Detecting%20Particles:%20How%20to%20

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Detecting Particles How to see without seeing
Interactions of Particles with Matter Electromagn
etic and Nuclear Interactions

• Prof. Robin D. Erbacher
• University of California, Davis

References R. Fernow, Introduction to
Experimental Particle Physics, Ch. 2, 3
D. Green, The Physics of Particle
Detectors, Ch. 5,6
http//pdg.lbl.gov/2004/reviews/pardetrpp.pdf
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Interactions of Particles with Matter
The fact that particles interact with matter
allows us to measure their properties, and
reconstruct high energy interactions. Dominant
interaction is due to the electromagnetic force,
or coulomb interactions. Ionization and
excitation of atomic electrons in matter are the
most common processes. Radiation can become
important, particularly for electrons. The
nuclear interactions play a less significant role
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Elastic Scattering
Incoming particle charge z Target nucleus
charge Z Elastic cross section (valid spin
0, small angles ?? low ?) Cross section diverges
for lt?gt0. For very small angles (large impact
b), get screening At 0 cross section goes
to a constant.
Rutherford Scattering Formula
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Elastic Scattering Cross Section
We can estimate ?min by localizing the incident
trajectory to within ?x atomic radius ra for a
chance at scattering. Incident momentum
uncertain by and
. Using atomic radius We find the
minimum angle Rutherford scattering breaks
down when becomes comparable to rn, nucleus size.
Similar to diffraction Integrating from
to , we get Total elastic xs falls off as ???.
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Multiple Scattering
For any observed angle ? of a particle, we dont
know if it underwent a single scattering event or
multiple small angle scattering. We determine
distns for processes, so the probability of a
process resulting in angle ??can be
found. Approximation
Expectation of ??
X0 radiation length
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Detecting Charges Particles
Particles can be detected if they deposit energy
into matter. How do they lose energy in
matter? Discrete collisions with the atomic
electrons of absorber.

Collisions with nuclei not so important
(meltltmN) for energy loss
Ne electron density
If are in the right range, we
get ionization.
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Classical dE/dx
Charged particles passing through matter have
collisions with nuclei and electrons in atoms.
Momentum kick obtained from coulomb field can be
written as (Fernow 2.1)
Incident particle of mass M, charge z1e, velocity
v1. Matter particle of mass m, charge z2e.
(For Z electrons in an atom with A2Z)
If mme and z21 for e, MAmp and z2Z for n
Total energy lost by incident particle per unit
length
?? characteristic orbital frequency for the
atomic electron. This classical form Is an
approximation.
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Range of Particles
When electromagnetic scattering dominates as a
source of energy loss, a pure beam of charged
particles travel about the same range R in
matter. Example A beam of 1 GeV/c protons has a
range of about 20 g/cm2 in lead (17.6 cm). The
number of heavy charged particles in a beam
decreases with depth into the material. Most
ionization los occurs near the end of the path,
where velocities are small. Bragg peak increase
in energy loss at end of path. Mean Range depth
at which 1/2 the particles remain.
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Real Ionization Energy Loss
Want average differential energy loss .
Energy loss at a single encounter with an
electron
?
Introduce classical electron radius
Number of encounters proportional to electron
density in medium
Full-blown Bethe-Block
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Bethe-Bloch Formula for Ionization

• High energy charged particles kick off electrons
  in atoms while passing thru
• Ionization energy loss.
• Characterized by
• 1/?2 fall off (indep of m!)
• predictable minimum
• relativistic rise
• The Point High energy particles lose energy
  slowly due to ionization, so they leave tracks.
• Many kinds of
• tracking detectors!

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Energy Loss Distributions

• In a thin detector, a charged particle deposits
  a certain amount of energy (ionizes a certain
  number of atoms) described by a Landau
  distribution
• Notice nice gap between zero charge and
  minimum, and long tail on high side.

Landau Distribution
Plot of signal pulse height made using
300-?m-thick Si strip detector
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Silicon Tracking Detectors

• In the past 20 years detectors fabricated
  directly on silicon wafers have become dominant
  for inner tracking
• large (200V) reverse bias applied
• ionization e/h drift rapidly, inducing signal
  (25k e)

sx 10 µm
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Silicon Vertex Detectors
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Silicon Pixel Detectors

• we are presently building a detector for the LHC
  experiment CMS which uses 100x150 micron pixels

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Electrons and Positrons

• Electrons and positrons lose energy via
  ionization just as other charged particles.
• However, their smaller masses mean they lose
  significant energy due to radiation as well
• Bremsstrahlung
• Elastic scattering
• Pair production and electromagnetic showers
• Since they have similar electromagnetic
  interactions, use electron as primary example.
• Ionization One difference is Bhabha scattering
  of e- and e instead of e- e- Moller scattering.
  Bethe-Block using both cross sections is similar,
  so to first order, all singly-charged particles
  with 1 lose energy at same rate.

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Bremsstrahlung
The dominant mechanism for energy loss for high
energy electrons is electromagnetic
radiation. Synchrotron radiation For circular
acceleration. Bremsstrahlung radiation For
motion through matter.
Time-rate of energy loss depends quadratically on
acceleration
Semiclassical calculation Bremsstrahlung cross
section for a relativistic particle.
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Positron Annihilation
In almost all cases, positrons that pass through
matter annihilate with an electron, to create
photons Single photons are possible if the
electron is bound to a
nucleus this occurs at only
20 the rate for two photons. A high energy
positron will lose energy by collision and
radiation, until it has a low enough energy to
annihilate. Positronium e and e- can form a
temporary bound state, similar to the hydrogen
atom.
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Photons and Matter

• Interactions for charged particles small
  perturbations.
• ??Energy is small
• slight change in trajectory
• Number of incident particles remains basically
  unchanged.
• ? Photons large probability to be removed upon
  interaction.
• Beam of photons number N removed from beam while
  traversing dx of material is dN -?Ndx. The
  beam intensity is then
• ? is the linear attenuation coefficient,
  dependent on the material.

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Photon Interactions

• low energies (lt 100 keV) Photoelectric effect
• medium energies (1 MeV) Compton scattering
• high energies (gt 10 MeV) ee- pair
  production
• Note that each of these processes leads to the
  ejection of electrons from atoms!
• electromagnetic showers

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PhotoElectric Effect
Interaction between photon and whole atom.
Photons with energies above the Work Function,
or binding energy of an electron, can eject an
atomic electron, with kinetic energy T
Einstein Quantized photon
energies Feynman QED!
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Compton Scattering
Compton Effect Scattering an incident photon
with an atomic electron. Wavelength difference
between incoming and outgoing photon
Frequency of Scattered Photon
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Conversions (ugh!)
Otherwise known as pair production. Large
background fake real electron/positron signals.
Total cross section increases rapidly with
photon energy, approximately proportional to
Z2. Comparing pair production with
bremsstrahlung Total mass attenuation
coefficient
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Electromagnetic Showers

• a beam of electrons impinging on solid matter
  will have a linear absorption coefficient of 1/X0
• this process repeats, giving rise to an e.m.
  shower
• the process continues until the resulting photons
  and electrons fall below threshold
• so how do we get some sort of signal out?
• ultimately we need ionization
• Will discuss more when we talk about calorimetry

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Radiative ??Energy Loss
Optical behavior of medium characterized by
complex dielectric constant
Sometimes instead of ionizing an atom or exciting
matter, the photon can escape the medium
(transition, C, etc).
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Nuclear Interactions
Next Monday, finish up with nuclear interactions.
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Strong Interactions
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Weak Interactions