Overview of the (e,e'p) Reaction

Transcription

1 Overview of the (e,e'p) Reaction Paul Ulmer Old Dominion University EEP03: International Workshop on Probing Nucleons and Nuclei via the (e,e'p) Reaction October 14-17, 2003 Grenoble, France

2 Nuclei Spectroscopic factors NN correlations Reaction mechanism Outline Deuteron and the NN interaction Nucleons Elastic form factors Medium modifications Color transparency Pion electroproduction Virtual Compton Scattering

3 Kinematics scattering plane e out-of-plane angle e' (ω,q) p φ x p A 1 θ pq reaction plane In ERL e : Q 2 q µ q µ = q 2 ω 2 = 4ee' sin 2 θ/2 Missing momentum: p m = q p = p A 1 = p 0 Missing mass: ε m = ω T p T A 1 PWIA

4 Response Functions (OPEA) electron kinematics. depend only on the (known) ' the where ) ( ] )cosφ ( )sin φ [( ] )sin 2φ ( )cos 2φ [( ] )sin φ ( )cosφ [( ) ( ) ( σ (2π) dp dω d d σ d } { x x x x x x M 3 p e 6 s v S R S R hv S R S R S R R hv S R S R S R R v S R S R S R R v S R R v S R R v pe t t TT l l TT TT t t LT l l LT n n LT LT LT t t TT l l TT n n TT TT TT t t LT l l LT n n LT LT LT n n T T T n n L L L LAB = Ω Ω

5 The Spectral Function In nonrelativistic PWIA: dω e 6 d σ dω dpdω p = K σ ep S( p m,ε m ) e-p cross section nuclear spectral function For bound state of recoil system: dω e 5 d σ dω p dω = K σ proton momentum distribution ep Φ( p m ) 2

6 Final State Interactions (FSI) FSI p A 1 e' p 0' e q p 0 A r r r r q p = p p A 1 0

7 Distorted Wave Impulse Approximation (DWIA) Treat outgoing proton distorted waves in presence of potential produced by residual nucleus (optical potential). dω e 6 d σ dω dpdω p = K σ ep S D ( p m,ε m, p) Distorted spectral function

8 Nuclei

9 1964: Frascati Synchrotron 12 C(e,e'p) U. Amaldi, Jr. et al., Phys. Rev. Lett. 13, 341 (1964).

10 1976: Saclay Cross Section (10-34 cm 2 /MeV 2 /sr 2 ) 12 C(e,e'p) 0 p m 36 MeV/c Missing Energy (MeV) J. Mougey et al., Nucl. Phys. A262, 461 (1976).

11 1988: NIKHEF S(E x,p m ) [(MeV/c) -3 MeV -1 ] 12 C(e,e'p) p m = 29 MeV/c 1s 1/2 knockout E x [MeV] G. van der Steenhoven et al., Nucl. Phys. A484, 445 (1988).

12 1p knockout from 12 C 12 C(e,e'p) 11 B ρ(p m ) [(MeV/c) 3 ] DWIA calculations give correct shapes, but: Missing strength observed. p m [MeV/c] NIKHEF G. van der Steenhoven, et al., Nucl. Phys. A480, 547 (1988).

13 Spectroscopic Factors

14 Normalization factors z target mass A V. Pandharipande, I. Sick and Peter K.A. dewitt Huberts, Rev. Mod. Phys. 69, 981 (1997).

15 Transfer Reactions and Normalization Factors B.A. Brown et al., Phys. Rev. C 65, (2002).

16 12 C(e,e'p) S 1p S 1s Low Q 2 : optical potential High Q 2 : Glauber Discontinuity seen with strength nearly saturated at high Q 2. Q 2 [(GeV/c) 2 ] L. Lapikás, et al., Phys. Rev. C 61, (2000).

17 16 O(e,e'p) Data: M. Leuschner et al. The same spectroscopic factors used throughout: (p 1/2 ) and (p 3/2 ). Data: J. Gao et al. Marco Radici, W.H. Dickhoff and E. Roth Stoddard, Phys. Rev. C 66, (2002).

18 12 C(e,e'p) For ω<ω QE, essentially no quenching is observed. Bates Linear Accelerator J.H. Morrison et al., Phys. Rev. C 59, 221 (1999).

19 Where does the missing strength go? Short-range correlations?

20 3 He n(k) 2-body ε m MeV total ε m 300 MeV SRC dominate high k (=p m ) and are related to large values of ε m. ε m 50 MeV C. Ciofi degli Atti, E. Pace and G. Salmè, Phys. Lett. 141B, 14 (1984).

21 3 He(e,e'p) Calculations by Laget: dashed=pwia dot-dashed=dwia solid=dwiamec Arrows indicate expected position for correlated pair. C. Marchand et al., Phys. Rev. Lett. 60, 1703 (1988). Saclay

22 3 He(e,e'p)d 3 He(e,e'p)np 3BBU similar to d np C. Marchand et al., Phys. Rev. Lett. 60, 1703 (1988).

23 4 He(e,e'p) Peak roughly tracks kinematics of knockout of correlated 2N pair E A 2 A 1 p 2m 2 m m E thr Laget: full Laget: no MEC/IC J.J. van Leeuwe et al., Nucl. Phys. A631, 593c (1998). AmPS NIKHEF-K

24 PRELIMINARY Data CBF GF Data do not seem to follow naïve expectation for NN correlation peak. Data: D. Rohe, E (Preliminary) GF: H. Müther et al., Phys. Rev. C 52, 2955 (1995). CBF: O. Benhar et al., Nucl. Phys. A579, 493 (1994). JLab Hall C

25 Reaction Mechanism

26 Delta Between dip and Peak of 12 C(e,e'p) Quasielastic Q 2 =0.30 Q 2 =0.48 Q 2 =0.58 H. Baghaei et al., Phys. Rev. C 39, 177 (1989). Bates Linear Accelerator L.B. Weinstein et al., Phys. Rev. Lett. 64, 1646 (1990). Bates Linear Accelerator

27 12 C(e,e'p) L/T Separations Q 2 =0.15 GeV 2 Q 2 =0.64 GeV 2 P.E. Ulmer et al., Phys. Rev. Lett. 59, 2259 (1987). Bates Linear Accelerator D. Dutta et al., Phys. Rev. C 61, (2000). JLab Hall C

28 Excess transverse strength at high ε m. Persists, though declines, at higher Q 2. JLab Hall C D. Dutta et al., Phys. Rev. C 61, (2000).

29 Transverse Enhancement T/L ratio (η) [-] Li 10 B 12 C E m E 2-body threshold [MeV] J.J. Kelly, Adv. Nucl. Phys. 23, 75 (1996).

30 Relativity

31 A LT 2 H(e,e'p)n A LT de Forest Mosconi/Ricci Arenhövel/Fabian NR de Forest CC1 nucleon cross section gives same qualitative features as more complete calculations here, relativistic effects mainly in nucleonic current. Arenhövel/Fabian NR Hummel/Tjon de Forest Wilbois/Arenhövel Wilbois/Arenhövel G. van der Steenhoven, Few-Body Syst. 17, 79 (1994).

32 Saclay data: L. Chinitz et al. RCC1 RCC2 NIKHEF data: C.M. Spaltro et al. PCC1 PCC2 16 O(e,e'p) Discrepancy reported earlier was based on nonrelativistic calculations. Relativistic treatment is required even at these modest momenta. J.M. Udías et al., Phys. Rev. C 64, (2001). Previous non-relativistic analysis

33 16 O(e,e'p) Q 2 =0.8 GeV 2 Quasielastic 1p 1/2 Effect of spinor distortion significant. Calculations: Udías, et al. 1p 3/2 JLab Hall A J. Gao et al., Phys. Rev. Lett. 84, 3265 (2000) and K.G. Fissum et al., in preparation, to be submitted to Phys. Rev. C.

34 16 O(e,e'p) Q 2 =0.8 GeV 2 Quasielastic Two-body calculations (Janssen et al.) reproduce flat distribution, but underpredict by roughly a factor of two. JLab Hall A J. Gao et al., Phys. Rev. Lett. 84, 3265 (2000) and K.G. Fissum et al., in preparation, to be submitted to Phys. Rev. C.

35 The deuteron and the NN interaction

36 M. Bernheim et al., Nucl. Phys. A365, 349 (1981). Saclay

37 2 H(e,e'p) varying Q 2, x 2 H(e,e'p) Q 2 =0.23 GeV 2 near Mainz Bonn FSIMECIC PWBAFSIMECIC FSI PWBAFSI PWBAFSIMEC K.I. Blomqvist et al., Phys. Lett. B 424, 33 (1998). Calculations: H. Arenhövel H. Breuker et al., Nucl. Phys. A455, 641 (1986). Calculations: Leidemann and Arenhövel

38 2 H(e,e'p)n Q 2 = 0.67 GeV 2 x = 0.96 High momentum structure of 2 H? JLab Hall A Evidence for large FSI P.E. Ulmer et al., Phys. Rev. Lett. 89, (2002).

39 D. Jordan et al., Phys. Rev. Lett. 76, 1579 (1996).

40 2 r r H( e, e p) Sensitive to D-state AmPS NIKHEF-K I. Passchier et al., Phys. Rev. Lett. 88, (2002). 0 [ d V d T ( d V d 1 A P A h A P A P A T )] σ = σ P1 d 2 d e 1 ed 2 ed

41 The Nucleon

42 Proton Polarization and Form Factors = = = 2 θ tan τ ) 2 (1 1 τ 2 θ tan τ ) τ (1 2 θ tan τ ) τ (1 2 e e e 0 scattering Free M E M z M E x G G I G m e e P I G G P I p e r * M E G G ~ ~ = 2 θ tan 2 e m e e P P G G z x M E in nucleus model assumptions * R. Arnold, C. Carlson and F. Gross, Phys. Rev. C 23, 363 (1981).

43 Proton Elastic Form Factors via 1 H(e,e'p) O. Gayou, et al., Phys. Rev. Lett. 88, (2002).

44 Searching for Medium Effects on the Nucleon In parallel kinematics: ] [ σ (2π) dω d d d σ d M 3 p e 6 T T L L R v R v pe p = Ω Ω E M L T G G G R R Q m q R ~ ~ 2 2 r PWIA This relies on (unrealistic) model assumption.

45 Medium Modifications or FSI? Schrödinger LDA Dirac DWIA R G (1p 3/2 ) Dirac PWIA Q 2 [GeV 2 ] Calculations ( 16 O): T.D. Cohen, J.W. Van Orden, A. Picklesimer, Phys. Rev. Lett. 59, 1267 (1987). Data ( 12 C): G. Van der Steenhoven et al., Phys. Rev. Lett. 57, 182 (1986).

46 Another, less model-dependent, method Polarization Transfer

47 4 He(e,e'p) Mainz: S. Dieterich et al., Phys. Lett. B500, 47 (2001). E93-049: S. Strauch et al., Phys. Rev. Lett. 91, (2003). E03-104: Projected Data, Strauch, Ent, Ransome, Ulmer, cospokespersons

48 Color Transparency? K. Garrow, et al., Phys. Rev. C 66, (2002).

49 p(e,e'p)π 0 and γ * N Dynamical Model MAID pqcd 100% pqcd constant Sabit S. Kamalov et al., Phys Rev. C 64, (2001). JLab Hall C data (Q 2 =2.8, 4.0 GeV 2 ): V.V. Frolov et al., Phys. Rev. Lett. 82, 45 (1999); their analysis shown by stars.

50 Summary Single-particle picture describes some gross features of experiments at least in quasielastic kinematics. Quenching of strength gives indirect evidence of NN correlations. Also, some direct evidence, but Reaction dynamics still not well understood. Relativistic treatment essential at moderate/high Q 2, but also essential at low Q 2 for certain observables. NN interaction studies via d(e,e'p)n now being fully exploited: reaction dynamics/short-range structure of NN force. A wealth of new information now coming out on the nucleon: elastic and inelastic structure, medium modifications, color transparency, polarizabilities,