Interaction of Particles with Matter

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Interaction of Particles withMatter
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Overview

• EVERY experimental observation of nature is made
  possible through the interaction of the object
  under study with the experimental apparatus. In
  our case, the objects under study are particles,
  which create signals in our detectors through the
  interactions we are about to discuss.
• An understanding of how particles interact with
  matter is essential to understanding what your
  detector is telling you about the particles you
  are studying.

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Types of Interactions

• Electromagnetic interactions of charged particles
  with matter
• Interactions of photons with matter.
• Hadronic (strong) interactions.
• This is a lot to cover in 1 hour!

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Interaction of Charged Particles in Matter

• A charged particle passing through a block of
  material interacts electro-magnetically with the
  electrons (and to a much lesser extent, the
  nuclei) in that material.
• The charged particle provides an impulse to the
  atomic electrons as it passes them, resulting in
  a net energy loss to the particle, and either
  excitation or ionization of the atomic electron.
• The charged particle undergoes MANY such
  interactions in its passage through the material,
  the strength of each depending upon how close the
  particle came to a given electron. Therefore
  this energy loss is a statistical process if I
  sent an ensemble of identical particles through
  the same material the amount of energy lost would
  vary for each, but there would be a well defined
  average energy loss.

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Average Energy Loss

• Consider the interaction of our charged particle
  with a single atomic electron

m
b
M,v,qe
Impulse perpendicular to path I
Rough approx
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Ave. Energy Loss (2)

• More exact calc. Consider circular cylinder
  centered on path and passing through the position
  of the electron. Let e be the electrostatic
  field due to the charged particle. Now use
  Gausss law

KE is energy transfered to atomic electron
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Ave Energy Loss (3)
We now have energy transferred to a single atomic
electron. The Total average energy loss per unit
path length is given by. (h number density of
atomic electrons.)
Bmin determined by max. classical velocity
transfer to electron (2v) Bmax detemined by QM.
If 1/t less than electron vibrational frequency,
no energy transfer possible.
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Ave Energy Loss
Where I is the ionization potential of the
medium. (Comes in from Bmax.) A slightly
refined version of this formula is called the
Bethe-Bloche formula. Features dE/dx 1/v2
at low energy. dE/dx ln(v2)
at high energy.
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Ave Energy Loss vs Energy
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Energy Loss Distribution

• The quantity we obtained previously is the
  AVERAGE energy loss per unit path length. As
  stated earlier, if we send many identical
  particles though the same material, and the
  thickness of the material is such that the
  particle does not lose a substantial fraction of
  its initial energy, we will see a distribution of
  energy, called the Landau Distribution.

dE/dx ave
Note long high energy tail. This results from
small impact parameter interactions
making ionized electrons, called delta rays.
n
dE/dx
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Landau Distribution vs Absorber Thickness
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Energy Loss Summary

• The average energy loss of charged particles in
  matter increases at low energy as 1/v2, and at
  high energy as ln(v2).
• At the energy at which the minimum amount of
  energy loss is occuring, particles lose on
  average roughly 2MeV for every g/cm2 of material.
  Materials with a high electron density (H2)
  cause higher dE/dx, and materials with lower
  electron density (U) cause lower. Range of dE/dx
  is from 4 MeV/gm-cm2 (H2) to 1.1 MeV/gm-cm2 (U).
  (Note if the charged particle looses all of its
  energy in the material, it is said to have
  ranged out, and in this case the range of the
  particle is an excellent measurement of its
  initial energy)
• There are substantial fluctuations in the amount
  of energy loss in a thin layer of material

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Interaction of Electrons with Matter

• Electrons, being charged particles, undergo
  ionization energy loss as described earlier. In
  addition, due to their low masses a high energy
  electron can undergo radiative energy losses,
  Bremsstrahlung (braking radiation), and in the
  presence of a magnetic field, synchrotron
  radiation.
• Brem is the radiation produced as the
  electron de-accelerates in collision with attomic
  nuclei. A high energy muon will undergo energy
  loss through these mechanisms as well, although
  the threshold energy at which these become
  dominant is of course higher in this case.

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Interaction of Electrons and HE Muons with Matter
For electrons, rad. energy loss becomes dominant
_at_ 10 MeV. For muons, which are 1000 times
heavier, radiative processes become
important for muon energies 100 GeV. Note that
Brem. energy loss roughly proportional to E.
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Interaction of Photons with Matter

• 3 processes result in energy conversion of
  photons in matter, each dominating over a given
  energy region.
• Photoelectric Effect (E
• Compton Scattering (10 keV
• Pair Production (E 1 MeV)
• These energy regimes are approximate, and depend
  upon material

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Interaction of Photons with Matter (2)
Note that cross sections are higher for high Z
materials. If you are designing a detector to
convert photon energy to other forms, high Z
absorbers are typically used.
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Electromagnetic Cascades

• When a high energy electron or photon passes
  through matter, an electromagnetic cascade is
  created.
• If the initial particle is a photon, the initial
  photon will typically pair produce, and this
  electron/positron pair will the radiate lower
  energy photons through brem.
• If the initial particle was an electron, it will
  brem photons, which then pair produce, etc.
• In both cases, this process continues with the
  formation of more and more particles of lower and
  lower energy, until the particles produced have
  energies such that ionization processes dominate.

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Electromagnetic Cascades (2)

• EM showers have a characteristic energy
  deposition profile, which in turn has a
  characteristic length called the radiation
  length. It is related both to the mean free
  path for pair production of a high energy photon,
  and the path length over which a high energy
  electron will lose all but 1/e of its energy
  though brem. Although every individual shower
  will develop somewhat differently, overall
  agreeement with the expected shower profile can
  be used to identify electrons and photons from
  hadrons.

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Hadronic Interactions

• Hadronic interactions occur for particles which
  are quark composites (mesons and baryons).
• Hadronic interactions at low energies (low energy
  here meaning at energies below the hadron rest
  mass), exhibit a rich set of behavior, the nature
  of which often depends upon the detailed quantum
  structure of the target nuclei.
• Neutron absorbsion is best accomplished in a
  light atom target (sometime called a moderator).
  Particular nuclei, such as boron, have enhanced
  neutron cross sections, and are often used in
  neutron shielding.
• A full treatment of low energy hadronic
  interactions would take an entire lecture itself!

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Typical Neutron Scattering Cross Section vs
Energy
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High Energy Hadronic Interactions

• At high energies, hadronic interactions result in
  the production of secondary hadrons (typically
  pions), often resulting in a hadronic shower,
  similar in some ways to an EM shower, but a
  shower in which secondary hadrons are generated,
  rather than electron/positron pairs.
• Lets finish be discussing some of the general
  characteristics of these high energy hadronic
  interactions.

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Proton-Proton cross section vs Energy
Over a very wide energy range, the total cross
section is roughly constant. Consequently, the
interaction length of hadrons in matter is
roughly energy independent. A typical value (for
Fe) is 132 g/cm2. Hadronic interaction
lengths INCREASE with target Z, while Radiation
lengths DECREASE. This is often exploited in
detectors designed to discriminate between
hadrons and leptons.

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Secondary Hadron Multiplicities

• Unlike the simpler EM showers, in which charged
  particles are always produced in pairs, the more
  complicated strong interaction allows any number
  of secondary hadrons to be produced. The average
  multiplicity in a given interaction is energy
  dependent, given by
• 1.5 0.9ln(E/GeV)
• E primary particle energy.

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A Typical Hadronic Shower _at_ 120 GeV
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How that Shower Started
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Hadronic Shower Summary

• Although every hadronic shower contains an EM
  component, the overall topology of these showers
  differs, due to the difference between the
  radiation length and hadronic interaction
  lengths.
• Hadronic interactions are typically more extended
  and clumpier.
• More on this when you learn about particle ID
  using calorimetry.