1. Detailed Study of the 4 He Nuclei through Response Function Separations at High Momentum Transfers Spokespersons Fatiha Benmokhtar Carnegie Mellon, Pittsburgh, PA 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 4 He(e,e’p) 3 H and 4 He(e,e’p)X

2.  = E e – E e’ q = p e - p e ’ Response functions R X depend on q, , p’, and  V X and f rec are known kinematical factors. One photon exchange cross section for two body breakup 2 e e’e’ q p’p’ z x y φ θ  Response functions depend on nuclear currents.

3. Kinematics Perpendicular Kinematics, x B ~ 1 E = 4.8 GeV and 1.25 GeV, q = 1.5 GeV/c,  = 0.84 GeV Cross Sections p miss : from 0 to 1.2 GeV/c A TL,R TL p miss : from 0 to 0.5 GeV/c R T, R L+TT p miss : 0, 0.4, 0.5 GeV/c Parallel Kinematics E = 0.85 to 4.8 GeV x B ~1, p miss =0 q = 1.0, 1.5,2.0, 3.0 GeV/c Cross Sections, R T, R L, R L /R T E = 1.25 and 4.8 GeV x B =1.86, p miss = 0.4 GeV/c q = 1.5 GeV/c 3 Non-parallel Kinematics, x B = 1.2, complement to E07-006 E = 4.8 GeV, q = 1.6 GeV/c,  = 0.85 GeV Cross Sections: p miss = 0.1 to 0.3 GeV/c

4. Definition of perpendicular kinematics,       4

5. Quasielastic peak and the Bjorken variable x B 3,4 He(e,e’)X 3 He 4 He RLRL RTRT 5

6. Physics Motivation Provide a large and precise data set for testing and constraining theoretical models in few-body nuclei Microscopic wave functions + relativistic kinematics Relativistic mean-field modelsmodels Study short range structure of 4 He (and other nuclei) Is R L quenched in 4 He(e,e’p) 3 H? R L seems to be quenched in 4 He(e,e’). Measure the q dependence.quenched Look for NN correlations at high p miss and e miss 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

7. Why Study 4 He ? 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 p miss region as a measure of final state interactions plus initial state correlations. High quality data exist for 2 H and 3 He. 4 He data are needed to complete the systematic survey of the few body nuclei. 7

8. Perpendicular Kinematics Measurements in quasielastic kinematics ( x B ~1) emphasize the electron-single nucleon interaction aspect of the reaction. Low p miss allows both relativistic mean field models and microscopic models to be compared to the data.relativistic microscopic High p miss allows investigation of short range structure.short range structure Extreme p miss and q may reveal non-hadronic degrees of freedom in nuclear structure. Example 3 He ?Example 3 He ? E97111 looked for the dip in the cross section at 425 MeV/c. Theory Laget and Ryckebusch. However, R L+TT from p miss = 0.4 to 0.5 GeV/c may show effects due to the minimum in the 4 He wave function.LagetRyckebuschR L+TT The asymmetry A TL is predicted to be sensitive to dynamical relativistic effects in the 4 He wave function.asymmetry 8

9. Parallel Kinematics At low p miss (~ 0 MeV/c) both relativistic mean field theory and microscopic theory should be able to predict the nuclear w.f. 4 He(e,e’p) data show a reduction in R L at lower q.show a reduction in R L at lower q Polarization transfer data Polarization transfer data show a reduction in GEp/GMp in 4He compared to the free proton. Study q dependence of R L and R T. Only R L and R T contribute to the cross section. FSI are minimized but not negligible. High quality parallel Kinematics data were measured for 3 He(e,e’p) 2 H.High quality parallel Kinematics For p miss = 0.4 GeV/c and x B = 1.86 we expect minimal effects from MEC and pion production for NN correlations. Experience from e89044 at x B =1 shows strong FSI effects. 9

10. Beam Time Request Perpendicular Kinematics (i) Response function separations (0-0.5 GeV/c) 227 hours (ii) High p miss (0.6 – 1.2 GeV/c) 128 hours Parallel Kinematics ( x B ~ 1) 12 hours Parallel Kinematics (x B = 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 x B = 1.2, 12 hours

11. Summary In perpendicular kinematics (x B ~ 1 and 1.2) (i)Cross sections will be measured over an unprecedented Range of p miss, up to 1.2 GeV/c (ii) Response functions will be extracted to 0.5 GeV/c Parallel kinematics (x B ~1) measure R L /R T vs. q Parallel kinematics (x B = 1.86) look for NN correlations This will produce high quality data to be compared to (i) 3 He(e,e’p) over the same kinematical conditions (ii) Modern theoretical interpretations 11

12. Experiment is Ready to Run There is a strong collaboration of experimentalists and theorists on the proposal. 59 physicists have signed on as collaborators.collaboration 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

13. Some Recent Theoretical Calculations for 4 He at JLab energies relativistic models Microscopic 4 He 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 (C. Ciofi degli Atti et al., EFB 20, Sept. 2007) 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 A TL Generally improved spectroscopic factors for A>4 Medium modifications of nucleon EM form factors 13 Goto 6

14. A = 3 3 He(e,e’p) 2 H, E89044 data M. Rvachev et al., Phys. Rev. Lett. 94 (2005) 192302 Data exceed old calculation by a factor of 26 at p miss = 1 GeV/c This region must be studied in 4 He. 14 Goto 8 New rescattering calculation GEA calculation

15. PRL 69 (1992) 41 Z.- E. Meziani et al., Is there a q dependence to the quenching of the longitudinal vs transverse response? 15 Goto 6

16. 4 He(e,e’p) 3 H Response function The minimum in the pt spectral function should produce an observable break in the slope of R L+TT. 16 Goto 8 Calculations done with Laget’s most recent code (PLB609(2005) 49) using the AV14 potential. Code is being updated to include AV18. Shaded areas show spectrometer coverages at 400 and 500 MeV/c.

17. Relativistic calculations for 4 He(e,e’p) Nucl. Phys. A278 (2003) 226 J. Ryckebusch et al. A TL Response functions at proposed kinematics 17 Goto 8

18. New response function calculations by J. M. Laget Perpendicular kinematics A = 4 18 Goto 8

19. A TL 4 He(e,e’p) 3 H 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 3 He(e,e’p) 2 H. In 4 He the RPWIA produces significant oscillation in A TL. In 3 He the RPWIA gives a monotonic dependence of A TL on p m. For 4 He A TL depends both on FSI and on the lower component of the wave function. 19 Goto 8 Expand 3He

20. Preliminary E97111 data from Bodo Reitz, calculation by J. –M. Laget, private communication. Modern calculations fill in the dip in cross section. 4 He(e,e’p) 3 H A=4 20 Goto 8

21. p m = 30 MeV/c p m = 90 MeV/c p m = 190 MeV/c 0. 0.5 1.0 0. 0.5 1.0 3006009000 q MeV/c 0300600900 4 He(e,e’p) 3 H Is the longitudinal response quenched? R R R = ratio of theoretically corrected longitudinal to corrected transverse spectral function, S L (corr)/S T (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

22. Preliminary JLab data, 4 He(e,e’p) 3 H, 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<Q 2 <.89 (GeV/c) 2 22

23. New cross section calculation by J. M. Laget Perpendicular kinematics A = 4 23

24. Calculations: M. Avioli et al., arXiv:nucl-th/03123123v1 29Dec, 2003 A = 3 24 Note: Calculations by J.-M. Laget show a similar strong FSI effect Goto 30

25. A = 3 25

26. 26 ab c a a+b a+b+c+mec a+b+c, see effect in p m =620 MeV/c E miss Goto 8 Also in triple coincidence JLab exp F. Benmokhtar et al. Phys. Rev. Lett 94 (2005) 082305 Goto 49

27. A = 3 3 He(e,e’p) 2 H, E89044 Marat Rvachev, MIT thesis, 2003 Calculations, Madrid group, private communication 27

28. A = 3 3 He(e,e’p) 2 H, E89044 data Marat Rvachev, MIT thesis, 2003 Calculations: Madrid group, private communications 28 The oscillation in the calculated A TL is caused by FSI. Goto 19

29. 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 2 H(e,e’p)n, JLab data and recent theoretical fits A = 2 29 Also E01-020 finished data taking. Q 2 survey to study short range structure, FSI, and to obtain R LT. Data analysis in progress

30. E89044, Parallel kinematics A = 3 Theoretical calculations by J.-M. Laget 30 Goto 9

31. J.J. van Leeuwe et al., Phys. Lett. 523B(2001)6  = 215 MeV q = 401(MeV/c) x B = 0.28 Q 2 = 0.11 (GeV/c) 2 31 4 He(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

32. Effects of Short Range Correlations in 4 He(e,e’p)X at high p miss and E miss From 4 He(e,e’p)X of van Leeuwe et al and calculations by Laget Minimize  pq to minimize MEC and IC; do response function separations Q 2 = 0.11 (GeV/c) 2, x B = 0.28 From 3 He(e,e’p)X of E89044 and calculations by Laget Large Q 2 suppresses MEC ; even at small  pq FSI dominate the cross section Q 2 = 1.55 (GeV/c)2, x B = 0.96, perpendicular kinematics From 4 He(e,e’)X of K. Egiyan et al. Phys. Rev. C68, 014313 (2003) SRC dominate the nuclear wave function for p miss > 300MeV/c and are seen clearly for Q 2 >1.4 (GeV/c) 2 and x B >1.5 because of the scaling of (e,e’) cross sections with A. 32 proposal: separate R L /R T, x B = 1.86, Q 2 = 1.94 (GeV/c) 2 Goto 9

33. 33 Madrid group calculation, data from e89044 Goto 19 For 3 He only FSI causes the oscillation in A TL.

34. 34 Data – e89044, calculation – Madrid group For 3 He A TL is determined only by FSI Goto 19 Laget, Schiavilla calculations

35. K. Aniol, California State University, Los Angeles 35

36. 36

37. 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 4 He 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

38. R L fm 3 38 R L (fm 3)

39. Looking for the effect of the minimum in 4 He 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 p miss, MeV/c Both the magnitude and shape of the response function are sensitive to the 4 He wave function and reaction dynamics Udias prediction Goto 20 R L (fm 3)

40. Preliminary results from the SRC group. For p miss > 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 3 He(e,e’p), SRC

41. Polarization transfer measurements at low p miss. The date at Q 2 = 0.7 and 1.3 (GeV/c) 2 from E03-104 are preliminary. Fig from S. Strauch. Medium modifications of proton electromagnetic form factors? 4 He(e,e’p) 3 H 41 Goto 9 charge exchange and MEC ?charge exchange and MEC ? OR

42. Preliminary cross from the 4 He(e,e’p) 3 H 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 Also EFB20, Sept., 2007

43. 43

44. R. Schiavilla et al., arXiv.nucl-th/0412020v1 No medium modifications employed to explain super ratio in 4 He(e,e’p) 3 H 44 Goto 41

45. Goto 12

46. Goto 8 46

47. 47

48. 48 Goto 14

49. 49 Goto 26

50. E89044 data, including three body mechanism by J.-M. Laget Goto 14 50

51. A TL, asymmetry data and fits for E89-044 Rocco – R. Schiavilla J.-M. Laget 51 Goto 19