Hampton University Graduate Studies 2003

1
(e,e'p) and Nuclear Structure
Paul Ulmer Old Dominion University
Hampton University Graduate Studies 2003
2
Thanks to

• W. Boeglin
• T.W. Donnelly (Nuclear physics course at MIT)
• J. Gilfoyle
• R. Gilman
• R. Niyazov
• J. Kelly (Adv. Nucl. Phys. 23, 75 (1996))
• B. Reitz
• Saha
• S. Strauch
• E. Voutier
• L. Weinstein

3
Outline

• Introduction
• Background
• Experimental
• Theoretical
• Nuclear Structure
• Medium-modified nucleons
• Cross sections
• Polarization transfer
• Studies of the reaction mechanism
• Few-body nuclei
• The deuteron
• 3,4He

4
A(e,e'p)B
e'
B
p
q
e
A
Known e and A Detect e' and p
Infer pm q p pB
5
(e,e'p) - Schematically
e'
?v

A
e
i.e. bound

Etc.
6
Kinematics
p
e'
scattering plane
?pq
reaction plane
(?,q)
e
pA1
?x
out-of-plane angle
In ERLe Q2 ? q?q ? q2 ? 2 4ee'
sin2?/2 Missing momentum pm q p
pA1 Missing mass ?m ? Tp
TA1
7
Some (Very Few) Experimental Details
8
accidental (uncorrelated)
e
e'
real (correlated)
p
e
9
events
?r
?a
relative time te tp
10
Accidentals Rate Re ? Rp ? ??/DF ? I 2 ??/DF
Reals Rate Reep ? I
SN Reals/Accidentals ? DF /(???I)
Compromise Optimize SN and Reep
11
Extracting the cross section
e'
NN (cm-2)
Ne
e
(??e, ?pe)
(??p, ?pp)
p
12
Some Theory
13
Cross Section for A(e,e'p)B in OPEA
A-1
where
Current-Current Interaction
14
Square of Matrix Element
???
W??
15
Cross Section in terms of Tensors
Mott cross section
Electron tensor
Nuclear tensor
16
Consider Unpolarized Case Lorentz Vectors/Scalars
17
Nuclear Response Tensor
Xi are the response functions
18
Impose Current Conservation
Get 6 equations in 10 unknowns 4 independent
response functions
19
Putting it all together
20
The Response Functions
Use spherical basis with z-axis along q
21
Response functions depend on scalar quantities
Note no ?x dependence in response functions
22
Including electron and recoil proton polarizations
23
Extracting Response Functions For instance RLT
and A? (A LT)
24
Plane Wave Impulse Approximation (PWIA)
spectator
A-1
q p pA-1 pm p0
25
The Spectral Function
In nonrelativistic PWIA
e-p cross section
nuclear spectral function
For bound state of recoil system
proton momentum distribution
26
The Spectral Function, contd.
Note S is not an observable!
27
Elastic Scattering from a Proton at Rest
(m,0)
(?,q)
Before
After
Proton is on-shell ?
(? m)2 ? q2 m2 ?2 2m? m2 ? q2 m2 ?
Q2 ? 2m
28
Scattering from a Proton , contd.



structure/anomalous moment
29
Scattering from a Proton , contd.
Vertex fcn
Dirac FF
Pauli FF
Sachs FFs
GE and GM are the Fourier transforms of the
charge and magnetization densities in the Breit
frame.
30
Form Factor
r
k
k'
Amplitude at q
31
Cross section for ep elastic
However, (e,e'p) on a nucleus involves scattering
from moving protons, i.e. Fermi motion.
32
Elastic Scattering from a Moving Proton
Before
(? E)2 (qp)2 m2 ?2 2E? E2 ? q2 ?2pq
? p2 m2 Q2 2E? ?2pq ? (E/m) (Q2 ? 2m)
pq ? m
33
Cross section for ep elastic scattering off
moving protons
Follow same procedure as for unpolarized (e,e'p)
from nucleus
We get same form for cross section, with 4
response functions
34
Response functions for ep elastic scattering off
moving protons
35
Quasielastic Scattering
For E ? m ? ? (Q2 ? 2m) pq ? m
If we quasielastically scatter from nucleons
within nucleus
Expect peak at ? ? (Q2 ?
2m) Broadened by Fermi motion pq ? m
36
Electron Scattering at Fixed Q 2
Elastic
Nucleus
Deep Inelastic
?
Quasielastic
N
?
Proton
Elastic
Deep Inelastic
?
N
?
37
Quasielastic Electron Scattering
R.R. Whitney et al., Phys. Rev. C 9, 2230 (1974).
38
Data P. Barreau et al., Nucl. Phys. A402,
515 (1983). y-scaling analysis J.M. Finn, R.W.
Lourie and B.H. Cottman,
Phys. Rev. C 29, 2230 (1984).
39
Nuclear Structure
40
First, a bit of history The first (e,e'p)
measurement
Frascati Synchrotron, Italy
12C(e,e'p)
27Al(e,e'p)
U. Amaldi, Jr. et al., Phys. Rev. Lett. 13, 341
(1964).
41
(e,e'p) advantages over (p,2p)

• Electron interaction relatively weak OPEA is
  reasonably accurate.
• Nucleus is very transparent to electrons Can
  probe deeply bound orbits.

However ejected proton is strongly interacting.
The cleanness of the electron probe is
somewhat sacrificed. FSI must be taken into
account.
42
Recall, in nonrelativistic PWIA
where q p pm p0
FSI destroys simple connection between the
measured pm and the proton initial momentum (not
an observable).
43
Final State Interactions (FSI)
p
A1
FSI
e'
p0'
q
e
p0
A
44
Distorted Wave Impulse Approximation (DWIA)
Treat outgoing proton distorted waves in presence
of potential produced by residual nucleus
(optical potential).
Distorted spectral function
45
Optical potential is constrained by proton
elastic scattering data.

• Problems with this approach
• Residual nucleus contains hole state, unlike the
  target in pA scattering.
• Proton scattering data is surface dominated,
  whereas ejected protons in (e,e'p) are produced
  within entire nuclear volume.

46
100 MeV data is significantly overestimated by
DWIA near 2nd maximum.
NIKHEF-K Amsterdam
J.W.A. den Herder, et al., Phys. Lett. B 184, 11
(1987).
47
At pm?160 MeV/c, wf is probed in nuclear interior.
J.W.A. den Herder, et al., Phys. Lett. B 184, 11
(1987).
48
Adjusting optical potential renders good
agreement while maintaining agreement with pA
elastic.
J.W.A. den Herder, et al., Phys. Lett. B 184, 11
(1987).
49
Saclay Linac, France
12C(e,e'p)11B
J. Mougey et al., Nucl. Phys. A262, 461 (1976).
50
12C(e,e'p)11B
p-shell l1
Saclay Linac, France
s-shell l0
J. Mougey et al., Nucl. Phys. A262, 461 (1976).
51
12C(e,e'p)11B
NIKHEF-K Amsterdam
G. van der Steenhoven et al., Nucl. Phys. A484,
445 (1988).
52
12C(e,e'p)11B
NIKHEF-K Amsterdam
G. van der Steenhoven et al., Nucl. Phys. A484,
445 (1988).
53
12C(e,e'p)11B
NIKHEF-K Amsterdam
DWIA calculations fit data reasonably well.
Missing strength observed however.
G. van der Steenhoven, et al., Nucl. Phys. A480,
547 (1988).
54
12C(e,e'p)
Bates Linear Accelerator
L.B. Weinstein et al., Phys. Rev. Lett. 64, 1646
(1990).
55
MAMI Mainz, Germany
K.I. Blomqvist et al., Phys. Lett. B 344, 85
(1995).
56
MAMI Mainz, Germany
Factorization violated. DWIA calculations
underpredict at high pm. Neglected MECs
relativistic effects. Offshell effects uncertain
at high pm.
K.I. Blomqvist et al., Phys. Lett. B 344, 85
(1995).
57
208Pb(e,e'p)
AmPS NIKHEF-K Amsterdam
I. Bobeldijk et al., Phys. Rev. Lett. 73, 2684
(1994).
58
208Pb(e,e'p)
AmPS NIKHEF-K Amsterdam
Long-range correlations important. SRC and TC
less so, but expected to grow with ?m.
I. Bobeldijk et al., Phys. Rev. Lett. 73, 2684
(1994).
59

• Some of the lessons learned
• (e,e'p) sensitive probe of single-particle
  orbits.
• Proton distortions (FSI) must be accounted for
  to reproduce shape of spectral function. Energy
  dependence of FSI breaks factorization.
• Missing strength in valence orbits, even after
  accounting for FSI
• At high Pm significant discrepancies found
  relative to calculations.

60
Where does the missing strength go?
One possibility
Detected
populates high ?m
recoils
61
SRC dominate high k (pm ) and are related to
large values of ?m.
C. Ciofi degli Atti, E. Pace and G. Salmè, Phys.
Lett. 141B, 14 (1984).
62
Similar shapes for few-body nuclei and nuclear
matter at high k (pm).
C. Ciofi degli Atti, E. Pace and G. Salmè,

Phys. Lett. 141B, 14
(1984).
63
Medium-Modified Nucleons
64
Searching for Medium Effects on the Nucleon
In parallel kinematics
Can write ep elastic cross section as
65
Relate RT/RL to in-medium proton FFs
This relies on (unrealistic) model assumptions!
Nonetheless
66
2H(e,e'p)n
6Li(e,e'p)
J.E. Ducret et al., Phys. Rev. C 49, 1783 (1994).
J.B.J.M. Lanen et al., Phys. Rev. Lett. 64, 2250
(1990).
NIKHEF-K Amsterdam
67
12C(e,e'p) and 12C(e,e')
68
JLab Hall C
D. Dutta et al., Phys. Rev. C 61, 061602 (2000).
69
However, large FSI effects can mimic this
behavior
70
FSI calculations for 16O 1p3/2 Data for 12C 1p3/2
71
Another, less model-dependent, method
Polarization Transfer
72
Proton Polarization and Form Factors

in nucleus
model assumptions
R. Arnold, C. Carlson and F. Gross, Phys. Rev.
C 23, 363 (1981).
73
Polarization Transfer in Hall A
spectrometer
1H and (2H or 4He)
spectrometer FPP
74
Measuring the Proton Polarization FPP
75
Density Dependent Form Factors
Quark-Meson Coupling Model (QMC)

D.H. Lu, , A.W. Thomas, K. Tsushima, A.G.
Williams, K. Saito, Phys. Lett. B 417, 217 (1998).
76
Quark-Meson Coupling Model
4He
D.H. Lu, K. Tsushima, A.W. Thomas, A.G. Williams
and K. Saito, Phys. Lett. B417, 217 (1998) and
Phys. Rev. C 60, 068201 (1999).
77
JLab
Preliminary
Preliminary
Calculations by Arenhövel
RDWIA calculations by Udias et al.
78
Induced Polarization 4He
JLab E93-049
Preliminary
Py0 in PWIA test of FSI
79
S. Malov et al., Phys. Rev. C 62, 057302 (2000).
80
Studies of the Reaction Mechanism
81
Correlations and Interaction Currents
Correlations
MECs
ICs
82
Off-shell Effects
initial proton is bound
Vertex function is not well defined. The Gordon
identity leads to alternative forms, equivalent
only when proton is on-shell.
83
12C(e,e'p) L/T Separations
Q20.15 GeV2
Q20.64 GeV2
D. Dutta et al., Phys. Rev. C 61, 061602 (2000).
P.E. Ulmer et al., Phys. Rev. Lett. 59, 2259
(1987).
Bates Linear Accelerator
JLab Hall C
84
Excess transverse strength at high ?m.
Persists, though perhaps declines, at higher Q2.
JLab Hall C
D. Dutta et al., Phys. Rev. C 61, 061602 (2000).
85
6Li(e,e'p) T/L Ratio
DWIA (dashed) fails to describe overall
strength. Scaling transverse amplitude in DWIA
(solid) gives good agreement ? deduce scale
factor, ?.
NIKHEF-K Amsterdam
J.B.J.M. Lanen et al., Phys. Rev. Lett. 64, 2250
(1990).
86
6Li(e,e'p) T/L Ratio
J.B.J.M. Lanen et al., Phys. Rev. Lett. 64, 2250
(1990).
NIKHEF-K Amsterdam
87
The L/T separations suggest

• Additional transverse reaction mechanism above
  2-nucleon emission threshold.
• MECs primarily transverse in character.
  Suggestive of two-body current.

Reminiscent of
88
T/L anomaly in inclusive (e,e')
J.M. Finn, R.W. Lourie and B.H. Cottman, Phys.
Rev. C 29, 2230 (1984).
89
12C(e,e'p) in Dip Region
Bates Linear Accelerator
R.W. Lourie et al., Phys. Rev. Lett. 56, 2364
(1986).
Data from Bates Linear Accelerator
90
12C(e,e'p)
Quasielastic
Delta
Between dip and ?
Peak of ?
Q20.30
Q20.48
Q20.58
L.B. Weinstein et al.,
Phys. Rev. Lett. 64, 1646
(1990).
H. Baghaei et al.,
Phys. Rev. C 39, 177 (1989).
Bates Linear Accelerator
Bates Linear Accelerator
91
12C(e,e'p) q990 MeV/c, ?475 MeV
For 60lt?mlt100 MeV, continuum cross section
increases strongly with ?. Large continuum
strength continues up to 300 MeV.
200
300
100
0
Missing Energy (MeV)
Bates Linear Accelerator
Figure adapted from J.H. Morrison et al.,
Phys. Rev. C 59, 221 (1999).
92
12C(e,e'p) q970 MeV/c, ?330 MeV
Continuum strength increases strongly with
?. Continuum cross section is smaller at high ?m.
Bates Linear Accelerator
Figure adapted from J.H. Morrison et al.,
Phys. Rev. C 59, 221 (1999).
93
12C(e,e'p)
For ?lt?QE, spectroscopic factors consistent with
naïve expectations.
Bates Linear Accelerator
J.H. Morrison et al., Phys. Rev. C 59, 221
(1999).
94
16O(e,e'p)
Large discrepancy for 1p3/2. Relativistic effects
predicted to be small here. Two-body currents
responsible??
C.M. Spaltro et al., Phys. Rev. C 48, 2385 (1993).
Circles (solid) NIKHEF-K
Crosses (dashed) - Saclay
95
16O(e,e'p) Q20.8 GeV2 Quasielastic
Relativistic DWIA gives good agreement with data.
JLab Hall A
J. Gao et al., Phys. Rev. Lett. 84, 3265 (2000).
96
16O(e,e'p) Q 20.8 GeV2 Quasielastic
Two-body calculations of Ryckebusch et al., give
flat distribution, as seen in the data, but
underpredict by a factor of two.
JLab Hall A
N. Liyanage et al., Phys. Rev. Lett. 86, 5670
(2001).
97
At high energies, RLT interference response
function sensitive to relativistic effects. For
example, spinor distortion
98
Spinor Distortions
N.R. reduction SV ? Mean field SV relatively
small
Dirac spinor SV affects lower components SV
large
99
16O(e,e'p) Q 20.8 GeV2 Quasielastic
Udias BS SD only
Udias scatt. state SD only
Udias full
1p 1/2
Sensitive to spinor distortions
Udias - no SD
Kelly
1p 3/2
JLab Hall A
J. Gao et al., Phys. Rev. Lett. 84, 3265 (2000).
100
Few-body Nuclei
101
The Deuteron
102
Short-distance Structure
Low pm
n
High pm
n
For large overlap, nucleons may lose individual
identities Quark/gluon d.o.f.?
103
Saclay Linac, France
M. Bernheim et al., Nucl. Phys. A365, 349 (1981).
104
Arenhövel Full
Large FSI/non-nucleonic effects. Problem at pm0.
PWBA Jeschonnek or Arenhövel
Arenhövel DWBA
JLab Hall A
P.E. Ulmer et al., Phys. Rev. Lett. 89, 062301
(2002).
105
D. Jordan et al., Phys. Rev. Lett. 76, 1579
(1996).
106
Bernheim et al.
Blomqvist et al. data cover kinematics beyond ?.
Also neutron exchange diagram important.
Ducret et al.
Jordan et al.
MAMI Mainz, Germany
K.I. Blomqvist et al., Phys. Lett. B 424, 33
(1998).
107
FSIMECIC
FSI
K.I. Blomqvist et al., Phys. Lett. B 424, 33
(1998).
Calculations H. Arenhövel
108
2H(e,e'p) Q20.23 GeV2 near ?
? clearly important
PWBAFSIMECIC
Bonn Electron Synchrotron, Germany
PWBAFSI
PWBAFSIMEC
H. Breuker et al., Nucl. Phys. A455, 641 (1986).
Calculations Leidemann and Arenhövel
109
Proton spectator
p
q
e
n
Neutron hit (low pm)
Proton hit (high pm)
q
q
p
p
n
n
Final State
Final State
n
p
n
p
f
f
f
f
110
Q20.67 GeV2 Quasielastic
Large FSI effects. Also, substantial
non-nucleonic effects.
JLab Hall A
P.E. Ulmer et al., Phys. Rev. Lett. 89, 062301
(2002).
111
Final State Interactions Can be LARGE
q
inferred
p'
p
112
de Forest
Arenhövel/Fabian
NR
Mosconi/Ricci
Arenhövel/Fabian
Hummel/Tjon
NR
de Forest
Wilbois/Arenhövel
Wilbois/Arenhövel
G. van der Steenhoven, Few-Body Syst. 17, 79
(1994).
113
What do all these data and curves suggest?

• Relativistic effects substantial in A? (and
  RLT).
• de Forest CC1 nucleon cross section gives same
  qualitative features as more complete
  calculations ? here, relativity more related to
  nucleonic current, as opposed to deuteron
  structure.

114
D-state important
AmPS NIKHEF-K Amsterdam
I. Passchier et al., Phys. Rev. Lett. 88, 102302
(2002).
115
Lots more d(e,e'p) data on the way!
116
2H(e,e'p)n E01-020 Hall A
Perpendicular R LT Q 2 0.80, 2.10, 3.50
(GeV/c)2 x1 p m from 0 to ? 0.5 GeV/c
Parallel/Anti-parallel Q 2 2.10 (GeV/c)2
vary x p m from 0 to 0.5 GeV/c Neutron angular
distribution Q 2 0.80, 2.10, 3.50 (GeV/c)2
117
2H(e,e'p)n E01-020 Hall A
118
2H(e,e'p)n E01-020 Hall A
119
2H(e,e'p)n with JLab 12 GeV upgrade
120
Preliminary Hall B E5 Data 2H(e,e'p)
Hall B data covers large range of Q2 and
excitation as well as ? coverage to separate RLT,
RLT' and RTT.
121
3,4He
122
3He(e,e'p)
Calculations by Laget dashedPWIA
dot-dashedDWIA solidDWIAMEC
Arrows indicate expected position for correlated
pair.
Saclay Linear Accelerator
C. Marchand et al., Phys. Rev.
Lett. 60, 1703 (1988).
123
3He(e,e'p)d
3He(e,e'p)np
3BBU similar to d?np
C. Marchand et al., Phys. Rev. Lett. 60, 1703
(1988).
124
Large effects from FSI and non-nucleonic
currents. Highest pm shows excess strength.
JLab Hall A
125
General features reproduced but not at correct
values of pm.
JLab Hall A
126
The most direct way to look for correlated
nucleons? Detect both of them ? JLab Hall B
127
3He(e,e'pp)n Hall B
128
Hall B
3He(e,e'pp)n 2 GeV
pperp lt 300 MeV/c
cos(?nq)
Isotropic fast pairs ?
pair not involved in reaction.
PRELIMINARY
cos(?pq)
129
Hall B
3He(e,e'pp)n
pperp lt 300 MeV/c
Pair momentum along q GeV/c
Pair momentum along q GeV/c
Small momentum along q ? pair not
involved in reaction.
PRELIMINARY
Little Q2 or isospin dependence.
2 GeV has acceptance corrections
130
Direct evidence of NN correlations
Before
After
p
n
n
p
p
p
131
4He(e,e'p)3H
ArgonneMod 7
Data and calculations corrected for MECIC
(Laget). Longitudinal overpredicted.
UrbanaMod 7
pm90 MeV/c
pm90 MeV/c
Saclay
A. Magnon et al., Phys. Lett. B 222, 352 (1989).
132
4He(e,e'p)3H
Calculations predict q dependence.
Saclay
J.E. Ducret et al., Nucl. Phys. A556, 373 (1993).
133
4He(e,e'p)3H
Again, calculations predict q dependence.
J.E. Ducret et al., Nucl. Phys. A556, 373 (1993).
134
4He(e,e'p)3H
MEC/3B
Laget
MEC/2B
Minimum filled in by FSI and 23-body currents.
FSI
PWIA
2-body
Schiavilla
FSI
PWIA
treeone-loop
Nagorny
AmPS NIKHEF-K Amsterdam
PWIA
tree
J.J. van Leeuwe et al., Phys. Rev. Lett. 80, 2543
(1998).
135
FSI dependence on kinematics
q
actual
inferred
p'
p
q
p
p'
136
4He(e,e'p)3H
It looks like the minimum is filled in here as
well.
JLab Hall A Experiment E97-111, J. Mitchell, B.
Reitz, J. Templon, cospokesmen
137
Summary

• (e,e'p) sensitive to single-particle aspects of
  nucleus, but
• More complicated physics is clearly important.
• Spectroscopic factors reduced compared to naïve
  shell model (including FSI corrections).
• Missing strength at least partly due to
  interaction currents direct interaction with
  with exchanged mesons or interaction with
  correlated pairs (spreads strength over ?m).

138
Summary contd.

• After several decades of experimental and
  theoretical effort, there are still unanswered
  questions.
• What is the nature of the interaction of the
  virtual photon with the nucleon medium and
  offshell effects?
• Handling FSI and other reaction currents still
  problematic, though realistic calculations are
  now available for the lighter systems.
• High energy program is underway, pushing to
  shorter distance scales, emphasizing relativistic
  effects,