eep03: international workshop on probing nucleons and nuclei via the (e,e'p) reaction october...
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EEP03: International Workshop on
Probing Nucleons and Nuclei via the (e,e'p) Reaction
October 14-17, 2003
Grenoble, France
Overview of the (e,e'p) Reaction
Paul Ulmer
Old Dominion University
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OutlineNuclei
Spectroscopic factors
NN correlations
Reaction mechanism
Deuteron and the NN interaction
NucleonsElastic form factors
Medium modifications
Color transparency
Pion electroproduction
Virtual Compton Scattering
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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= – p0
Missing mass: m = –Tp – TA–1
scattering plane
“out-of-plane” angle
reaction plane
PWIA
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Response Functions (OPEA)
.kinematicselectron (known) on theonly depend ' thewhere
)(
]φcos)(φsin)[(
]φ2sin)(φ2cos)[(
]φsin)(φcos)[(
)()(σπ)2(dω dpdd
σd
}
{
xx
xx
xx
M3pe
6
sv
SRSRhv
SRSRSRRhv
SRSRSRRv
SRSRSRRv
SRRvSRRvpE
ttTTl
lTTTT
ttTLl
lTLn
nTLTLTL
ttTTl
lTTn
nTTTTTT
ttLTl
lLTn
nLTLTLT
nnTTTn
nLLL
LAB
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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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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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Nuclei
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U. Amaldi, Jr. et al., Phys. Rev. Lett. 13, 341 (1964).
1964: Frascati Synchrotron
12C(e,e'p)
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J. Mougey et al., Nucl. Phys. A262, 461 (1976).
1976: Saclay
Cro
ss
Se
cti
on
(1
0-34 c
m2/M
eV
2/s
r2)
0 10 20 30 40 50 60 70Missing Energy (MeV)
12C(e,e'p)
0 pm 36 MeV/c
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G. van der Steenhoven et al., Nucl. Phys. A484, 445 (1988).
1988: NIKHEF
12C(e,e'p)
pm = 29 MeV/c
1s1/2 knockout
Ex [MeV]
S(E
x,p
m)
[(M
eV/c
)-3 M
eV-1]
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G. van der Steenhoven, et al., Nucl. Phys. A480, 547 (1988).
NIKHEF
12C(e,e'p)11B
DWIA calculations give correct shapes,
but:
Missing strength observed.
(p
m)
[(M
eV/c
)3]
pm [MeV/c]
1p knockout from 12C
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“Spectroscopic” Factors …
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V. Pandharipande, I. Sick and Peter K.A. deWitt Huberts, Rev.
Mod. Phys. 69, 981 (1997).
Normalization factors
z
target mass A
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B.A. Brown et al., Phys. Rev. C 65, 061601 (2002).
Transfer Reactions and Normalization Factors
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L. Lapikás, et al., Phys. Rev. C 61, 064325
(2000).
12C(e,e'p)S
1p +
S1
s
Q2 [(GeV/c)2]
Low Q2: optical potential
High Q2: Glauber
Discontinuity seen with strength nearly saturated at high Q2.
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16O(e,e'p)
Marco Radici, W.H. Dickhoff and E. Roth Stoddard, Phys. Rev. C 66, 014613 (2002).
Data: M. Leuschner et al.
Data: J. Gao et al.
The same spectroscopic factors used throughout:
0.644 (p1/2) and 0.537 (p3/2).
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J.H. Morrison et al., Phys. Rev. C 59, 221 (1999).
12C(e,e'p)
For <QE, essentially no quenching is
observed.
Bates Linear
Accelerator
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Where does the missing strength
go?
Short-range correlations? …
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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.
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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
Arrows indicate
expected position for correlated
pair.
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C. Marchand et al., Phys. Rev. Lett. 60, 1703 (1988).
3He(e,e'p)d 3He(e,e'p)np
3BBU similar
to dnp
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J.J. van Leeuwe et al., Nucl. Phys. A631, 593c (1998).
thr
2
21
2E
m
p
A
AE mm
Laget: full
Laget: no MEC/IC
4He(e,e'p)Peak roughly
tracks kinematics of knockout of
correlated 2N pair
AmPS NIKHEF-K
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Data do not seem to follow naïve
expectation for NN
correlation peak.
JLab Hall C
Data: D. Rohe, E97-006 (Preliminary)
GF: H. Müther et al., Phys. Rev. C 52, 2955 (1995).
CBF: O. Benhar et al., Nucl. Phys. A579, 493 (1994).
DataCBFGF
PRELIMINARY
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Reaction Mechanism
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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
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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
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D. Dutta et al., Phys. Rev. C 61, 061602 (2000).
Excess transverse strength at high m.
Persists, though declines, at higher Q2.
JLab Hall C
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J.J. Kelly, Adv. Nucl. Phys. 23, 75 (1996).
Em – E 2-body threshold [MeV]
T/L
rat
io ()
[-]
0.5
1.0
1.5
2.0
0 10 20
Transverse Enhancement
6Li10B12C
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Relativity …
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G. van der Steenhoven, Few-Body Syst. 17, 79 (1994).
Wilbois/ArenhövelWilbois/Arenhövel
de Forest
de Forest
Hummel/TjonArenhövel/Fabian
Mosconi/Ricci
NR
AL
T2H(e,e'p)n ALT
Arenhövel/Fabian NR
de Forest “CC1” nucleon cross section gives same qualitative features as more complete calculations here, relativistic effects mainly in nucleonic current.
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J.M. Udías et al., Phys. Rev. C 64, 024614 (2001).
Previous non-relativistic
analysis
Saclay data: L. Chinitz et al. NIKHEF data: C.M. Spaltro et al.
Discrepancy reported earlier was based on non-relativistic calculations.
Relativistic treatment is
required even at these modest
momenta.
16O(e,e'p)RCC1
RCC2
PCC1PCC2
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16O(e,e'p) Q2=0.8 GeV2 Quasielastic
JLab Hall A
Effect of spinor
distortion significant.1p 1/2
1p 3/2
Calculations: Udías, et al.
J. Gao et al., Phys. Rev. Lett. 84, 3265 (2000) and K.G. Fissum et al., in preparation, to be submitted to Phys. Rev. C.
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16O(e,e'p) Q2=0.8 GeV2 Quasielastic
Two-body calculations
(Janssen et al.) reproduce flat
distribution, but underpredict by roughly a factor of two.
JLab Hall AJ. Gao et al., Phys. Rev. Lett. 84, 3265 (2000) and K.G. Fissum et al.,
in preparation, to be submitted to Phys. Rev. C.
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The deuteron and the NN interaction
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M. Bernheim et al., Nucl. Phys. A365, 349 (1981).
Saclay
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FSI+MEC+IC
FSI
2H(e,e'p) Q2=0.23 GeV2 near
PWBA+FSI
PWBA+FSI+MEC+IC
PWBA+FSI+MEC
Bonn
H. Breuker et al., Nucl. Phys. A455, 641 (1986).
Calculations: Leidemann and Arenhövel
K.I. Blomqvist et al., Phys. Lett. B 424, 33 (1998).
Calculations: H. Arenhövel
Mainz
2H(e,e'p) varying Q2, x
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High momentum structure of 2H?
2H(e,e'p)n Q2 = 0.67 GeV2 x = 0.96
P.E. Ulmer et al., Phys. Rev. Lett. 89, 062301 (2002).
Evidence for large FSI
JLab Hall A
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D. Jordan et al., Phys. Rev. Lett. 76, 1579 (1996).
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I. Passchier et al., Phys. Rev. Lett. 88, 102302 (2002).
),(H2 pee
Ted
dVed
de
Td
dVd
d APAPAhAPAP 21210 1σσ
Sensitive to D-state
AmPS NIKHEF-K
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The Nucleon
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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
*
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O. Gayou, et al., Phys. Rev. Lett. 88, 092301 (2002).
Proton Elastic Form Factors via 1H(e,e'p)
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Searching for Medium Effects on the Nucleon …
][σπ)2(dω ddd
σdM3
pe
6
TTLL RvRvpE
p
In parallel kinematics:
E
M
L
TG G
G
R
R
Q
qmR ~
~2
2
PWIA
This relies on (unrealistic) model assumption.
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Medium Modifications or FSI?
Data (12C): G. Van der Steenhoven et al., Phys. Rev. Lett. 57, 182 (1986).
Calculations (16O): T.D. Cohen, J.W. Van Orden, A. Picklesimer, Phys. Rev. Lett. 59, 1267 (1987).
Dirac PWIA
Dirac DWIASchrödinger LDA
Q2 [GeV2]
RG
(1
p3
/2)
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Another, less model-dependent, method …
Polarization Transfer
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Mainz: S. Dieterich et al., Phys. Lett. B500, 47 (2001).
E93-049: S. Strauch et al., Phys. Rev. Lett. 91, 052301 (2003).
E03-104: Projected Data, Strauch, Ent, Ransome, Ulmer, cospokespersons
4He(e,e'p)
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K. Garrow, et al., Phys. Rev. C 66, 044613 (2002).
Color Transparency?
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Sabit S. Kamalov et al., Phys Rev. C 64, 032201 (2001).
p(e,e'p)0 and *N
JLab Hall C data (Q2=2.8, 4.0 GeV2): V.V. Frolov et al., Phys. Rev. Lett. 82, 45 (1999); their analysis shown by stars.
MAID
Dynamical Model
pQCD 100% pQCD constant
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Summary
• Single-particle picture describes some gross features of experiments at least in quasielastic kinematics.
• Quenching of strength gives indirect evidence of NN correlations. Also, some direct evidence, but …
• Reaction dynamics still not well understood.
• Relativistic treatment essential at moderate/high Q2, but also essential at low Q2 for certain observables.
• NN interaction studies via d(e,e'p)n now being fully exploited: reaction dynamics/short-range structure of NN force.
• A wealth of new information now coming out on the nucleon: elastic and inelastic structure, medium modifications, color transparency, polarizabilities, …