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Nuclear Physics and Electron Scattering

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• 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

“Nuclear” Physics = Strong Force

3

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 Quarks gluons freed Plasma created

http://www.bnl.gov/rhic/physics.aspat 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

e-

e-

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

Electron scattering can be used to study1. Nuclear structure2. Nuclei at large (local) density3. Quantum chromodynamics

Jefferson Lab was constructed to be a state of the art, electron scattering facility

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Jefferson Lab

Accelerator2 cold superconducting linacsEe up to 6 GeVContinuous polarized electron beam (P=85%)

Jefferson Lab is the site of an electron scattering facility in Newport News, Virginia (USA)

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 simultaneouslyGood 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

TargetElectronbeam

Detector

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A Generic Electron Scattering Experiment

TargetElectronbeam

Detector

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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 directionDetermine particle speciesMeasure 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 quark-gluon 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:

Target

Electronbeam

Detector with solid angle DW

€

dσ =(# particles scattered into solid angle ΔΩ/s)

(# particles incident/sec)(# scattering centers/area)

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Electron Scattering Basics

Cross section:

Target

Electronbeam

Detector with solid angle DW

€

dσ =(# particles scattered into solid angle ΔΩ/s)

(# particles incident/sec)(# scattering centers/area)

Luminosity

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IncidentElectron beam

g*

Qe

Scattered electron

Fixed target with mass M

Electron Scattering kinematics

Virtual photon kinematics

N

€

Pe = (Ee,r k )

€

′ P e = ( ′ E e,r ′ k )

€

Q2 = −(Pe − ′ P e )2 = 4Ee ′ E esin2 ϑ e /2( ) me = 0

€

ν =Ee − ′ E e

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Z

Coulomb Scattering

Cross section for electron scattering from a fixed Coulomb potential

€

V0 = Zα

r

€

dσ

dΩ=

2ZαE

Q2

⎛

⎝ ⎜

⎞

⎠ ⎟2

1− sin2 θ

2

⎡ ⎣ ⎢

⎤ ⎦ ⎥ g

*

Qe

Mott Cross Section

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Electron Muon Scattering

Cross section for electron scattering from a spin ½ particle with no structure

g*

Qe

€

dσ

dΩ=

2ZαE

Q2

⎛

⎝ ⎜

⎞

⎠ ⎟2

1− sin2 θ

2

⎡ ⎣ ⎢

⎤ ⎦ ⎥E

E '1+

Q2

2M 2 sin2 θ

2

⎛

⎝ ⎜

⎞

⎠ ⎟

€

dσ

dΩ=

dσ

dΩ

⎛

⎝ ⎜

⎞

⎠ ⎟Mott

E

E '1+

Q2

2M 2 sin2 θ

2

⎛

⎝ ⎜

⎞

⎠ ⎟

Muon

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Electron Nucleon Scattering

Cross section for electron scattering from a spin ½ particle with some (quark) structure

g*

Qe

Nucleon

€

dσ

dΩ=

dσ

dΩ

⎛

⎝ ⎜

⎞

⎠ ⎟Mott

′ E eEe

{F12(Q2)

+ τ κ 2F22(Q2) + 2 F1(Q

2) + κF2(Q2)( )2tan2 θ e

2

⎡ ⎣ ⎢

⎤ ⎦ ⎥}

F1 and F2 describe the internal structure of the nucleon - commonly written,

€

GE (Q2) = F1(Q2) −τκF2(Q2)

€

GM (Q2) = F1(Q2) +κF2(Q2)

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

g*

Qe

€

dσ

dΩdE=

4α 2(E ')2

Q4 cos2 θ

2W2(ν ,Q2) + 2W1(ν ,Q2)sin2 θ

2

⎧ ⎨ ⎩

⎫ ⎬ ⎭

W1, W2 are the inelastic structure functionsAt very large Q2, they become a function of one dimensionless variable x=Q2/2Mn

€

MW1(ν ,Q2) →F1(x)

€

νW2(ν ,Q2) →F2(x)

F1, F2 related to quark distributions in nucleon/nucleus

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e

e'

x

pA–1

pq

p

(,q)

Four-momentum transfer: Q2 – qq = q2 – 2 = 4ee' sin2/2

Missing momentum: pm = q – p = pA–1= – p0

Missing energy: m = –Tp – TA–1

scattering plane

“out-of-plane” angle

reaction plane

PWIA

Kinematics

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ωd

σ2

d

d

Elastic

Quasielastic

N*

Deep Inelastic

€

Q2

2M m

Q

2

2

MeV3002

2

m

QNucleus

Elastic

N*

Deep Inelastic

m

Q

2

2

MeV3002

2

m

QProton

ωd

σ2

d

d

Electron Scattering at Fixed Q2

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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

Simple Theory Of Nucleon Knock-out

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)ε,( ω

6

mmeppe

pSKdpddd

d

nuclear spectral function

In nonrelativistic PWIA:

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)( ω

σ mep

pe

pKddd

d′

For bound state of recoil system:

proton momentum distribution

e-p cross section

Spectral Function

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01 pppq A

e

e'

q

p

p0

FSI A–1

A

p0'

Example: Final State Interactions (FSI)

Reaction Mechanisms

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Distorted Wave Impulse Approximation (DWIA)

),ε,( ω

6

ppSKdpddd

dmm

Dep

pe

“Distorted” spectral function

Improve Theory

34G. 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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Results from (e,e’p) Measurements

Independent-Particle Shell-Modelis based upon the assumption thateach nucleon moves independentlyin an average potential (mean field)induced by the surrounding nucleonsThe (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.

Target Mass

SP

EC

TR

OS

CO

PIC

ST

RE

NG

TH

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Short-Range Correlations

Nucleons

1.7fermi

2N-SRC 5o

o = 0.17 GeV/fermi3

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Questions

• 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)?

Benhar et al., Phys. Lett. B 177 (1986) 135.

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Questions

• 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)?

Benhar et al., Phys. Lett. B 177 (1986) 135.

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Questions

• 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)?

Benhar et al., Phys. Lett. B 177 (1986) 135.

BUT Other Effects Such As A Final State Rescattering

Can Mask The Signal…

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• 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

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The EMC effect

)()()( 222 xNFxZFxF npA

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• It turns out that the above assumption is not true!

• Nuclear dependence of structure functions, (F2

A/F2D), discovered

over 25 years ago; “EMC Effect”

• Quarks in nuclei behave differently than the quarks in free nucleon

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The EMC effect

)()()( 222 xNFxZFxF npA

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

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.

Main goals of new Jefferson Lab experiments

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.

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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.

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If the EMC effect is a local density effect, then it seems reasonable to look for connections to other local

density effects.