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Methods of Experimental
Particle Physics
Alexei Safonov
Lecture #10
1
PDG: Passage of Particles Through Matter
• Section 30 of the
“PDG Book”
(using 2012
edition) provides
a very detailed
review
• We will only walk
over some of it,
please see PDG
and references
therein for further
details
2
Ionization: “Heavy” Charged Particles
• Heavy (much heavier than electron)
charged particles
• Scattering on free electrons: Rutherford
scattering
• Account that electrons are not free (Bethe’s
formula):
• Energy losses: from moments of
• Ne is in “electrons per gram”
• J=0: mean number of collisions
• J=1: average energy loss – interesting one
3
Energy Losses
• Energy loss (MeV per cm of path length) depends both
on the material and density (and of course on
momentum)
• Convenient to divide by density [g/cm3] for “standard plots”
• If you need to know actual energy loss, you should multiply what
you see in the plot by density (rho)
4
Different Materials and Particles
• Energy loss (Bethe’s
equation:
• Note that dE/dx depends
on bg
• The same energy loss in gas
(or liquid gas, e.g. in a
bubble chamber) for 10 GeV
muon and 100 GeV proton
• Can possibly use to
distinguish particle
types if you can measure
these losses as the
particle goes through
gas and know their
momentum
• E.g. CDF tracker, a drift
chamber, could do that
5
Multiple Scattering
• In more dense media (or thick layers of
material), charged particles can encounter
many single scatters
• Multiple scattering
• The distribution of the q scatter is ~gaussain with
width
• In applications, mostly important for muons, we will
talk about this in more detail when discussing muon
detectors
6
Higher Momentum: Energy Losses
• At a few hundred GeV, a new contribution for
muons and pions: radiative losses
• Radiating muons is
something one has to
remember at LHC
• 100 GeV is not all that
much at LHC
7
More Material
• What we talked about until now is relevant for
small amounts of material (like gases)
• Most interactions are radiative in nature
• If there is a lot of material, pions and muons will
interact differently with it:
• Pions and protons can undergo nuclear interactions
• This is because they have quarks inside, which can interact
with quarks and gluons in the atoms of the media
• Muons can’t
• They interact weakly or electromagentically only
• We will talk about nuclear interactions closer to
the end of today lecture
8
Energy Losses by Electron
• What we discussed before works for
“heavy” charged particles, but what about
electrons?
• Ionization at very low energy, but then
Bremsstrahlung (electrons are light, easy to
emit a photon)
9
Electrons: Low Energy
• Electron losses as a function of Energy
• Note the new variable in the Y-axis label: X0
10
Radiation Length
• Length over which an electron loses all
but 1/e of it’s energy due to
Bremsstrahlung
• a=aZ
11
Electrons: Higher Energy
• At high energy: Bremsstrahlung
• k – energy of the photon produced by
“Bremming” electron
• Y-axis: photons per radiation length
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Radiation Length
• Take steel:
• r=8g/cm3
• X0=14/8=2 cm
• A 100 GeV
electron will
loose 63 GeV
of energy over
just 2 cm
• It’s easy to
stop an
electron
13
Passage of Photons Through Matter
• It’s easy to stop a photon
• A little harder at high
energies
• On the left: crosssections for photon
interactions in carbon
and lead
• Great, but how do you
read it – is it big or small?
14
Photons: Attenuation Length
• A.L. is basically the average distance traveled by a
photon before it interacts
• Above 1 GeV ~100% of the time it’s convertion into an electron
pair)
• Divide by density of the material to get it in cm
• Steel:
• r=8g/cm3
• A 100 GeV
photon on
average travels
mere 10/8~1cm
• Then you get a
pair of electrons
• Go back a
couple of slides
to see how much
those will travel
15
Electromagnetic Showers
• Because both electrons and photons interact
almost immediately producing photons or
electron pairs, our calculations are a little silly
• You always have a cascade of these electrons and
photons, so these probabilities somehow interplay
• Simulation of a
cascade produced
by a 30 GeV
electron:
• Shower maximum
somewhere near
6X0
• A useful number
to remember
16
Lateral Profile
• We discussed the
longitudinal profile of
an “EM shower”, but
what about lateral?
• 90% of the shower
energy is within a
cylinder of radius
• Called Moliere radius
• ES=21 MeV
• EC is critical energy
(plot on the right)
17
Nuclear Interactions
• Nuclear Interaction length is defined very
similar to radiation length
• But refers to the probability for a hadron to interact
with a nuclei in the material
• In this case it is
also makes more
sense to talk
about showers
than just single
particles
• More when we talk
about calorimeters
18
Next Time
• We mostly covered the basics of particle interactions
• But so far we cared about what happens with the particle (energy
losses, stopping power etc.)
• Next time we will talk about effects on the media from
passing particle
• Cherenkov radiation
• Scintillation
• Transitional radiation
• And some reminders of basics:
• Measurement of the momentum for a particle in magnetic field
• Then we will talk about actual detectors
• Types, characteristics
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