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Introduction
• Up to now have covered
Quarks and Hadron
Spectroscopy – Lecture III
Nomenclature for baryons and their resonances
QCD principles
Basics of electron scattering
The constituent quark model
• In the next two lectures
Daniel Watts
Nuclear Physics Group
University of Edinburgh
Electron and photon beam facilities
Nucleon properties
Nucleon resonance properties
Then hand back to Dave for the last two lectures!
Types of photon Polarisation
•
•
Both real and virtual photons can have polarisation
Measuring observables based on these polarisations gives
powerful additional information
Transverse polarisation
(Electric field vector
oscillates in a plane)
Circular polarisation
(Electric field rotates
Clockwise or anticlockwise)
Virtual photon
Longitudinal
polarisation
Virtual photons can also
have a longitudinal
polarisation component related to coulomb (charge)
scattering
EM probe facilities
How do we generate intense electron beams?
Microtron
(MAMI,
Jefferson Lab)
Electron beam accelerated
by rf cavities.
MAMI, Mainz, Germany
Tune magnetic field to ensure path
through magnets multiple of
Wavelength of accelerating field.
- electrons arrive back in phase
with the accelerating field.
Hermes, DESY, Germany
Postcard
collection
Gives “continuous” beam
(high duty factor)
Strecher rings
Jefferson Lab, USA
(SPring8, Bonn, Frascati,)
Electron beams fed in from linac
Then accelerated and stored in ring.
Useable beam bled off slowly
Many stretcher rings built for
synchrotron radiation - can
exploit infrastructure for multiuse
(e.g. Spring8)
Tend to have poorer duty factors
, less stable operation and poorer
beam properties than microtrons
Spring 8, Japan
More on Tagged Bremsstrahlung
Real photon beams from electron beams
•
Laser back-scattering
(LEGS, FRASCATI, DUKE, Spring8)
Eγ smaller than beam energy
Facilities up to 4 GeV
• Positron annihilation in flight
Only successful up to ~50 MeV
Bremsstrahlung background also present
e+
Bremsstrahlung cone
eRadiator
θe
γ
Radiator must be thin
Don’t want each e- to
produce more than
one photon
γ
Keep radiator to target
distance small to keep
beamspot small
•
Tagged Bremsstrahlung
γ
Log Nγ
(MAMI, Bonn, Lund, Jlab)
Eγ up to ~beam energy
Facilities up to 2.5 GeV
(12 GeV planned at JLab )
Bremsstrahlung
spectrum
Collimator
Tagging spectrometer should
have large acceptance for
scattered electron
θe= (me/Ee).( Eγ/(Ee-Eγ) )
Ideally the electron detectors
at focal plane of spectrometer
should have:
Generally collimate
beam to give better
defined beam spot
and enhance
polarisation (see later)
Good timing resolution
Cover wide Eγ range
Highly segmented
Polar angle of cone
around beam direction
Containing 50% of γ
Reals/Randoms ~ D/Ret
D = Duty factor of beam
Re = mean electron rate
t = resolving time
e-
Target
Θc = me/Ee(MeV) rads
e.g. MAMI – 855 MeV
Θc = 0.6mrad
More on Coherent bremsstrahlung
Polarisation in real photon beams
Bremsstrahlung facilities:
Linear polarisation: Use a
Linear Polarisation
crystalline radiator e.g. thin
diamond. Orient diamond to
give polarised photons in
certain photon energy ranges
Circular polarisation: Use
helicity polarised electrons and
produce bremsstrahlung in
amorphous radiator. Electrons
polarised at input to the
accelerator (e.g photo electrons
produced from circularly polarised
laser light on strained GaAs)
Bremsstrahlung cone
eDiamond
radiator
y
Collimator
Coh. Brem.
From [022]
plane
Degree of
Polarisation
(fraction of beam
Which is polarised)
Laser backscattering:
Circular Polarisation
Linear polarisation:
Use a linearly polarised laser
beam to backscatter from the
electron. High degrees of
polarisation (~100%) achievable
Detector systems used with γ beams
Collimate beam
to achieve linear γ
polarisations up to ~90%
Detector systems used with γ beams
γ
CLAS at Jefferson Lab
∆Eγ ~ 2 MeV
108 γ sec-1
γ
TAPS
528 BaF2 crystals
Crystal Ball
672 NaI crystals
Crystal
Ball and
TAPS at
MAMI
Electron scattering facilities
What do we use photon detectors for?
Primarily used to reconstruct neutral mesons which decay to photons
Eg. π0→2γ, η→2γ
Require good determination of incident electron 4-vector and scattered
electron 4-vector.
e.g. A1 at MAMI, Mainz, Germany
• Track path of scattered
electron in a magnetic field
• Determine momenta from path
in the magnetic field (wire chambers
and focal plane detectors)
• Electrons have high energies
→ large path length in magnet
and intense B field
Hall A at Jefferson Lab
Recap
• New generation of intense electron beam facilities
give high quality polarised beams of electrons and
photons
• Have large scale detector systems to detect
scattered electron as well as charged and uncharged
reaction products (p, n , π, η, ω, ρ ...)
Hermes at DESY
• For the rest of lecture will look at experimental work
carried out at these facilities start with:
elastic electron scattering
W =M
Q2
⇒ω =
2M
Elastic electron scattering and nuclear form factors
Nuclear Shapes
Cos2 term only difference
From Rutherford formula
Arises from Dirac theory
For spin ½ particle
ρ (r ) =
1
sin (qr / = )
F (q )
4πr 2 dr
(qr / = )
2π ∫
Elastic electron scattering - discussion
Rosenbluth separation
If we keep Q2 fixed and vary ε we can disentangle
the magnetic and electric form factors
• Information on the charge distribution of nuclei arises from
coulomb scattering BUT what about magnetic scattering – does
that not also contribute??
( )
( )
Q
2
2
2
2
θ ⎫⎪
dσ ⎛ dσ ⎞ ⎧⎪ GE Q + 4 M 2 GM Q
Q2 2 2
+
GM Q tan 2 ⎬
=⎜
⎟ ⎨
2
2
Q
dΩ ⎝ dΩ ⎠ Mott ⎪
2M
2⎪
1 + 4M 2
⎩
⎭
2
( )
• Nuclei with total angular momentum 0 do not have a magnetic
moment (e.g. 12C, 16O, 208Pb) – therefore contribution from
magnetic scattering negligible
• Nuclei that are not spin 0 will have contributions from charge
and magnetic scattering (as will protons & neutrons!!)
• How can we separate effects from charge and magnetic
contributions in the scattering process?
Major drawback - Gm weighted with Q2
Q2 < ~1 GeV2 both form factors make measurable contributions
Q2 > ~1 GeV2 contributions from electric form factor become very small –
large systematic errors in extraction
Polarisation observables in form factor
measurements
Nuclear magnetic
form factors
•
Need polarisation observables to get more accurate information on
nucleon form factors – particularly the electric form factors at high
Q2
•
Only have suitable experimental facilities available in recent years
•
Longitudinally polarised electron will transfer it’s polarisation to the
recoiling proton
•
Charge and magnetic form factors are accessible from the nucleon
polarisation components.
Give information
on distribution of
magnetization in
the nucleus
GE
P E + Ee '
⎛θ ⎞
=− t e
tan ⎜ e ⎟
⎝ 2⎠
GM
Pl 2M
Aside: How do we measure the polarisation of a nucleon ??
Nucleon Scattering and polarisation
n(θ,φ) =no(θ){1+A(θ)[Pycos(φ)–Pxsin(φ)]
Number of nucleons
scattered In the
direction θ, φ
Polar angle distribution
for unpolarised nucleons
x and y (transverse) components
of nucleon polarisation
Analysing power of
scatterer
Proton form factors - the Shape of the Proton
GE/GM gives the ratio of the electric charge and magnetisation
distributions in the proton
A surprising effect was noted in the recent experiment. Ratio of
magnetic and electric form factors change with Q2 ?!
The recent polarisation data
question the results using Rosenbluth
separation – latest thinking is that
double photon exchanges cause the
discrepancy between the 2 methods
θ
Imply proton’s charge distribution
not the same as it’s magnetization!!
Neutron Form Factor GEn
• Neutron is very interesting object to study
no net charge but has charged quark
components. How are they distributed?
• Good quality data only obtained in
recent years. Double polarisation technique
e-Beam+target polarised:
e-Beam+recoil nucleon:
Simultaneous fit to all
4 Form factors – recently
conjectured that we see
evidence of a pion
cloud from new accurate data
Bump at Q2~0.3 ?
Pion
Cloud?
P E + Ee '
GE
⎛θ ⎞
=− t e
tan ⎜ e ⎟
⎝ 2⎠
GM
Pl 2M
To access z component of nucleon polarisation need to precess spin in
a magnet before the nucleon Polarimeter δ – precession angle
r2ρ(r)
Aside
p
π-
Evidence for negative pion cloud?
neutron dissociates to p & π- ~7-20% of time
Friedrich and Walcher, hep-ph-0303054
•
RMS radii related to slope of form factor at Q2=0
< (rpE)2>1/2
0.895±0.018 fm
< (rpM)2>1/2
< (rnE)2>1/2
< (rnM)2>1/2
0.855±0.035 fm
-0.119±0.003 fm2
0.87±0.01 fm
Excellent agreement
With QED calculation
of Lamb Shift !