Nuclear Physics and Electron
Scattering
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“Nuclear” Physics = Strong Force
• Four forces in nature
– Gravity
– Electromagnetic
– Weak
– Strong  Responsible for binding protons and neutrons
together to make nuclei, holds together quarks that make
protons and neutrons
• Why study the strong force?
– The nucleus makes up 99.9% of the mass of the atoms
around you
– Nuclear reactions crucial to understanding how the universe
was formed
– Because it’s hard! The underlying theory is simple, but it’s
difficult to understand how we get from that theory to real
protons, neutrons, nuclei
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Scope of Nuclear Physics
• Topics that fall under the umbrella of the label “nuclear
physics” depends to some degree on where you are
• In the United States, includes
– Nuclear structure (how protons and neutrons
combine to make atomic nucleus)
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Scope of Nuclear Physics
• Nuclear structure (how protons and neutrons combine
to make atomic nucleus)
Exploration of “stable”
nuclei – study highly
excited states to
understand nuclear
structure
http://fribusers.org/2_INFO/2_crucial.html
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Scope of Nuclear Physics
• Nuclear structure (how protons and neutrons combine
to make atomic nucleus)
Exploration of “stable”
nuclei – study highly
excited states to
understand nuclear
structure
 Expand the study to
highly unstable nuclei to
understand the limits of
nuclear matter
http://fribusers.org/2_INFO/2_crucial.html
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Scope of Nuclear Physics
• Topics that fall under the umbrella of the label “nuclear
physics” depends to some degree on where you are
• In the United States, includes:
– Nuclear structure (how protons and neutrons
combine to make atomic nucleus)
– Relativistic heavy ions – smashing together heavy
nuclei at high energies to explore new states of
strongly interacting matter
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Scope of Nuclear Physics
• Relativistic heavy ions – smashing together heavy
nuclei at high energies to explore new states of
strongly interacting matter
Ions about to collide
Ion collision
http://www.bnl.gov/rhic/physics.asp
Quarks gluons freed
Plasma created
at the beginning of the universe there were
no protons and neutrons, only free quarks
and gluons
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Scope of Nuclear Physics
• Topics that fall under the umbrella of the label “nuclear
physics” depends to some degree on where you are
• In the United States, includes:
– Nuclear structure (how protons and neutrons
combine to make atomic nucleus)
– Relativistic heavy ions – smashing together heavy
nuclei at high energies to explore new states of
strongly interacting matter
– Quantum Chromodynamics  how quarks and
gluons interact to form protons and neutrons and
eventually nuclei
– Symmetry tests  searches for physics beyond the
Standard Model
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Electron Scattering and Nuclear Physics
Electron scattering is a powerful tool for studying the physics of
nuclei and nucleons
 The electromagnetic interaction is very well described by
Quantum electrodynamics (QED) – the probe is understood
 The electromagnetic coupling is weak (a=1/137) - electrons
probe the whole volume without bias
e-
Electron scattering can be used to
study
1. Nuclear structure
2. Nuclei at large (local) density
3. Quantum chromodynamics
e-
Jefferson Lab was constructed to be a state of the art, electron scattering facility
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Jefferson Lab
Jefferson Lab is the site of an
electron scattering facility in
Newport News, Virginia (USA)
Accelerator
2 cold superconducting linacs
Ee up to 6 GeV
Continuous polarized electron
beam (P=85%)
3 Experimental Halls with complementary capabilities
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Experimental Hall A
2 High Resolution Spectrometers
 Good for clean ID of hard to see final states
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Experimental Hall B
CEBAF Large Acceptance Spectrometer (CLAS)
Detects particles emitted in all
directions simultaneously
Good for measurements of reactions
with complicated final states
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Experimental Hall C
Short Orbit Spectrometer
High Momentum Spectrometer
High accuracy measurements of absolute probabilities for processes
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A Generic Electron Scattering Experiment
Detector
Electron
beam
Target
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A Generic Electron Scattering Experiment
Detector
Electron
beam
Target
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What we measure
• In the “simplest” experiments, we measure the
probability for an electron to scatter in a particular
direction with a specific momentum
• In more complicated experiments, we measure the
above, in combination with the probability to produce
another particle
– The relative (and absolute) probabilities for different
processes can tell us about the structure of the
nucleus (or proton/neutron) we are probing
• The common analogy is that it’s like trying to learn how
a watch is made by throwing it against the wall and
looking at the pieces!
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Tools of the Trade: Magnetic Spectrometers
Magnets focus and bend charged particles into our detectors
Dipole: acts like a prism, separates
particles with different momenta
Quadrupoles: act like lenses, focusing
particles
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Tools of the Trade: Detectors
Detectors after spectrometer
magnets:
Track charged particles to
determine momentum and direction
Determine particle species
Measure time of arrival of particle
in spectrometer
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Jefferson Lab’s Original Mission Statement
• Key Mission and Principal Focus (1987):
– The study of the largely unexplored transition
between the nucleon-meson and the quarkgluon descriptions of nuclear matter.
The Role of Quarks in Nuclear Physics
• We can describe nuclei, for the most part just using
protons, neutrons, and other exchange particles: does
there come a point at which we must describe in terms
of quarks and gluons?
– If not, why not?
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Related Topics
• Do individual nucleons change their size, shape,
and quark structure in the nuclear medium?
• How do quarks and gluons come together to
determine the structure of the proton?
– What is the distribution of charge and magnetism in
the nucleon?
– How is the spin of the proton built up from quarks
and gluons?
• What are the properties of the strong force
(“QCD”) in the regime where quarks are confined?
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Electron Scattering Basics
Cross section:
d 
(# particles scattered into solid angle DW/s)
(# particles incident/sec)(# scattering centers/area)
Detector
with solid
angle DW
Electron
beam
Target
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Electron Scattering Basics
Cross section:
d 
(# particles scattered into solid angle DW/s)
(# particles incident/sec)(# scattering centers/area)
Detector
with solid
angle DW
Luminosity
Electron
beam
Target
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Electron Scattering kinematics
Scattered electron
Qe
Incident
Electron
beam
r
Pe  (E e , k )
g*
r
Pe ( Ee , k )

N
Fixed target with
mass M
Virtual photon kinematics
Q2  (Pe  Pe) 2  4 E e E e sin 2  e /2
me = 0
  E e  Ee

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Coulomb Scattering
Cross section for electron scattering from a fixed Coulomb potential
V0  Z
a
r
2



d
2ZaE 
2
  2  1  sin 
dW  Q  
2 
Mott Cross Section
Qe
g*
Z
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Electron Muon Scattering
Cross section for electron scattering from a spin ½ particle
with no structure
2
2





d
2ZaE 

E
Q
2
2
  2  1  sin  1

2 sin
dW  Q  
2 E'  2M
2 

d d  E  Q
2
  
1

2 sin
dW dW Mott E'  2M
2 
2
Qe
g*
Muon
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Electron Nucleon Scattering
Cross section for electron scattering from a spin ½ particle
with some (quark) structure
d d  E e 2 2
  
{F (Q )
dW dW Mott E e 1
 2 2 2

2
2 2
2 e
   F2 (Q )  2F1 (Q )  F2 (Q ) tan
}


2 
Qe
F1 and F2 describe the internal structure of
the nucleon - commonly written,
GE (Q2 )  F1 (Q2 )  F2 (Q2 )
GM (Q2 )  F1 (Q2 )  F2 (Q2 )
g*
Nucleon
Distribution of charge and magnetization in the nucleon
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(inelastic) Electron Nucleon Scattering
Cross section for electron scattering from a spin ½ particle
 target does not remain intact, an inelastic reaction

d
4a 2 (E') 2  2 
2
2
2
cos W 2 ( ,Q )  2W1( ,Q )sin 

4

dWdE
Q
2
2 
Qe
W1, W2 are the inelastic structure functions
At very large Q2, they become a function of
one dimensionless variable  x=Q2/2M
MW1 (,Q2 ) F1 (x)
W 2 (,Q ) F2 (x)
2
g*
F1, F2 related to quark distributions in nucleon/nucleus
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Kinematics
p
e'
scattering
plane
e
“out-of-plane” angle
pq
(,q)
x
pA–1
reaction
plane
Four-momentum transfer: Q2  – qq  = q2 – 2 = 4ee'
sin2/2
Missing momentum:
Missing energy:
pm = q – p = pA–1PWIA
= – p0
m =  –Tp –28 TA–1
Electron Scattering at Fixed Q2
d 2σ
dωdW
Elastic
Quasielastic
Nucleus

d 2σ
dωdW
Proton
Q2
2M
Q2
2m
Elastic
D
N*
Deep
Inelastic
Q2
 300MeV
2m
D
N*
Q2
2m
Q2
 300MeV
2m

Deep
Inelastic

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Simple Theory Of Nucleon Knock-out
Plane Wave Impulse Approximation
(PWIA)
spectator
A–1
e'
p
p0
q
e
A-1
p0
A
q – p = pA-1= pm= – p0
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Spectral Function
In nonrelativistic PWIA:
d 6
 K  ep S ( pm , ε m )
dωdW e dpdW p
e-p cross section
nuclear spectral function
For bound state of recoil system:
proton momentum distribution
d 5σ
2

 K  ep  ( pm )
dω dW e dW p
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Reaction Mechanisms
Example: Final State Interactions
(FSI)
A–1
p
FSI
e'
e
p0'
q
p0
A
  

q  p  p A1  p0
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Improve Theory
Distorted Wave Impulse Approximation (DWIA)
d 6
D
 K  ep S ( pm , ε m , p )
dW e dW p dpdω
“Distorted” spectral function
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1p knockout from 12C
12C(e,e'p)11B
(pm) [(MeV/c)3]
DWIA calculations
give correct shapes,
but:
Missing strength
observed.
NIKHEF
pm [MeV/c]
G. van der Steenhoven, et al., Nucl. Phys. A480, 547 (1988).
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Independent-Particle Shell-Model
is based upon the assumption that
each nucleon moves
independently
in an average potential (mean
field)
induced by the surrounding
nucleons
The (e,e'p) data for knockout of
valence and deeply bound orbits in
nuclei gives spectroscopic factors
that are 60 – 70% of the mean field
prediction.
SPECTROSCOPIC STRENGTH
Results from (e,e’p) Measurements
Target Mass
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Short-Range Correlations
2N-SRC
  5o
1.7fermi
o = 0.17 GeV/fermi3
Nucleon
s
36
Questions
Benhar et al., Phys. Lett. B 177 (1986) 135.
• What fraction of the momentum
distribution is due to 2N-SRC?
• What is the relative momentum
between the nucleons in the
pair?
• What is the ratio of pp to pn
pairs?
• Are these nucleons different from
free nucleons (e.g. size)?
37
Questions
Benhar et al., Phys. Lett. B 177 (1986) 135.
• What fraction of the momentum
distribution is due to 2N-SRC?
• What is the relative momentum
between the nucleons in the
pair?
• What is the ratio of pp to pn
pairs?
• Are these nucleons different from
free nucleons (e.g. size)?
38
Questions
Benhar et al., Phys. Lett. B 177 (1986) 135.
• What fraction of the momentum
distribution is due to 2N-SRC?
• What is the relative momentum
between the nucleons in the
pair?
• What is the ratio of pp to pn
pairs?
• Are these nucleons different from
free nucleons (e.g. size)?
BUT Other Effects Such As A Final State
Rescattering
Can Mask The Signal…
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The EMC effect
•
Typical energy scale of nuclear process ~ MeV
•
Typical energy scale of DIS ~ GeV
•
Compared to energy scale of the probe, binding energies are less for nuclear
targets.
•
So naïve assumption (at least in the intermediate xbj region) ;
Nuclear quark distributions = sum of proton + neutron quark distributions
F ( x)  ZF ( x)  NF ( x)
A
2
p
2
n
2
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40
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The EMC effect
F ( x)  ZF ( x)  NF ( x)
A
2
p
2
•
It turns out that the above
assumption is not true!
•
Nuclear dependence of structure
functions, (F2A/F2D), discovered
over 25 years ago; “EMC Effect”
•
Quarks in nuclei behave
differently than the quarks in free
nucleon
n
2
Aubert et al., Phys. Lett. B123, 275 (1983)
EMC effect fundamentally challenged our understanding of nuclei and
remains as an active area of interest.
( SPIRES shows 887 citations for the above publication)
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The EMC effect: models
Interpretation of the EMC effect requires better understanding of traditional
nuclear effects (better handle at high x).
Fermi motion and binding often considered uninteresting part of EMC effect, but
must be properly included in any examination of “exotic” effects.
Data are limited at large x, where one can evaluate binding models, limited at
low-A, where nuclear structure uncertainties are small.
Main goals of new Jefferson Lab experiments
 First measurement of EMC effect on 3He for x > 0.4
 Increase in the precision of 4He ratios.
 Precision data at large x for heavy nuclei.
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•
•
•
What is the EMC Effect?
EMC effect is simply the fact the
ratio of DIS cross sections is not
one
– J.J. Aubert et al. PLB 123 (1983)
275.
– Simple Parton Counting Expects One
– MANY Explanations
SLAC E139
– J. Gomez et al., PRD 49 (1994)
4348.
– Precise large-x data
– Nuclei from A=4 to 197
Conclusions from SLAC data
–
–
–
–
Q2-independent
Universal x-dependence (shape)
Magnitude varies with A
Average Nuclear Density Effect
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New Jefferson Lab EMC Effect Data
J. Seely et al., Phys, Rev. Lett. 103 (2009) 202301.
•
•
Plot shows slope of ratio σA/σD at EMC region.
EMC effect correlated with local density not average density.
44
If the EMC effect is a local density
effect, then it seems reasonable to
look for connections to other local
density effects.
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