Interaction of Heavy Charged Particles with Matter

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Interaction of Heavy ChargedParticles with Matter

• NE162 Lecture 7
• Chapter 5 of Text book
• JASMINA VUJIC

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Interaction of heavy charged particles with matter

• Heavy charged particles all charged particles
  other than the electron or positron
• Include muons (M 207 me), pions (M 270 me),
  kaons (M 967 me), protons (M 1836 me), alpha
  particles, deuterons, tritons, fission fragments,
  other heavy ions
• Energy-Loss Mechanisms
• (a) collisions with electrons (b) radiative
• Ionization of atoms
• Excitation of atoms

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Sketch of alpha particles paths in a medium

• Can transfer only a small fraction of its energy
  in a single collision with an electron. Thus,
  heavy charged particles
• travel almost in straight lines (straight line
  trajectory)
• lose energy almost continuously in small amounts
• have a very small range

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Ionization
http//en.wikibooks.org/wiki/Basic_Physics_of_Nucl
ear_Medicine/Interaction_of_Radiation_with_Matter
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Maximum Energy Transfer in a Single Collision
Before
After
Conservation of total kinetic energy and momentum
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Maximum Energy Transfer in a Single Collision

• From the first two equations we obtain
• V1 (M-m)/(Mm) V
• and the maximum energy transfer is given by
• Qmax ½ MV² - ½ MV1² E4mM/(Mm)²

E mV2/2, the initial kinetic energy of incident
particle
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Maximum Energy Transfer in a Single Collision

• For incoming electron
• Qmax E, if M me
• For muon
• Qmax 4me(207 me)/(208 me)2E
• Qmax 0.0192 E

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Maximum Energy Transfer in a Single Collision
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STOPPING POWER

• Stopping power is defined as the average energy
  loss of a charged particle per unit path length
• where µ is the probability of collision per unit
  path length, and Qave is the average energy loss
  per collision.
• The mass stopping power is given as

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Bethe Formula for stopping power

• Where
• ko 8.99 x 109 N m² C-1
• Z atomic number of heavy particle e - electron
  charge
• n number of electron per unit volume m
  electron rest mass
• c speed of light in vacuum
• ß V/c speed of the particle relative to c
• I mean excitation energy of the medium

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MEAN EXCITATION ENERGY OF THE MEDIUM

• For a compound or mixture, the stopping power can
  be calculated by simpling adding the separate
  contributions from the individual constituent
  elements
• where i corresponds to an individual element.

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Stopping power of water for various heavy charged
particles
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Stopping Power vs. Energy for protons, deuterons
and alpha particles in Si and Ge
http//www.ortec-online.com/detectors/review_physi
cs/interaction.htm
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Bragg Curve

• A curve showing the average number of ions per
  unit distance along ( or a specific ionization) a
  beam of initially monoenergetic ionizing
  particles, usually alpha particles, passing
  through a gas. Also known as a Bragg ionization
  curve.

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Energy Deposition of Alpha particles

• Specific ionization - SI
• SI (dE/dx)/EI
• Number of ion pairs per unit path length
• EI,air 36 eV/ip
• EI,tissue 22 eV/ip

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RANGE

• The range of a charged particle is the distance
  it travels before coming to rest.
• For a particles in air, the following approximate
  empirical relations exist

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Range of alpha particles
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Range Measurement
http//www.med.harvard.edu/JPNM/physics/didactics/
physics/charged/lect.html
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RANGE

• The ranges of two heavy particles with the same
  initial speed could be determined from the
  following ratio
• The range of other charged particles in terms of
  proton range
• For example, the range of alpha particle from
  214Po decay (E7.69 MeV) is
• in air about 6cm
• in tissue about 0.007 cm

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Ranges
http//www.ortec-online.com/detectors/review_physi
cs/interaction.htm
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Table 5.3 Mass stopping power and ranges for
protons in water
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Figure 5.7 Ranges of p, ?, electrons in water,
muscle, bone, lead
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Figure 5.8 Ranges of p, ?, electrons in air