hampton university graduate studies 2003
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(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 Saha S. Strauch - PowerPoint PPT PresentationTRANSCRIPT
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Hampton University Graduate Studies 2003
(e,e'p) and Nuclear Structure
Paul Ulmer
Old Dominion University
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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
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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
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A(e,e'p)B
Known: e and A Detect: e' and p
e
e'
q A
pB
Infer: pm = q – p = pB
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e'
e
v
A B + p
(e,e'p) - Schematically
B =
A–1
A–2 + N
Etc.
i.e. bound
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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
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Some (Very Few) Experimental Details …
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“accidental” (uncorrelated)
e
e
e
e'
e' p
e' p“real” (correlated)
Detected
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# events
relative time: te– tp
ra
Accidental)(Real)()(
xCxCxCa
r
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Accidentals Rate = Re Rp /DF I 2 /DF
Reals Rate = Reep I
S:N = Reals/Accidentals DF /(I)
Compromise:
Optimize S:N and Reep
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Extracting the cross section
Ne
e
e'NN (cm-2)
(e, pe)
pepeNepe ppNNpp
Counts
d ddd
σd
pe
6
(p, pp)
p
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Some Theory …
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)(δπ)2(
π)2(π)2(β
1σ
144
3
3
3
32___
lab
AA
e
iffi
e
PQPP
pd
E
mkd
e
mM
e
md
AJBpkjkQ
M fiμ
μ2λ λ
πα4
Cross Section for A(e,e'p)B in OPEA
where
Current-Current Interaction
“A-1”
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Square of Matrix Element
___ν
*μ
___
ν
*
μ
2
2
___2
λ λ λ λ πα4
if
ififfi
AJBpAJBp
kjkkjkQ
M
W
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μνμνM
pe
6
ησdω dpdd
σdW
Electron tensor
Nuclear tensor
Mott cross section
Cross Section in terms of Tensors
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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 Case
Lorentz Vectors/Scalars
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)ε like termsPV(
σρμνρσ
νμ10
νμ9
νμ8
νμ7
νμ6
νμ5
νμ4
νμ3
νμ2μν1
μν
pq
ppX
ppXqpXpqX
qpXpqXppX
ppXqqXgXW
i
i
ii
ii
Nuclear Response Tensor
Xi are the response functions
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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
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Putting it all together …
θ/2tan 2
θ/2tan2
θ/2sin4
θ/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
q
Q
q
Qv
q
Qv
q
Qv
q
Qv
e
RvRv
RvRvpE
p
LTTT
TL
TTTTLTLT
TTLL
LAB
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The Response Functions
Use spherical basis with z-axis along q:
yfi
xfifi
zfifi
iJJJ
qJJ
2
1
ρω
1
fi0
Nuclear 4-current
)()()(ρRe2
)()(Re2
)()(
)(ω
)(ρ
11fi
11
2121
202
2
qJqJqR
qJqJR
qJqJR
qJq
qR
fifiLT
fifiTT
fifiT
fifiL
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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
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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
v
q
Qv
q
Qv
SRSRhv
SRSRSRRhv
SRSRSRRv
SRSRSRRv
SRRvSRRvpE
TTTL
ttTTl
lTTTT
ttTLl
lTLn
nTLTLTL
ttTTl
lTTn
nTTTTTT
ttLTl
lLTn
nLTLTLT
nnTTTn
nLLL
LAB
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)()0(
)()0(
2
)()0(
eepeep
eepeep
eepeep
xx
xx
LTM
xxLT
A
vKR
Extracting Response Functions
For instance: RLT and A (=A LT)
]φ2cosφcos[σσ xxMeep TTTTLTLTTTLL RvRvRvRvK
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Plane Wave Impulse Approximation (PWIA)
e
e'
q
p
p0
A
A–1
A-1
spectator
p0
q – p = pA-1= pm= – p0
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)ε,( ω
6
mmeppe
pSKdpddd
d
nuclear spectral function
In nonrelativistic PWIA:
25
)( ω
σ mep
pe
pKddd
d
For bound state of recoil system: proton momentum distribution
The Spectral Function
e-p cross section
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The Spectral Function, cont’d.
energy initial ω
momentum initial where
)εδ(E)()E,(
0
0
m0
2
000
EE
pp
ApaBpS
m
ff
Note: S is not an observable!
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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
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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
+ + +
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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
m
Q
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r
k
k'
Amplitude at q: rqierArdqF )()(
rk
1 rk
2
Phase difference:
rqrkk
Form Factor
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Cross section for ep elastic
2222
M 2
θtanτ2
τ1
τσ
σM
MErec G
GGf
d
d
However, (e,e'p) on a nucleus involves scattering from moving
protons, i.e. Fermi motion.
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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
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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 …
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2212
22
211
12pq
22
12pq0
12pq
22
2
22
2
1
2
0
)κ( )τ(κ
with
θsin
θsin)(
θsinτW2
42
)(
FFWFFW
Wm
pR
Wm
pEER
Wm
pR
Wm
qW
m
EER
TT
LT
T
L
Response functions for ep elastic scattering off moving protons
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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:
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ωd
σ2
d
d
Elastic
Quasielastic N*
Deep Inelastic
M
Q
2
2
m
Q
2
2
MeV3002
2
m
Q
Nucleus
Elastic
N*
Deep Inelastic
m
Q
2
2
MeV3002
2
m
Q
Proton
Electron Scattering at Fixed Q 2
ωd
σ2
d
d
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6Li
181Ta
89Y58Ni40Ca
24Mg12C
118Sn 208Pb
R.R. Whitney et al., Phys. Rev. C 9, 2230 (1974).
Quasielastic Electron Scattering
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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).
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Nuclear Structure
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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)
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(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.
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)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).
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01 pppq A
e
e'
q
p
p0
FSI A–1
A
p0'
Final State Interactions (FSI)
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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
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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.
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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
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J.W.A. den Herder, et al., Phys. Lett. B 184, 11 (1987).
2
α
0
*(-)α
thα
d)(ψ)exp(
),(χ),(ρ
ppp
p
r
m
rrrqi
prSppc
At pm160 MeV/c, wf is probed in nuclear interior.
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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.
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J. Mougey et al., Nucl. Phys. A262, 461 (1976).
Saclay Linac, France
12C(e,e'p)11B
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J. Mougey et al., Nucl. Phys. A262, 461 (1976).
Saclay Linac, France
12C(e,e'p)11Bp-shell l=1
s-shell l=0
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G. van der Steenhoven et al., Nucl. Phys. A484, 445 (1988).
NIKHEF-K Amsterdam
12C(e,e'p)11B
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G. van der Steenhoven et al., Nucl. Phys. A484, 445 (1988).
NIKHEF-K Amsterdam
12C(e,e'p)11B
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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.
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L.B. Weinstein et al., Phys. Rev. Lett. 64, 1646 (1990).
12C(e,e'p)
Bates Linear
Accelerator
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K.I. Blomqvist et al., Phys. Lett. B 344, 85 (1995).
MAMI Mainz,
Germany
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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.
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I. Bobeldijk et al., Phys. Rev. Lett. 73, 2684 (1994).
AmPS NIKHEF-K Amsterdam
208Pb(e,e'p)
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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.
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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.
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Where does the “missing” strength go?
One possibility:
Detected
recoils
populates high m
![Page 61: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/61.jpg)
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.
![Page 62: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/62.jpg)
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).
![Page 63: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/63.jpg)
Medium-Modified Nucleons
![Page 64: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/64.jpg)
Searching for Medium Effects on the Nucleon …
22Mσ
σMTTELLrec GkvGkvf
d
d
][σπ)2(dω ddd
σdM3
pe
6
TTLL RvRvpE
p
In parallel kinematics:
Can write ep elastic cross section as:
2
2
2
2
2 and with
m
Qk
Q
qk TL
![Page 65: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/65.jpg)
E
M
L
TG G
G
R
R
Q
qmR ~
~2
2
PWIA
Relate RT/RL to in-medium proton FF’s
This relies on (unrealistic) model assumptions!
Nonetheless …
![Page 66: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/66.jpg)
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).
![Page 67: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/67.jpg)
12C(e,e'p) and 12C(e,e')
![Page 68: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/68.jpg)
D. Dutta et al., Phys. Rev. C 61, 061602 (2000).
JLab Hall C
![Page 69: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/69.jpg)
However, large FSI effects can mimic this
behavior …
![Page 70: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/70.jpg)
Dirac PWIA
Dirac DWIASchrödinger LDA
FSI calculations for 16O 1p3/2
Data for 12C 1p3/2
![Page 71: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/71.jpg)
Another, less model-dependent, method …
Polarization Transfer
![Page 72: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/72.jpg)
Proton Polarization and Form Factors
2
θtan)τ1(21τ
2
θtan)τ1(τ
2
θtan)τ1(τ2
e2220
e220
e0
scattering Free
ME
Mz
MEx
GGI
Gm
eePI
GGPI
pe
2
θtan
2e
m
ee
P
P
G
G
z
x
M
E
* R. Arnold, C. Carlson and F. Gross, Phys. Rev. C 23, 363 (1981).
M
E
G
G~
~in nucleus
model assumptions
*
![Page 73: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/73.jpg)
spectrometer + FPP
1H and (2H or 4He)
spectrometer
e
e
p
),(H
H),(He ),(H
1
342
pee
peenpee
Polarization Transfer in Hall A
![Page 74: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/74.jpg)
Measuring the Proton Polarization: FPP
![Page 75: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/75.jpg)
Density Dependent Form Factors
)(
))(,( )()(
3
23
2
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):
![Page 76: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/76.jpg)
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
![Page 77: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/77.jpg)
npee )',(H2
Calculations by Arenhövel
H)',(He 34 pee
JLab
RDWIA calculations by Udias et al.
Preliminary Preliminary
![Page 78: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/78.jpg)
Induced Polarization – 4He
JLab E93-049
Py=0 in PWIA: test of FSI
Preliminary
![Page 79: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/79.jpg)
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).
![Page 80: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/80.jpg)
Studies of the Reaction Mechanism
![Page 81: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/81.jpg)
Correlations
MEC’s
IC’s
Correlations and Interaction Currents
![Page 82: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/82.jpg)
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
![Page 83: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/83.jpg)
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
![Page 84: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/84.jpg)
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
![Page 85: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/85.jpg)
J.B.J.M. Lanen et al., Phys. Rev. Lett. 64, 2250 (1990).
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
![Page 86: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/86.jpg)
J.B.J.M. Lanen et al., Phys. Rev. Lett. 64, 2250 (1990).
DWIA
6Li(e,e'p) T/L Ratio
NIKHEF-K Amsterdam
![Page 87: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/87.jpg)
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 …
![Page 88: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/88.jpg)
J.M. Finn, R.W. Lourie and B.H. Cottman, Phys. Rev. C 29, 2230 (1984).
T/L anomaly in inclusive
(e,e'):
![Page 89: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/89.jpg)
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
![Page 90: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/90.jpg)
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
![Page 91: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/91.jpg)
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 dωdd
σd
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
![Page 92: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/92.jpg)
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 dωdd
σd
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
![Page 93: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/93.jpg)
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
![Page 94: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/94.jpg)
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)
![Page 95: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/95.jpg)
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
![Page 96: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/96.jpg)
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
![Page 97: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/97.jpg)
At high energies, RLT interference response function sensitive to relativistic effects.
For example, spinor distortion …
![Page 98: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/98.jpg)
Spinor Distortions
VSmE
p
N.R. reduction
S+V Mean field
S+V relatively small
Dirac spinor
S–V affects lower components
S–V large
![Page 99: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/99.jpg)
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
![Page 100: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/100.jpg)
Few-body Nuclei …
![Page 101: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/101.jpg)
The Deuteron
![Page 102: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/102.jpg)
Short-distance Structure
Low pm p n
High pm p n
For large overlap, nucleons may lose individual identities:
Quark/gluon d.o.f.?
![Page 103: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/103.jpg)
M. Bernheim et al., Nucl. Phys. A365, 349 (1981).
Saclay Linac, France
![Page 104: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/104.jpg)
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.
![Page 105: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/105.jpg)
D. Jordan et al., Phys. Rev. Lett. 76, 1579 (1996).
![Page 106: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/106.jpg)
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.
![Page 107: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/107.jpg)
K.I. Blomqvist et al., Phys. Lett. B 424, 33 (1998).
Calculations: H. Arenhövel
FSI
FSI+MEC+IC
![Page 108: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/108.jpg)
Bonn Electron Synchrotron,
Germany
2H(e,e'p) Q2=0.23 GeV2 near
Calculations: Leidemann and Arenhövel
H. Breuker et al., Nucl. Phys. A455, 641 (1986).
PWBA+FSI
PWBA+FSI+MEC+IC
PWBA+FSI+MEC
clearly important
![Page 109: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/109.jpg)
qpn
f
Final State
nf
p
Proton hit (high pm)
q
np
Final State
nf
pf
Neutron hit (low pm)
e q
fpn
f
n p
Proton spectator
![Page 110: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/110.jpg)
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
![Page 111: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/111.jpg)
Final State Interactions Can be LARGE
p
q
fp'
fp
p'pp
actualinferred
![Page 112: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/112.jpg)
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
![Page 113: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/113.jpg)
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.
![Page 114: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/114.jpg)
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
![Page 115: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/115.jpg)
Lots more d(e,e'p) data on the way!
![Page 116: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/116.jpg)
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
![Page 117: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/117.jpg)
2H(e,e'p)n E01-020 Hall A
![Page 118: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/118.jpg)
2H(e,e'p)n E01-020 Hall A
![Page 119: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/119.jpg)
2H(e,e'p)n with JLab 12 GeV upgrade
![Page 120: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/120.jpg)
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.
![Page 121: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/121.jpg)
3,4He
![Page 122: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/122.jpg)
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.
![Page 123: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/123.jpg)
C. Marchand et al., Phys. Rev. Lett. 60, 1703 (1988).
3He(e,e'p)d 3He(e,e'p)np
3BBU similar
to dnp
![Page 124: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/124.jpg)
JLab Hall A
Large effects from FSI and non-nucleonic
currents.
Highest pm shows excess
strength.
![Page 125: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/125.jpg)
AL
T
JLab Hall A
General features
reproduced but not at
correct values of pm.
![Page 126: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/126.jpg)
The most direct way to look for correlated
nucleons?
Detect both of them JLab Hall B
![Page 127: Hampton University Graduate Studies 2003](https://reader035.vdocuments.us/reader035/viewer/2022062723/56813f6a550346895daa3ceb/html5/thumbnails/127.jpg)
3He(e,e'pp)n Hall B
2 GeVPN>250 MeV/c
4 GeVPN>250 MeV/c
fast pn leading p
fast pn leading p
PR
EL
IMIN
AR
Y
0 0.5 1Tp2/
0 0.5 1Tp2/
0
0.5
1T
p1/
0
0.5
1
Tp
1/
-1 -0.5 0 10.5cos(2 fast nucleon angle)
-1 -0.5 0 10.5cos(2 fast nucleon angle)
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Hall B 3He(e,e'pp)n 2 GeVpperp < 300 MeV/c
PR
EL
IMIN
AR
Y
cos(nq)
cos(pq)
Isotropic fast pairs pair not involved in reaction.
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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.
pp
erp <
300
MeV
/cP
RE
LIM
INA
RY
2 GeV has acceptance corrections
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Before
p
np
After
np
p
Direct evidence of NN correlations
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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
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J.E. Ducret et al., Nucl. Phys. A556, 373 (1993).
Saclay
4He(e,e'p)3H
Calculations predict q
dependence.
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J.E. Ducret et al., Nucl. Phys. A556, 373 (1993).
4He(e,e'p)3H
Again, calculations
predict q dependence.
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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/3B
Laget
Schiavilla
Nagorny
Minimum filled in by FSI and
2&3-body currents.
4He(e,e'p)3H
AmPS NIKHEF-K Amsterdam
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FSI: dependence on kinematics
p
q
fp'
fpp'pp
actualinferred
Large FSI
qp
fp p'
fp'
pp
Small FSI
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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.
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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).
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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, …