16.451 lecture 9: inelastic scattering and excited states 2/10/2003 inelastic scattering refers to...
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16.451 Lecture 9: Inelastic Scattering and Excited States 2/10/2003
Inelastic scattering refers to the process in which energy is transferred to the target,exciting internal degrees of freedom.
Experimental Scenario:
• Electrons are detected in a spectrometer set at angle
• The momentum of the scattered electrons at given depends on whether they scatter elastically or inelastically
• Peaks in the cross-section for inelastic scattering correspond to excitation of higher energy states in the target.
• Good resolution in the scattered electron momentum measurement is important to be able to resolve the energy spectrum of the target particle.
e
p
q
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elasticelastic
1st ex. (4.43 MeV)
7.65 MeV
9.64 MeV
Example: Early days at SLAC, inelastic scattering from Carbon
R. Hofstadter, Rev. Mod. Phys. 28, 214 (1956)
Scattered electron momentum = energy; energy loss by e- is gained by the recoiling 12C
Resolution 5 x 10-3
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Kinematics for inelastic scattering: 3
• Essential point: the mass of the recoiling particle is greater when it absorbs energy from the electron beam.
• Total energy of the recoil particle is: W = M’ + K = (M + E) + K where E is the internal energy transfer (excitation energy).
eoo pE
,
proton
e
pE ,'
qW
,
M
M
Square the momentum equation, use relativistic relation of K to p .... Mlargefor
)cos1(1
2
2
EpEp
p o
Mop
M
Eo
qppKEMEWEME oo
','
conserve energy and momentum....
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Mlargefor)cos1(1
2
2
EpEp
p o
Mop
M
Eo
e
p
q
Check that this works for the old 12C data:
12
34
187 MeV beam
Energy loss in target: 2 MeV (few mm thick)
4
Peak cp' (MeV) dE (MeV) 12-C level1 185 0 ground state2 180.7 4.3 4.44 MeV3 177.2 7.8 7.66 MeV4 175.2 9.8 9.64 MeV
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Modern High Resolution data from Jefferson Lab, Hall A:
20x betterresolution thanthe old SLACspectrometer
What are we looking at?
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Electrons are tracked in a high resolution magnetic spectrometer ...
Jefferson Lab “Hall A”
po <= 5.9 GeV
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for more information and photos:
http://education.jlab.org/sitetour/
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Analysis: deflection of electrons in a magnetic field
B
p
pd
dt
pdBeF
v
(correct, with relativistic momentum — see Griffiths “Introduction to Electrodynamics”)
Lorentz force:
p
pdp
pd
d
dB
dBd
BdeBdtepd
pe
pe
pdp
) v(
Deflection , even if B is not uniform:
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Deflection in magnetic field measures the particle’s momentum!
ies trajectorcentralfor .
p
constdB
p
e
Hall A High Resolution Spectrometer (HRS) at JLab:
http://hallaweb.jlab.org/equipment/HRS.htm
start of particledetection system
main bending magnet,nominal = 45°
quadrupole magnetsimprove “optics”, for better resolution
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Momentum Range 0.3 – 4.0 GeV/c
Magnet configuration QQDQ
Bend angle 45°
Optical length 23.4 m
Momentum acceptance 4.5 %
Dispersion (D) 12.4 cm/%
Momentum Resolution (FWHM) 1 x 10-4
Acceptance: Horizontal Vertical
28 mr 60 mr
Solid angle (rectangular approx) 6.7 msr
Angular resolution Horizontal Vertical
0.6 mr2.0 mr
Transverse length acceptance 5 cm
Transverse position resolution 1.5 mm (FWHM)
Spectrometer angle position accuracy
0.1 mr
Properties of the Hall A “HRS” spectrometer: 9
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Position shift of inelastic peaks at the focal plane determines their momentum:
Dispersion: D = 12.4 cm/ %
A 1% shift from the central momentum corresponds to a deflection at the focal plane of 12.4 cm more than the elastic peak.
inelastic e- path
elastic e- path
x
cm4.12x
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Experimental requirements:
HRS detector package:
JLab Hall A HRS: (state of the art)
positioning error: = 0.1 mr
resolution: x = 0.6 mr (momentum direction)
y = 2.0 mr
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• accurate position-sensitive detector package (“vertical drift wire chambers” VDC)
• accurate spectrometer field map for particle tracking (numerical fitting algorithm)
• fast timing scintillation detectors to define events • Cerenkov detectors for particle identification (fire on electrons only to reduce background)
• accurate position/angle survey of components
• “thin” detector packages to minimize resolution smearing caused by scattering in the apparatus...
• accurate position-sensitive detector package (“vertical drift wire chambers” VDC)
• accurate spectrometer field map for particle tracking (numerical fitting algorithm)
• fast timing scintillation detectors to define events • Cerenkov detectors for particle identification (fire on electrons only to reduce background)
• accurate position/angle survey of components
• “thin” detector packages to minimize resolution smearing caused by scattering in the apparatus...
Picture show, courtesy of Jefferson Labweb page
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Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab, USA
(45 MeV)
built for 400 MeV (1995), nowextended up to 570 MeV per linac (500 MHz). Max beam energy: 5.7 GeV
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Two spectrometers! One for electrons and one for scattered protons, etc.
Experimental Hall A at Jefferson Lab
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Here they are, but not without some distortion from the camera lens... 14
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Electron arm detectors:Cerenkov cell (blue)shower counters behind...
Assembly of position-sensitivevertical drift chamber (VDC)
Some of the electron-arm detection equipment: 15
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What happens when we look at protons with a spectrometer like this?
We see excited states, but on a completely different energy scale!!
What are these, what sets the energy scale, and why are the peaks so broad compared to 12C ? (ANSWERS NEXT WEEK!)
inelastic peaks
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W. Bartel et al., Phys. Lett. 28B, 148 (1968)