Spokespersons Fatiha Benmokhtar Carnegie Mellon, Pittsburgh, PA

1. Detailed Study of the 4He Nuclei through Response Function Separations at High Momentum Transfers 4He(e,e’p)3H and 4He(e,e’p)X 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

2. One photon exchange cross section for two body breakup p’ x θ q g w = Ee – Ee’ y e’ z e q = pe - pe’ φ Response functions RX depend on q, w, p’, and g. VX and frec are known kinematical factors. Response functions depend on nuclear currents. 2

3. Kinematics Perpendicular Kinematics, xB ~ 1 E = 4.8 GeV and 1.25 GeV, q = 1.5 GeV/c, w = 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 Non-parallel Kinematics, xB = 1.2, complement to E07-006 E = 4.8 GeV, q = 1.6 GeV/c, w = 0.85 GeV Cross Sections: pmiss = 0.1 to 0.3 GeV/c Parallel Kinematics Cross Sections, RT, RL, RL/RT E = 0.85 to 4.8 GeV xB ~1, pmiss=0 q = 1.0, 1.5,2.0, 3.0 GeV/c E = 1.25 and 4.8 GeV xB=1.86, pmiss = 0.4 GeV/c q = 1.5 GeV/c 3

4. Definition of perpendicular kinematics, S1 , S2 , S3 4

5. 3,4He(e,e’)X 4He 3He RT RL Quasielastic peak and the Bjorken variable xB 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 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 We need to understand the impact of reaction dynamics, relativity, and final state interaction effects on the observables. Find thelimits of hadronic degrees of freedom in the nucleus 6

7. 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

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

9. Parallel Kinematics 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)2H. 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. 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=1shows strong FSI effects. 9

10. Beam Time Request Perpendicular Kinematics (i) Response function separations (0-0.5 GeV/c) 227 hours (ii) High pmiss(0.6 – 1.2 GeV/c) 128 hours xB = 1.2, 12 hours Parallel Kinematics ( xB ~ 1) 12 hours Parallel Kinematics (xB = 1.86) 57 hours • Setup and Calibrations • 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

11. Summary In perpendicular kinematics (xB ~ 1 and 1.2) • 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 • 3He(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. 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 4He at JLab energies relativistic models Non-relativistic models Microscopic 4He wave function generated from modern nucleon-nucleon potentials, e.g., R. Schiavilla + others. Mean field wave function Ghent Madrid Relativistic multiple scattering Glauber approximation Optical potential 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) Effect of lower component of w. f. on ATL Generally improved spectroscopic factors for A>4 Glauber approximation, Finite Formation Time effects, Rome INFN, Juelich, Landau Institute Medium modifications of nucleon EM form factors Glauber/eikonal approx. color transparency 13 Goto 6

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

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

16. 4He(e,e’p)3H Response function 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. Goto 8 16 The minimum in the pt spectral function should produce an observable break in the slope of RL+TT.

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

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

19. 4He(e,e’p)3H In 4He the RPWIA produces significant oscillation in ATL. In 3He the RPWIA gives a monotonic dependence of ATL on pm. Ee=4.8 GeV q=1.5 GeV/c w = 0.84 GeV ATL For 4He ATL depends both on FSI and on the lower component of the wave function. Goto 8 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. 19 Expand 3He

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

21. Goto 9 4He(e,e’p)3H 1.0 pm = 30 MeV/c Data - J. E. Ducret et al., NP A556 (1993) 373 R pm = 90 MeV/c 0.5 pm = 190 MeV/c A R = ratio of theoretically corrected longitudinal to corrected transverse spectral function, SL(corr)/ST(corr) 0. 0 300 600 900 1.0 A – ratio calculated by J.-M. Laget B – ratio calculated by R. Schiavilla R 0.5 However, at q=685 MeV/c R. Florizone et al. did not observe a quenching of the longitudinal response. (MIT thesis 1999) B 0. 0 300 600 900 q MeV/c Is the longitudinal response quenched? 21

22. Preliminary JLab data, 4He(e,e’p)3H, Bodo Reitz Calculation by C. Ciofi degli Atti and H. Morita, private communication A = 4 Distorted spectral function from JLab experiment E97-111, in parallel (Py2) and perpendicular (cq2) kinematics cq2, (w,q)=(0.53,1.70)GeV/c; py2, 0.59<Q2<.89 (GeV/c)2 22

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

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

25. A = 3 25

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

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

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

29. A = 2 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 Also E01-020 finished data taking. Q2 survey to study short range structure, FSI, and to obtain RLT . Data analysis in progress 29

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

31. 4He(e,e’p)X J.J. van Leeuwe et al., Phys. Lett. 523B(2001)6 w = 215 MeV q = 401(MeV/c) xB = 0.28 Q2 = 0.11 (GeV/c)2 Calculation – Laget Variational Monte Carlo wf, Urbanna NN potential dashed – 1 body+FSI solid – includes MEC and IC MEC&IC more important for large gpq. 31 goto 32

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 Q2 = 0.11 (GeV/c)2 , xB = 0.28 Minimize gpq to minimize MEC and IC; do response function separations From 3He(e,e’p)X of E89044 and calculations by Laget Q2 = 1.55 (GeV/c)2 , xB = 0.96, perpendicular kinematics Large Q2 suppresses MEC ; even at small gpq FSI dominate the cross section 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. proposal: separate RL/RT , xB = 1.86, Q2 = 1.94 (GeV/c)2 Goto 9 32

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

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

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

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 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

38. RL (fm3) RL fm3 38

39. Both the magnitude and shape of the response function are sensitive to the 4He wave function and reaction dynamics Spectral function fit from Van Leeuwe data RL (fm3) The minimum in the W.F. should produce a break in the slope according to Laget’s prediction. Laget prediction Udias prediction Goto 20 pmiss, MeV/c Looking for the effect of the minimum in 4He wave function 39

40. 40 3He(e,e’p), SRC 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.

41. 41 Medium modifications of proton electromagnetic form factors? 4He(e,e’p)3H OR charge exchange and MEC ? 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. Goto 9

42. 42 CQW2 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. Also EFB20, Sept., 2007 Goto 8

43. 43

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

45. Goto 12

46. 46 Goto 8

47. 47

48. Goto 14 48

49. 49 Goto 26

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