4511_Lec4_30Jan08

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• Homework 3 is back.
• Because of my travels I am late on everything
  this week. I made a formal request to myself to
  delay until March 5 the deadline for completing
  my Homework 4 solutions. I agreed (what a
  relief!), and you get the extension too.

2

• Interactions of Charged Particles with Matter
• Ionization dominant for heavy charged particles
• Bremsstrahlung dominant for electrons at
  typical EPP energy
• For hadrons, nuclear interactions also contribute

• Interactions of Photons with Matter
• Photoelectric effect
• Compton scattering
• Pair production dominant by 10 MeV

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Interactions of Particles with Materials
Projectile charges E interacts with atom,
accelerating electron, perhaps ionizing it, with
minimal deviation in its own trajectory.
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• Observations

?Interactions with electrons are responsible for
most energy loss.
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• Stopping Power S(t) -dT/dx
• Total energy transferred to the medium (electron
  density ne ?ZA0/A) is obtained by integrating
  the energy transfer to the electrons in a shell
  from b to b db over all values of b that could
  contribute

• b cant go to zero, because model of the target
  as a fixed pointlike charge breaks down. Min.
  impact parameter is that for which ?p 2mv.

• b cant go to ?, because model of the target as a
  free electron breaks down. Max. impact parameter
  has collision time comparable to orbital period.

Captures many of the true features of energy
loss, but a better job required
This gives
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• The better treatment incorporates the quantum
  nature of energy transfer, the wave nature of
  particles, and relativistic effects

Bethe-Bloch Equation
About 20 eV per electron-ion pair in Ar.
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• Observations about Bethe-Bloch (and its limits)
• Scaling with ?? - minimal dependence on
  particle mass
• 1/v-2 dependence at low speeds ? strong energy
  dependence.
• Relativistic rise for high speeds ?2 under
  ln
• Saturates for dense media charge screening
  suppresses long-range interactions
• dT/dxmin 3.5Z/A g/cm2 at ??3 (minimum
  ionizing particle)
• Min I occurs at higher momenta for more massive
  particles
• (dT/dx)min 1.5 MeV per g/cm2 for steel
• Weak dependence on medium (Z/A 0.5)
• dT/dx allows particle ID at low speeds and (esp.
  for electrons) in the relativistic rise.

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Relativistic Rise
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Weak Medium Dependence
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The Bigger Picture
Atomic effects dominate charge dependent
Everything weve talked about so far
Radiative Effects Bremsstrahlung
PDB p. 237
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Bremsstrahlung
Acceleration of a charged particle (esp.
electron) in the Coulomb field of a nucleus ?
radiation.

• Energy-loss rate by Brems is linearly
  proportional to energy, while ionization rises
  logarithmically
• Critical energy Ec is where the rates are equal,
  20 MeV for electrons in Cu, several hundred GeV
  for muons in Cu.
• New measure of amount of material Radiation
  Length

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Range and Straggling
Simple calculation of when particle runs out of
gas leads to predicted range.
Actual process of energy loss is random, observed
as range straggling, and a distribution of
energy-loss increments in small samples that is
not Gaussian, but follows the Landau
distribution.
Thin samples? big spread.
Tail hard scatters with energetic ?-ray es.