Hampton University Graduate Studies 2003 (e,e'p) and Nuclear Structure Paul Ulmer Old Dominion University
Jan 18, 2018
Hampton University Graduate Studies 2003
(e,e'p) and Nuclear Structure
Paul Ulmer
Old Dominion University
Thanks to:
W. BoeglinT.W. Donnelly (Nuclear physics course at MIT)
J. GilfoyleR. GilmanR. Niyazov
J. Kelly (Adv. Nucl. Phys. 23, 75 (1996))B. ReitzA. Saha
S. StrauchE. 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
Known: e and A Detect: e' and p
e
e'
q A
pB
Infer: pm = q – p = pB
e'
e
v
A B + p
(e,e'p) - Schematically
B =
A–1
A–2 + N
Etc.
i.e. bound
Kinematics
e
e'
x
pA–1
pq
p
(,q)
In ERLe: Q2 – qq = q2 – 2 = 4ee' sin2/2
Missing momentum: pm = q – p = pA–1
Missing mass: m = –Tp – TA–1
scattering plane
“out-of-plane” angle
reaction plane
Some (Very Few) Experimental Details …
“accidental” (uncorrelated)
e
e
e
e'
e' p
e' p“real” (correlated)
Detected
# events
relative time: te– tp
ra
Accidental)(Real)()(
xCxCxCa
r
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
e
e'NN (cm-2)
(e, pe)
pepeNepe ppNNpp
Counts
d dddσd
pe
6
(p, pp)p
Some Theory …
)(δπ)2(
π)2(π)2(β1σ
144
3
3
3
32___
lab
AA
e
iffi
e
PQPP
pdEmkd
emM
emd
AJBpkjkQ
M fiμ
μ2 λ λ πα4
Cross Section for A(e,e'p)B in OPEA
where
Current-Current Interaction
“A-1”
Square of Matrix Element
___ν*μ
___
ν
*
μ
2
2
___ 2
λ λ λ λ πα4
if
ififfi
AJBpAJBp
kjkkjkQ
M
W
μνμνM
pe
6
ησdω dpdd
σd W
Electron tensor
Nuclear tensor
Mott cross section
Cross Section in terms of Tensors
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
Consider Unpolarized CaseLorentz Vectors/Scalars
)ε like termsPV(
σρμνρσ
νμ10
νμ9
νμ8
νμ7
νμ6
νμ5
νμ4
νμ3
νμ2μν1
μν
pqppX
ppXqpXpqX
qpXpqXppX
ppXqqXgXW
i
i
ii
ii
Nuclear Response Tensor
Xi are the response functions
Impose Current Conservation
0 ,0 ,0
0 ,0 ,0 Then
0
0
μμ
μμ
μμ
νν
νν
νν
μνν
μ
μνμ
ν
TpTpTq
SpSpSq
WqT
WqS
i
i
Get 6 equations in 10 unknowns
4 independent response functions
Putting it all together …
θ/2tan 2
θ/2tan2
θ/2sin4θ/2cosα σ with
]φ2cosφcos
[σπ)2(dω ddd
σd
22
2
2
2
2
2
22
22
2
2
42
22
M
xx
M3pe
6
qQv
qQv
qQv
qQv
e
RvRv
RvRvpEp
LTTT
TL
TTTTLTLT
TTLL
LAB
The Response Functions
Use spherical basis with z-axis along q:
yfi
xfifi
zfifi
iJJJ
qJJ
21
ρω
1
fi0
Nuclear 4-current
)()()(ρRe2
)()(Re2
)()(
)(ω
)(ρ
11fi
11
2121
202
2
qJqJqR
qJqJR
qJqJR
qJqqR
fifiLT
fifiTT
fifiT
fifiL
Q • Pi = MA
P • Pi = E MA
Q • P = E – q p cos pq
In lab:
Can choose: Q2, , m , pm
Note: no x dependence in response functions
Response functions depend on scalar quantities
Including electron and recoil proton polarizations
before as defined s'other and
θ/2tanθ/2 tan θ/2 tan with
)}(
]φcos)(φsin)[(
]φ2sin)(φ2cos)[(
]φsin)(φcos)[(
)()({σπ)2(dω dpdd
σd
22
2
2
2
xx
xx
xx
M3pe
6
vqQv
qQv
SRSRhv
SRSRSRRhv
SRSRSRRv
SRSRSRRv
SRRvSRRvpE
TTTL
ttTTl
lTTTT
ttTLl
lTLn
nTLTLTL
ttTTl
lTTn
nTTTTTT
ttLTl
lLTn
nLTLTLT
nnTTTn
nLLL
LAB
)()0()()0(
2)()0(
eepeep
eepeep
eepeep
xx
xx
LTM
xxLT
A
vKR
Extracting Response FunctionsFor instance: RLT and A (=A LT)
]φ2cosφcos[σσ xxMeep TTTTLTLTTTLL RvRvRvRvK
Plane Wave Impulse Approximation (PWIA)
e
e'
q
p
p0
A
A–1
A-1
spectator
p0
q – p = pA-1= pm= – p0
)ε,( ω
6
mmeppe
pSKdpddd
d
nuclear spectral function
In nonrelativistic PWIA:
25
)( ω
σ meppe
pKddd
d
For bound state of recoil system: proton momentum distribution
The Spectral Function
e-p cross section
The Spectral Function, cont’d.
energy initial ω momentum initial where
)εδ(E)()E,(
0
0
m0
2
000
EEpp
ApaBpS
m
ff
Note: S is not an observable!
Elastic Scattering from a Proton at Rest
p(,q) (m,0)
p(+m, q)
Proton is on-shell ( + m)2 q2 = m2
2 + 2m + m2 q2 = m2
= Q2 2m
Before
After
Scattering from a Proton , cont’d.
ifif UUsqpJsp μμ ,,
Vertex fcn
+
+n
p
p
p
pp
p
0
p
p
μμ γpoint proton
structure/anomalous moment
+ + +
Scattering from a Proton , cont’d.
Dirac FF Pauli FF
)(κ2
σ)(γ 22
νμν21
μμ QFm
qiQF
)( κ)()(
)( τκ)()(2
22
12
22
21
2
QFQFQG
QFQFQG
M
E
Sachs FF’s
Vertex fcn:
GE and GM are the Fourier transforms of the charge and magnetization densities in the Breit
frame.
2
2
4τ with
mQ
rk
k'
Amplitude at q: rqierArdqF )()(
rk
1 rk
2
Phase difference: rqrkk
Form Factor
Cross section for ep elastic
2222
M 2θtanτ2
τ1τσσ
MME
rec GGGfdd
However, (e,e'p) on a nucleus involves scattering from moving
protons, i.e. Fermi motion.
Elastic Scattering from a Moving Proton
p(,q) (E,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
Before
p (+E, q+p)After
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 …
2212
22
211
12pq
22
12pq0
12pq
22
2
22
2
1
20
)κ( )τ(κ
with
θsin
θsin)(
θsinτW2
42)(
FFWFFW
Wm
pR
Wm
pEER
Wm
pR
WmqW
mEER
TT
LT
T
L
Response functions for ep elastic scattering off moving protons
Quasielastic Scattering
For E m:
(Q2 2m) + p•q m
Expect peak at: (Q2 2m)
Broadened by Fermi motion: p•q m
If we “quasielastically” scatter from nucleons within nucleus:
ωdσ2
dd
Elastic
Quasielastic N*
Deep Inelastic
MQ2
2
mQ2
2
MeV3002
2
m
Q
Nucleus
Elastic
N*
Deep Inelastic
mQ2
2
MeV3002
2
m
Q
Proton
Electron Scattering at Fixed Q 2
ωdσ2
dd
6Li
181Ta
89Y58Ni40Ca
24Mg12C
118Sn 208Pb
R.R. Whitney et al., Phys. Rev. C 9, 2230 (1974).
Quasielastic Electron Scattering
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
U. Amaldi, Jr. et al., Phys. Rev. Lett. 13, 341 (1964).
First, a bit of history: The first (e,e'p) measurement
Frascati Synchrotron,
Italy
12C(e,e'p)
27Al(e,e'p)
(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.
)ε,( ω
6
mmeppe
pSKdpddd
d
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).
01 pppq A
e
e'
q
p
p0
FSI A–1
A
p0'
Final State Interactions (FSI)
Treat outgoing proton distorted waves in
presence of potential produced by residual
nucleus (optical potential).
Distorted Wave Impulse Approximation (DWIA)
),ε,( ω
6
ppSKdpddd
dmm
Dep
pe
“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.
J.W.A. den Herder, et al., Phys. Lett. B 184, 11 (1987).
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).
2
α
0
*(-)α
thα
d)(ψ)exp(
),(χ),(ρ
ppp
pr
m
rrrqi
prSppc
At pm160 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. Mougey et al., Nucl. Phys. A262, 461 (1976).
Saclay Linac, France
12C(e,e'p)11B
J. Mougey et al., Nucl. Phys. A262, 461 (1976).
Saclay Linac, France
12C(e,e'p)11Bp-shell l=1
s-shell l=0
G. van der Steenhoven et al., Nucl. Phys. A484, 445 (1988).
NIKHEF-K Amsterdam
12C(e,e'p)11B
G. van der Steenhoven et al., Nucl. Phys. A484, 445 (1988).
NIKHEF-K Amsterdam
12C(e,e'p)11B
G. van der Steenhoven, et al., Nucl. Phys. A480, 547 (1988).
NIKHEF-K Amsterdam
12C(e,e'p)11B
DWIA calculations fit data reasonably
well.
Missing strength observed however.
L.B. Weinstein et al., Phys. Rev. Lett. 64, 1646 (1990).
12C(e,e'p)
Bates Linear
Accelerator
K.I. Blomqvist et al., Phys. Lett. B 344, 85 (1995).
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.
I. Bobeldijk et al., Phys. Rev. Lett. 73, 2684 (1994).
AmPS NIKHEF-K Amsterdam
208Pb(e,e'p)
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.
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
recoils
populates high m
C. Ciofi degli Atti, E. Pace and G. Salmè, Phys. Lett. 141B, 14 (1984).
n(k)
total
m 12.25 MeV
2-body
m 300 MeV
m 50 MeV
3He
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).
d
Nucl. Matter
3He4He
Similar shapes for few-body nuclei
and nuclear matter at high k (=pm).
Medium-Modified Nucleons
Searching for Medium Effects on the Nucleon …
22Mσσ
MTTELLrec GkvGkvfdd
][σπ)2(dω ddd
σdM3
pe
6
TTLL RvRvpEp
In parallel kinematics:
Can write ep elastic cross section as:
2
2
2
2
2 and with
mQk
k TL
E
M
L
TG G
GRR
Qqm
R ~~2
2
PWIA
Relate RT/RL to in-medium proton FF’s
This relies on (unrealistic) model assumptions!
Nonetheless …
J.E. Ducret et al., Phys. Rev. C 49, 1783 (1994).
2H(e,e'p)n 6Li(e,e'p)
DWIA
NIKHEF-K Amsterdam
J.B.J.M. Lanen et al., Phys. Rev. Lett. 64, 2250 (1990).
12C(e,e'p) and 12C(e,e')
D. Dutta et al., Phys. Rev. C 61, 061602 (2000).
JLab Hall C
However, large FSI effects can mimic this
behavior …
Dirac PWIA
Dirac DWIASchrödinger LDA
FSI calculations for 16O 1p3/2
Data for 12C 1p3/2
Another, less model-dependent, method …
Polarization Transfer
Proton Polarization and Form Factors
2θtan)τ1(21τ
2θtan)τ1(τ
2θtan)τ1(τ2
e2220
e220
e0
scattering Free
ME
Mz
MEx
GGI
Gm
eePI
GGPI
pe
2θtan
2e
mee
PP
GG
z
x
M
E
* R. Arnold, C. Carlson and F. Gross, Phys. Rev. C 23, 363 (1981).
M
E
GG~~in nucleus
model assumptions
*
spectrometer + FPP
1H and (2H or 4He)
spectrometer
ee
p
),(H
H),(He ),(H
1
342
pee
peenpee
Polarization Transfer in Hall A
Measuring the Proton Polarization: FPP
Density Dependent Form Factors
)(
))(,( )()(
3
232
rrwd
rQGrrwdQG B
)(),()exp( *)( rrprqiw
For (e,eFor (e,e''p)p)
D.H. Lu, , A.W. Thomas, K. Tsushima, A.G. Williams, K. Saito, Phys. Lett. B 417, 217 (1998).
Quark-Meson Coupling Model (QMC):
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).
Quark-Meson Coupling Model
4He
npee )',(H2
Calculations by Arenhövel
H)',(He 34 pee
JLab
RDWIA calculations by Udias et al.
Preliminary Preliminary
Induced Polarization – 4HeJLab E93-049
Py=0 in PWIA: test of FSI
Preliminary
PWIA DWIADWIA+spinor
distortion
DWIA+QMC
221516 (GeV/c) 8.0at N )O( Qpe,e
S. Malov et al., Phys. Rev. C 62, 057302 (2000).
Studies of the Reaction Mechanism
Correlations
MEC’s
IC’s
Correlations and Interaction Currents
Off-shell Effects
Vertex function is not well defined. The “Gordon identity” leads to alternative forms,
equivalent only when proton is on-shell.
e
e'
q
p
p0
A
A–1
initial proton is bound
D. Dutta et al., Phys. Rev. C 61, 061602 (2000).P.E. Ulmer et al., Phys. Rev. Lett. 59, 2259 (1987).
12C(e,e'p) L/T Separations
Q2=0.15 GeV2Q2=0.64 GeV2
Bates Linear Accelerator JLab Hall C
D. Dutta et al., Phys. Rev. C 61, 061602 (2000).
Excess transverse strength at high m.
Persists, though perhaps declines,
at higher Q2.
JLab Hall C
J.B.J.M. Lanen et al., Phys. Rev. Lett. 64, 2250 (1990).
6Li(e,e'p) T/L RatioDWIA (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).
DWIA
6Li(e,e'p) T/L Ratio
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 …
J.M. Finn, R.W. Lourie and B.H. Cottman, Phys. Rev. C 29, 2230 (1984).
T/L anomaly in inclusive
(e,e'):
R.W. Lourie et al., Phys. Rev. Lett. 56, 2364 (1986).
12C(e,e'p) in “Dip Region”
Data from: Bates Linear Accelerator
Bates Linear
Accelerator
L.B. Weinstein et al., Phys. Rev. Lett. 64, 1646 (1990).
H. Baghaei et al., Phys. Rev. C 39, 177 (1989).
12C(e,e'p)Quasielastic“Delta”
Q2=0.30
Q2=0.48
Q2=0.58
Between dip and Peak of
Bates Linear Accelerator Bates Linear Accelerator
Figure adapted from J.H. Morrison et al., Phys. Rev. C 59, 221 (1999).
Missing Energy (MeV)0 100 200 300
12C(e,e'p) q=990 MeV/c, =475 MeV
ω/2
ω-ω)ε(α
dε dωddσd
0
0
pe
6
max
lm
l
ll
m
P
For 60<m<100 MeV, continuum cross section
increases strongly with .
Large continuum strength continues up to 300 MeV.
Bates Linear
Accelerator
Figure adapted from J.H. Morrison et al., Phys. Rev. C 59, 221 (1999).
Missing Energy (MeV)
0 100 20050 150
ω/2
ω-ω)ε(α
dε dωddσd
0
0
pe
6
max
lm
l
ll
m
P
12C(e,e'p) q=970 MeV/c, =330 MeV
Continuum strength increases strongly
with .
Continuum cross section is smaller at
high m.
Bates Linear
Accelerator
J.H. Morrison et al., Phys. Rev. C 59, 221 (1999).
12C(e,e'p)
For <QE, spectroscopic
factors consistent with
naïve expectations.
Bates Linear
Accelerator
C.M. Spaltro et al., Phys. Rev. C 48, 2385 (1993).
Circles (solid) – NIKHEF-K Crosses (dashed) - Saclay
Large discrepancy
for 1p3/2.
Relativistic effects
predicted to be small here.
Two-body currents
responsible??
16O(e,e'p)
J. Gao et al., Phys. Rev. Lett. 84, 3265 (2000).
16O(e,e'p) Q2=0.8 GeV2 Quasielastic
Relativistic DWIA gives
good agreement with data.
JLab Hall A
N. Liyanage et al., Phys. Rev. Lett. 86, 5670 (2001).
Two-body calculations of Ryckebusch et
al., give flat distribution, as
seen in the data, but underpredict
by a factor of two.
16O(e,e'p) Q 2=0.8 GeV2 Quasielastic
JLab Hall A
At high energies, RLT interference response function sensitive to relativistic effects.
For example, spinor distortion …
Spinor Distortions
VSmEp
N.R. reductionS+V Mean field
S+V relatively small
Dirac spinorS–V affects lower components
S–V large
J. Gao et al., Phys. Rev. Lett. 84, 3265 (2000).
16O(e,e'p) Q 2=0.8 GeV2 Quasielastic
Udias fullUdias BS SD only
Udias scatt. state SD only
Udias - no SD
Kelly
1p 1/2
1p 3/2
Sensitive to “spinor
distortions”
JLab Hall A
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.?
M. Bernheim et al., Nucl. Phys. A365, 349 (1981).
Saclay Linac, France
P.E. Ulmer et al., Phys. Rev. Lett. 89, 062301 (2002).
pm (MeV/c)
Arenhövel DWBA
Arenhövel Full
PWBA Jeschonnek
or Arenhövel
JLab Hall A
Large FSI/non-nucleonic effects.
Problem at pm=0.
D. Jordan et al., Phys. Rev. Lett. 76, 1579 (1996).
K.I. Blomqvist et al., Phys. Lett. B 424, 33 (1998).
MAMI Mainz,
Germany
Ducret et al.Bernheim et al.
Jordan et al.
Blomqvist et al. data cover kinematics
beyond . Also neutron
exchange diagram
important.
K.I. Blomqvist et al., Phys. Lett. B 424, 33 (1998).
Calculations: H. Arenhövel
FSI
FSI+MEC+IC
Bonn Electron Synchrotron,
Germany
2H(e,e'p) Q2=0.23 GeV2 near
Calculations: Leidemann and ArenhövelH. Breuker et al., Nucl. Phys. A455, 641 (1986).
PWBA+FSI
PWBA+FSI+MEC+IC
PWBA+FSI+MEC
clearly important
qpn
f
Final State
nfp
Proton hit (high pm)
q
np
Final State
nfpf
Neutron hit (low pm)
e q
fpnf
n p
Proton spectator
pm (MeV/c)0 100 200 400 500300 600
P.E. Ulmer et al., Phys. Rev. Lett. 89, 062301 (2002).
Q2=0.67 GeV2 Quasielastic
Large FSI effects.
Also, substantial
non-nucleonic effects.
JLab Hall A
Final State Interactions Can be LARGE
p
q
fp'
fpp'pp
actualinferred
G. van der Steenhoven, Few-Body Syst. 17, 79 (1994).
Wilbois/ArenhövelWilbois/Arenhövel
de Forest
de Forest
Hummel/Tjon
Arenhövel/Fabian
Arenhövel/Fabian
Mosconi/Ricci
NR
NR
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.
I. Passchier et al., Phys. Rev. Lett. 88, 102302 (2002).
),(H2 pee
Ted
dVed
de
Td
dVd
d APAPAhAPAP 21210 1σσ
D-state important
AmPS NIKHEF-K Amsterdam
Lots more d(e,e'p) data on the way!
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 distributionQ 2 : 0.80, 2.10, 3.50 (GeV/c)2
2H(e,e'p)n E01-020 Hall A
2H(e,e'p)n E01-020 Hall A
2H(e,e'p)n E01-020 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
C. Marchand et al., Phys. Rev. Lett. 60, 1703 (1988).
3He(e,e'p)Calculations by Laget: dashed=PWIA
dot-dashed=DWIA solid=DWIA+MEC
Saclay Linear
Accelerator
Arrows indicate
expected position for correlated
pair.
C. Marchand et al., Phys. Rev. Lett. 60, 1703 (1988).
3He(e,e'p)d 3He(e,e'p)np
3BBU similar
to dnp
JLab Hall A
Large effects from FSI and non-nucleonic
currents.
Highest pm shows excess
strength.
ALT
JLab Hall A
General features
reproduced but not at correct
values of pm.
The most direct way to look for correlated
nucleons?
Detect both of them JLab Hall B
3He(e,e'pp)n Hall B
2 GeVPN>250 MeV/c
4 GeVPN>250 MeV/c
fast pn leading p
fast pn leading pPR
EL
IMIN
AR
Y
0 0.5 1Tp2/
0 0.5 1Tp2/
0
0.5
1T p
1/
0
0.5
1
T p1/
-1 -0.5 0 10.5cos(2 fast nucleon angle)
-1 -0.5 0 10.5cos(2 fast nucleon angle)
Hall B 3He(e,e'pp)n 2 GeV pperp < 300 MeV/cPR
ELIM
INA
RY
cos(nq)
cos(pq)
Isotropic fast pairs pair not involved in reaction.
Hall B 3He(e,e'pp)n
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.
p perp
< 3
00 M
eV/c
PRE
LIM
INA
RY
2 GeV has acceptance corrections
Before
pn
p
After
np
p
Direct evidence of NN correlations
A. Magnon et al., Phys. Lett. B 222, 352 (1989).
Saclay
4He(e,e'p)3HArgonne+Mod 7
Urbana+Mod 7 Data and calculations
“corrected” for MEC+IC (Laget).
Longitudinal overpredicted.pm=90 MeV/c pm=90 MeV/c
J.E. Ducret et al., Nucl. Phys. A556, 373 (1993).
Saclay
4He(e,e'p)3H
Calculations predict q
dependence.
J.E. Ducret et al., Nucl. Phys. A556, 373 (1993).
4He(e,e'p)3H
Again, calculations
predict q dependence.
J.J. van Leeuwe et al., Phys. Rev. Lett. 80, 2543 (1998).
PWIA
tree+one-loop
tree
PWIA
+FSI
+2-body
PWIA
+FSI+MEC/2B
+MEC/3BLaget
Schiavilla
Nagorny
Minimum filled in by FSI and
2&3-body currents.
4He(e,e'p)3H
AmPS NIKHEF-K Amsterdam
FSI: dependence on kinematics
p
q
fp'
fpp'pp
actualinferred
Large FSI
qp
fp p'
fp'pp
Small FSI
4He(e,e'p)3H
JLab Hall A Experiment E97-111, J. Mitchell, B. Reitz, J. Templon, cospokesmen
It looks like the minimum
is filled in here as well.
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, …