Transcript (e,e'p) and Nuclear Structure Paul Ulmer Old Dominion University Hampton University Graduate Studies 2003

(e,e'p) and Nuclear Structure
Paul Ulmer
Old Dominion University
Hampton University Graduate Studies 2003
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
A. Saha
S. Strauch
E. Voutier
L. Weinstein
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
A(e,e'p)B
e'
B
e
q
p
A
Known: e and A
Detect: e' and p
Infer: pm = q – p = pB
(e,e'p) - Schematically
v
e'
A
B
e
A–1
B
=
A–2
Etc.
i.e. bound
+
N
+
p
Kinematics
p
e'
scattering
plane
pq
(,q)
e
“out-of-plane” angle
In ERLe:
x
pA–1
reaction
plane
Q2  – qq  = q2 – 2 = 4ee' sin2/2
Missing momentum:
pm = q – p = pA–1
Missing mass:
m =  –Tp – TA–1
Some (Very Few)
Experimental Details …
e'
Detected
e
“accidental”
(uncorrelated)
p
e'
e
e'
“real”
(correlated)
e
p
#
events
a
r
relative time: te– tp
r
C ( x )  C ( x )  Real 
 C ( x )  Accidental
a
Accidentals Rate = Re  Rp  /DF
 I 2 /DF
Reals Rate = Reep
I
S:N = Reals/Accidentals  DF /(I)
Compromise:
Optimize S:N and Reep
Extracting the cross section
Ne
NN (cm-2)
e'
(e, pe)
e
(p, pp)
p
dσ
Counts

ded pdpe dp p
N e N N e  p pe p p
6
Some Theory …
Cross Section for A(e,e'p)B in OPEA
“A-1”
 me d 3k    m d 3 p 
M fi 

3 
3

if
 e (2π)   E (2π) 
 (2π)4 δ4 ( P  PA1  Q  PA )
1 me
dσ lab 
β e
___
2
where
4πα
μ


M fi  2 k λ jμ k λ Bp J A
Q
Current-Current Interaction
Square of Matrix Element

___
M
if
2
fi
 4πα 
  2 
Q 
___
2 ___

k  λ  jμ k λ
*
if
  Bp J A
μ
*
Bp J ν A
if
W
k  λ  jν k λ
Cross Section in terms of Tensors
dσ
μν
 σ M ημνW
dedpdp dω
6
Mott cross section
Electron tensor
Nuclear tensor
Consider Unpolarized Case
Lorentz Vectors/Scalars
3 indep. momenta: Q , Pi , P (PA–1= Q + Pi – P)
target nucleus
ejectile
6 indep. scalars: Pi2, P2, Q2, Q•Pi ,Q •P , P•Pi
= MA2
= m2
Nuclear Response Tensor
W μν  X 1 gμν  X 2 qμ q ν  X 3 piμ piν
 X 4 p p  X 5q p  X 6 p q
μ
ν
μ
ν
i
μ
i
ν
 X 7q p  X 8 p q  X 9 p p
μ
ν
 X 10 p p
μ
i
μ
ν
μ
ν
i
ν
 ( P V t erms like εμνρσ qρ pσ )
Xi are the response functions
Impose Current Conservation
S ν  qμW μν  0
T  qνW
μ
μν
0
T hen qν S  0, pν S  0, pi ν S  0
ν
ν
ν
qμT  0, pμT  0, pi μT  0
μ
μ
μ
Get 6 equations in 10 unknowns
4 independent response functions
Putting it all together …
6


d
σ

  pE 3 σ M [vL RL  vT RT
 d d dp dω 
 e p
 LAB ( 2π)
 vLT RLT cosφ x  vTT RTT cos2φ x ]
with
α 2cos2θ/2
σM  2 4
4e sin θ/2
Q
vL   2
q
2
vTT
Q2
 2
2q



2
Q2
vT  2  tan2 θ/2
2q
vLT
Q2
 2
q
Q2
2

tan
θ/2
2
q
The Response Functions
Use spherical basis with z-axis along q:
ω
J  J  ρfi
q
1
1
J xfi  iJ fiy 
J fi  
2
0
fi
Nuclear 4-current
z
fi
 2
 2 q
0  2
RL  ρ fi ( q )    J fi ( q )
ω
1  2
1  2
RT  J fi ( q )  J fi ( q )
1 
1 
RTT  2 ReJ fi ( q ) J fi ( q )

1 
1 
RLT  2 Reρfi ( q )J fi ( q )  J fi ( q ) 
Response functions depend on scalar quantities
Q • Pi =  MA
In lab:
P • Pi = E MA
Q • P =  E – q p cos pq
Can choose:
Q2,  , m , pm
Note: no x dependence in response functions
Including electron and
recoil proton polarizations
6


d
σ

  pE 3 σ M {vL ( RL  RLn Sn )  vT ( RT  RTn Sn )
 d d dp dω 
 e p
 LAB ( 2π)
n
l
t
 vLT [( RLT  RLT
Sn ) cosφ x  ( RLT
Sl  RLT
St ) sin φ x ]
n
l
t
 vTT [( RTT  RTT
Sn ) cos2φ x  ( RTT
Sl  RTT
St ) sin 2φ x ]
 hvLT  [( RLT   RLnT  Sn ) sin φ x  ( RLl T  Sl  RLt T  St ) cosφ x ]
 hvTT  ( RTl T  Sl  RTt T  St )}
with
vLT 
Q2
 2 tan θ/2
q
vTT 
Q2
 tan θ/2 2  tan2 θ/2
q
and other v ' s defined as before
Extracting Response Functions
For instance: RLT and A (=A LT)
σeep  KσM [vL RL  vT RT  vLT RLT cosφx  vTT RTT cos2φx ]
 eep ( x  0)   eep ( x   )
RLT 
2 K M vLT
 eep ( x  0)   eep ( x   )
A 
 eep ( x  0)   eep ( x   )
Plane Wave Impulse
Approximation (PWIA)
spectator
A–1
e'
p
p0
q
e
A-1
p0
A
q – p = pA-1= pm= – p0
The Spectral Function
In nonrelativistic PWIA:
d 6
 K  ep S ( pm , εm )
dωdedpd p
e-p cross section
For bound state of recoil
system:
nuclear spectral function
proton momentum distribution
d 5σ
2

 K  ep ( pm )
dωded p
The Spectral Function,
cont’d.
2


S ( p0 , E0 )   B f a ( p0 ) A δ(E0  ε m )
f
where


p0   pm  initialmomentum
E0  E  ω  initialenergy
Note: S is not an observable!
Elastic Scattering from a Proton at Rest
(,q)
Before
(m,0)
p
(+m, q)
After
p
Proton is on-shell 
( + m)2  q2 = m2
2 + 2m + m2  q2 = m2
 = Q2  2m
Scattering from a Proton , cont’d.
p, s f J p  q, si  U f  U i
μ
μ
Vertex fcn
p
p
+
p
+
+
n
p
 γ
μ
+
p
p
p
p
0
μ
point proton
structure/anomalous
moment
+
Scattering from a Proton , cont’d.
Vertex fcn:
qν
2
  γ F1 (Q )  iσ
κF2 (Q )
2m
μ
μ
μν
2
Dirac FF
Pauli FF
GE (Q )  F1 (Q )  τκ F2 (Q )
2
Sachs FF’s
2
2
GM (Q )  F1 (Q )  κ F2 (Q )
2
wit h
2
Q2
τ
4m 2
GE and GM are the Fourier transforms of the
charge and magnetization densities in the Breit
frame.
2
Form Factor
 
1  k  r
 
2  k   r
r
k
Phase difference:


    
  k  k   r  q  r
k'
  iqr
Amplitude at q: F (q)   dr A(r )e
Cross section for ep elastic
 G  τG
dσ
2 θ
2 
 f rec σ M 
 2τ tan GM 
d
2
 1 τ

2
E
2
M
However, (e,e'p) on a nucleus
involves scattering from moving
protons, i.e. Fermi motion.
Elastic Scattering from a Moving Proton
(,q)
Before
After
(E,p)
p
p
(+E, q+p)
( + E)2 – (q+p)2 = m2
2 + 2E + E2  q2 2p•q  p2 = m2
Q2 = 2E 2p•q
 (E/m) = (Q2  2m) + p•q  m
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 …
Response functions for ep elastic
scattering off moving protons
2
2
(
E

E
)
q


0
RL  
W1 
W2
2

2m
4m


2
p sin 2 θ pq
RT  2 τ W2 
W1
2
m

( E0  E ) p sin θ pq
RLT  
W1
2
m
2
p sin 2 θ pq
RTT 
W1
2
m
wit h
W1  F12  τ (κF2 ) 2
W2  ( F1  κF2 ) 2
Quasielastic Scattering
For E  m:
  (Q2  2m) + p•q  m
If we “quasielastically” scatter from
nucleons within nucleus:
Expect peak at:
  (Q2  2m)
Broadened by Fermi motion:
p•q  m
Electron Scattering at Fixed Q 2
d 2σ
dω d
Elastic
Q2
2M
d 2σ
dω d
Nucleus
Quasielastic 
N*
Q2
2m
Elastic
Q2
2m
Deep
Inelastic
Q2
 300MeV
2m

Proton
N*
Q2
 300MeV
2m

Deep
Inelastic

Quasielastic Electron Scattering
6Li
12C
24Mg
40Ca
58Ni
89Y
118Sn
181Ta
208Pb
R.R. Whitney et al., Phys. Rev. C 9, 2230 (1974).
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).
Nuclear
Structure
First, a bit of history:
The first (e,e'p) measurement
12C(e,e'p)
27Al(e,e'p)
Frascati
Synchrotron,
Italy
U. Amaldi, Jr. et al.,
Phys. Rev. Lett. 13,
341 (1964).
(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.
Recall, in nonrelativistic PWIA:
d 6
 K  ep S ( pm , εm )
dωdedpd p
where q – p = pm= – p0
FSI destroys simple connection
between the measured pm and the
proton initial momentum (not an
observable).
Final State Interactions (FSI)
FSI
p
e'
p0'
e
q
A–1
p0
  

q  p  pA1  p0
A
Distorted Wave Impulse
Approximation (DWIA)
Treat outgoing proton
distorted waves in
presence of potential
produced by residual
nucleus (optical potential).
d 6
 K  ep S D ( pm , εm , p)
dωdedpd p
“Distorted” spectral function
Optical potential is constrained by
proton elastic scattering data.
Problems with this approach:
• Residual nucleus contains hole
state, unlike the target in p+A
scattering.
• Proton scattering data is surface
dominated, whereas ejected protons
in (e,e'p) are produced within entire
nuclear volume.
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).

th
ρα ( pm , p )  Sα

χ
(-)*
 
( rp , p )
rc 0
 
  2
 exp(iq  rp )ψ α ( rp )drp
At pm160 MeV/c,
wf is probed in
nuclear interior.
J.W.A. den Herder, et al., Phys. Lett. B 184, 11 (1987).
Adjusting optical
potential renders
good agreement
while maintaining
agreement with
p+A elastic.
J.W.A. den Herder, et al., Phys. Lett. B 184, 11 (1987).
12C(e,e'p)11B
Saclay
Linac,
France
J. Mougey et al., Nucl. Phys. A262, 461 (1976).
p-shell
l=1
s-shell
l=0
12C(e,e'p)11B
Saclay
Linac,
France
J. Mougey et al., Nucl. Phys. A262, 461 (1976).
12C(e,e'p)11B
NIKHEF-K
Amsterdam
G. van der Steenhoven et al., Nucl. Phys. A484, 445 (1988).
12C(e,e'p)11B
NIKHEF-K
Amsterdam
G. van der Steenhoven et al., Nucl. Phys. A484, 445 (1988).
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).
12C(e,e'p)
Bates
Linear
Accelerator
L.B. Weinstein et al., Phys. Rev. Lett. 64, 1646 (1990).
MAMI
Mainz,
Germany
K.I. Blomqvist et al., Phys. Lett. B 344, 85 (1995).
MAMI
Mainz,
Germany
Factorization violated.
DWIA calculations
underpredict at high pm.
Neglected MEC’s &
relativistic effects.
Offshell effects uncertain
at high pm.
K.I. Blomqvist et al., Phys. Lett. B 344, 85 (1995).
208Pb(e,e'p)
AmPS NIKHEF-K
Amsterdam
I. Bobeldijk et al., Phys. Rev. Lett. 73, 2684 (1994).
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).
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.
Where does the
“missing” strength go?
One possibility:
Detected
populates high m
recoils
n(k)
3He
total
m 300 MeV
2-body
SRC
dominate high
k (=pm ) and
are related to
large values
of m.
m 12.25 MeV
m 50 MeV
C. Ciofi degli Atti, E. Pace and G. Salmè, Phys. Lett. 141B, 14 (1984).
Nucl. Matter
d
3He
4He
C. Ciofi degli Atti, E. Pace and G. Salmè,
Phys. Lett. 141B, 14 (1984).
Similar shapes for
few-body nuclei
and nuclear matter
at high k (=pm).
Medium-Modified
Nucleons
Searching for Medium Effects on the Nucleon …
In parallel kinematics:
dσ
pE

σ [v R  vT RT ]
3 M L L
dedpdp dω (2π)
6
Can write ep elastic cross section as:


dσ
2
2
 f rec σ M vL k LGE  vT kT GM
d
2
q
Q2
with kL  2 and kT 
2
Q
2m
Relate RT/RL to in-medium proton FF’s

mq
RG  2
Q
~
2 RT
GM
 ~
RL
GE
PWIA
This relies on (unrealistic) model
assumptions!
Nonetheless …
2H(e,e'p)n
6Li(e,e'p)
DWIA
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
12C(e,e'p)
and
12C(e,e')
JLab
Hall C
D. Dutta et al., Phys. Rev. C 61, 061602 (2000).
However, large FSI
effects can mimic this
behavior …
FSI calculations for 16O 1p3/2
Data for 12C 1p3/2
Schrödinger LDA
Dirac DWIA
Dirac PWIA
Another, less model-dependent,
method …
Polarization Transfer
Proton Polarization and Form Factors

*
Free e p scattering
θ 
I 0 Px  2 τ (1  τ )GE GM t an e 
 2 
e  e
2
2  θe 

I 0 Pz 
τ (1  τ )GM t an 

m
 2 
2 
2  θe
I 0  GE2  τGM
1

2
(
1

τ
)
t
an


 2

GE
Px e  e
 θe 
 
t an 
GM
Pz 2m
2
in nucleus
model assumptions



~
GE
~
GM
* R. Arnold, C. Carlson and F. Gross, Phys. Rev. C 23, 363 (1981).
Polarization Transfer in Hall A
e

e
1H
spectrometer
and (2H or 4He)

p
spectrometer + FPP
2
 
H ( e , ep )n
1
4
  3
He( e , ep ) H
 
H ( e , ep )
Measuring the Proton Polarization: FPP
Density Dependent Form Factors
Quark-Meson Coupling Model (QMC):
G (Q 2 ) 
3
2
d
rw
(
r
)
G
(
Q
,  B ( r ))
 
3
d
 rw (r)
For (e,e'p)
  ()   *
w  exp( iq  r ) 
( p , r )  (r )
D.H. Lu, , A.W. Thomas, K. Tsushima, A.G. Williams, K.
Saito, Phys. Lett. B 417, 217 (1998).
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).
2
 
H(e , e' p)n
4
  3
He(e , e' p) H
JLab
Preliminary
Calculations by Arenhövel
Preliminary
RDWIA calculations by Udias et al.
Induced Polarization – 4He
JLab E93-049
Preliminary
Py=0 in PWIA: test of FSI
16
  15
O(e ,ep) N at Q2  0.8 (GeV/c) 2
DWIA+QMC
PWIA
DWIA
DWIA+spinor
distortion
S. Malov et al., Phys. Rev. C 62, 057302 (2000).
Studies of the
Reaction Mechanism
Correlations and Interaction
Currents
Correlations
MEC’s
IC’s




Off-shell Effects
e'
p
q
e
initial proton is bound
A–1
p0
A
Vertex function is not well defined. The
“Gordon identity” leads to alternative forms,
equivalent only when proton is on-shell.
12C(e,e'p)
L/T Separations
Q2=0.15 GeV2
P.E. Ulmer et al., Phys. Rev. Lett. 59, 2259 (1987).
Bates Linear Accelerator
Q2=0.64 GeV2
D. Dutta et al., Phys. Rev. C 61, 061602 (2000).
JLab Hall C
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).
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).
6Li(e,e'p)
T/L Ratio
DWIA
J.B.J.M. Lanen et al., Phys. Rev. Lett. 64, 2250 (1990).
NIKHEF-K Amsterdam
The L/T separations suggest
• Additional transverse reaction mechanism
above 2-nucleon emission threshold.
• MEC’s primarily transverse in character.
Suggestive of two-body current.
Reminiscent of …
T/L anomaly
in inclusive
(e,e'):
J.M. Finn, R.W. Lourie and B.H. Cottman, Phys. Rev. C 29, 2230 (1984).
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
12C(e,e'p)
“Delta”
Between dip and 
Quasielastic
Peak of 
Q2=0.30
Q2=0.48
Q2=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
12C(e,e'p) q=990 MeV/c, =475 MeV
d 6σ

ded pdω dε m
 ω - ω0 
α l (ε m ) Pl 


 ω/2 
l 0
lmax
For 60<m<100 MeV,
continuum cross section
increases strongly with .
Large continuum strength
continues up to 300 MeV.
0
100
200
300
Missing Energy (MeV)
Figure adapted from J.H. Morrison et al.,
Phys. Rev. C 59, 221 (1999).
Bates Linear
Accelerator
12C(e,e'p) q=970 MeV/c, =330 MeV
d 6σ

ded pdω dε m
 ω - ω0 
α l (ε m ) Pl 


 ω/2 
l 0
lmax
Continuum strength
increases strongly
with .
0
50
100
150
Continuum cross
section is smaller at
high m.
200
Missing Energy (MeV)
Figure adapted from J.H. Morrison et al.,
Phys. Rev. C 59, 221 (1999).
Bates Linear
Accelerator
12C(e,e'p)
For <QE,
spectroscopic
factors
consistent with
naïve
expectations.
Bates Linear
Accelerator
J.H. Morrison et al., Phys. Rev. C 59, 221 (1999).
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
16O(e,e'p) Q2=0.8 GeV2 Quasielastic
Relativistic
DWIA gives
good
agreement
with data.
JLab Hall A
J. Gao et al., Phys. Rev. Lett. 84, 3265 (2000).
16O(e,e'p) Q 2=0.8 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).
At high energies, RLT
interference response
function sensitive to
relativistic effects.
For example, spinor
distortion …
Spinor Distortions
  
   
  
p
 

E  m  S V
N.R. reduction
S+V  Mean field
S+V relatively small
Dirac spinor
S–V affects lower components
S–V large
16O(e,e'p) Q 2=0.8 GeV2 Quasielastic
1p 1/2
Udias BS
SD only
Udias full
Udias scatt.
state SD only
Udias - no SD
Kelly
Sensitive to
“spinor
distortions”
1p 3/2
JLab Hall A
J. Gao et al., Phys. Rev. Lett. 84, 3265 (2000).
Few-body
Nuclei …
The Deuteron
Short-distance Structure
Low pm
p n
High pm
p n
For large overlap, nucleons may
lose individual identities:
Quark/gluon d.o.f.?
Saclay
Linac,
France
M. Bernheim et al., Nucl. Phys. A365, 349 (1981).
Arenhövel Full
Large
FSI/nonnucleonic
effects.
Arenhövel DWBA
PWBA
Jeschonnek
or Arenhövel
pm (MeV/c)
P.E. Ulmer et al., Phys. Rev. Lett. 89, 062301 (2002).
Problem
at pm=0.
JLab
Hall A
D. Jordan et al., Phys. Rev. Lett. 76, 1579 (1996).
Bernheim et al.
Ducret et al.
Jordan et al.
Blomqvist et al.
data cover
kinematics
beyond . Also
neutron
exchange
diagram
important.
MAMI
Mainz,
Germany
K.I. Blomqvist et al., Phys. Lett. B 424, 33 (1998).
FSI+MEC+IC
FSI
K.I. Blomqvist et al., Phys. Lett. B 424, 33 (1998).
Calculations: H. Arenhövel
2H(e,e'p)
Q2=0.23 GeV2 near 
 clearly
important
PWBA+FSI+MEC+IC
PWBA+FSI
PWBA+FSI+MEC
Bonn Electron
Synchrotron,
Germany
H. Breuker et al., Nucl. Phys. A455, 641 (1986).
Calculations: Leidemann and Arenhövel
nf p
Proton
spectator
f
q
e
Proton hit (high pm)
q
p
n
Final State
pf
nf
p
n
Neutron hit (low pm)
q
p
n
Final State
pf
nf
Q2=0.67 GeV2 Quasielastic
Large FSI
effects.
Also,
substantial
non-nucleonic
effects.
0
100 200 300 400 500 600
pm (MeV/c)
P.E. Ulmer et al., Phys. Rev. Lett. 89, 062301 (2002).
JLab
Hall A
Final State Interactions
Can be LARGE
q
actual
inferred
p  p
p'
f
p'
p
p
f
de Forest
Mosconi/Ricci
Arenhövel/Fabian
NR
Arenhövel/Fabian
NR
Hummel/Tjon
de Forest
Wilbois/Arenhövel
Wilbois/Arenhövel
G. van der Steenhoven, Few-Body Syst. 17, 79 (1994).
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.


2
H(e , ep)
D-state
important
AmPS
NIKHEF-K
Amsterdam
I. Passchier et al., Phys. Rev. Lett. 88, 102302 (2002).


V
T

σ  σ0 1  P1d AdV  P2d AdT  hAe  P1d Aed
 P2d Aed
Lots more d(e,e'p)
data on the way!
2H(e,e'p)n
E01-020 Hall A
Perpendicular: R LT
Q 2 : 0.80, 2.10, 3.50 (GeV/c)2
x=1: 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
2H(e,e'p)n
E01-020 Hall A
2H(e,e'p)n
E01020 Hall A
2H(e,e'p)n
with JLab 12 GeV upgrade
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.
3,4He
3He(e,e'p)
Calculations by Laget:
dashed=PWIA
dot-dashed=DWIA
solid=DWIA+MEC
Arrows
indicate
expected
position for
correlated
pair.
C. Marchand et al.,
Phys. Rev. Lett. 60, 1703 (1988).
Saclay
Linear
Accelerator
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).
Large effects
from FSI and
non-nucleonic
currents.
Highest pm
shows excess
strength.
JLab
Hall A
ALT
General
features
reproduced
but not at
correct
values of
pm.
JLab
Hall A
The most direct way
to look for correlated
nucleons?
Detect both of them
 JLab Hall B
PRELIMINARY
2 GeV
1
Tp1/
Tp1/
3He(e,e'pp)n
PN>250
MeV/c
Hall B
4 GeV
1
PN>250
MeV/c
0.5
0.5
0
0
0
-1
0.5
1
0
0.5
1
Tp2/
Tp2/
fast pn
leading p
fast pn
leading p
-0.5
0
0.5
1
cos(2 fast nucleon angle)
-1
-0.5
0
0.5
1
cos(2 fast nucleon angle)
PRELIMINARY
Hall B
3He(e,e'pp)n
2 GeV
pperp < 300 MeV/c
cos(nq)
Isotropic fast pairs
 pair not involved in reaction.
cos(pq)
3He(e,e'pp)n
PRELIMINARY
pperp < 300 MeV/c
Hall B
Pair momentum along q [GeV/c]
Pair momentum along q [GeV/c]
Small momentum along q
 pair not involved in reaction.
Little Q2 or isospin dependence.
2 GeV has acceptance corrections
Direct evidence of NN
correlations
Before
p
p
After
n
n
p
p
4He(e,e'p)3H
Argonne+Mod 7
Data and
calculations
“corrected” for
MEC+IC
(Laget).
Urbana+Mod 7
pm=90 MeV/c
pm=90 MeV/c
Longitudinal
overpredicted.
Saclay
A. Magnon et al., Phys. Lett. B 222, 352 (1989).
4He(e,e'p)3H
Calculations
predict q
dependence.
Saclay
J.E. Ducret et al., Nucl. Phys. A556, 373 (1993).
4He(e,e'p)3H
Again,
calculations
predict q
dependence.
J.E. Ducret et al., Nucl. Phys. A556, 373 (1993).
4He(e,e'p)3H
+MEC/3B
Laget
+MEC/2B
+FSI
PWIA
+2-body
Schiavilla
+FSI
PWIA
Minimum
filled in by
FSI and
2&3-body
currents.
tree+one-loop
Nagorny
PWIA
tree
AmPS
NIKHEF-K
Amsterdam
J.J. van Leeuwe et al., Phys. Rev. Lett. 80, 2543 (1998).
FSI: dependence on kinematics
actual
q
inferred
p  p
Large FSI
p'f
p'
p
p
f
Small FSI
p  p
q
p
p
f
p'
p'f
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
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).
Summary cont’d.
• 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, …