C68, 014313 (2003)

SRC dominate the nuclear wave function for pmiss > 300MeV/c and are seen clearly for Q2>1.4 (GeV/c)2 and xB>1.5 because of the scaling of (e,e’) cross sections with A.

32proposal: separate RL/RT , xB = 1.86, Q2 = 1.94 (GeV/c)2 Goto 9

33Madrid group calculation, data from e89044

Goto 19

For 3He only FSI causes the oscillation in ATL .

34

Data – e89044, calculation – Madrid group

For 3He ATL is determined only by FSI Goto 19

K. Aniol, California State University, Los Angeles

35

36

Theories and Models

Few body systems have attracted a great deal of interest.Many wave functions and reaction models are available.

Standard Nuclear Model Approach

Microscopic 4He wave function generated from modern nucleon-nucleon potentials, e.g., R. Schiavilla + others.

Diagrammatic expansion used by J.-M. Laget with success.

Relativisitic mean field wave functions and fully relativistic dynamics used by the Madrid group, Ghent group.

37

RL f

m3

38

RL

(f

m3)

Looking for the effect of the minimum in 4He wave function

Spectral function fit from Van Leeuwe data

Laget prediction

The minimum in the W.F. should produce a break in the slope according to Laget’s prediction.

39

pmiss, MeV/c

Both the magnitude and shape of the response function are sensitive to the 4He wave function and reaction dynamics

Udias predictionGoto 20

RL

(f

m3)

Preliminary results from the SRC group. For pmiss > Fermi momentum nearly every proton is correlated with an energetic neutron. This nearby partner enhances the local density by about a factor of 3 at 0.4 GeV/c.

40

3He(e,e’p), SRC

Polarization transfer measurements at low pmiss. The date at Q2 = 0.7 and 1.3 (GeV/c)2 from E03-104 are preliminary. Fig from S. Strauch.

Medium modifications of proton electromagnetic form factors?

4He(e,e’p)3H

41

Goto 9

charge exchange and MEC ?

OR

Preliminary cross from the 4He(e,e’p)3H experiment, e97-111. When the experiment was proposed in 1997 it was believed that the minimum in the 1S wave function would produce a dip in the cross section at 425 MeV/c. Modern calculations show the dip in the cross section is filled in. A response function separation may be sensitive to the dip, however. Calculations from J. Ryckebusch.

CQW2 42

Goto 8

43

R. Schiavilla et al., arXiv.nucl-th/0412020v1

No medium modifications employed to explain super ratio in 4He(e,e’p)3H

44

Goto 41

Goto 12