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[SQUEAKING]

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[RUSTLING]

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PROFESSOR: Welcome
back to 8.701.

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We are starting a new
chapter on instrumentation.

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And in this first section,
we'll discuss the interaction

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of particles with matter.

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So what happens when
particles traverse

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through a piece of material?

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The underlying
principle of detection

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is that we do have to have
some sort of interaction

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of the material of the detector
with the particles going

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through.

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And there needs to be some
sort of transfer of energy

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which can be identified.

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Then, that piece
of energy can be

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amplified, separated
from noise, and so on.

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But this first part of
any detection process

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is this interaction of
this particle with matter.

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We can ask, what
kind of particles

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can we actually identify?

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Electrons, muons, pions, kaons,
protons, neutrons, heavy ions,

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and photons.

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But the key here in
this list of particles

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is that those particles
have to be stable.

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So we cannot directly
identify tau,

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as the tau decays before it
has a chance to interact with

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the detector.

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The same for our top quark,
the Higgs boson, and so on.

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Interesting, neutrinos.

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Neutrinos interact with the
detector very, very rarely.

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When they do, they
actually detect a signal

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that is not of the neutrino
directly, but of the products

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of the interaction.

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So we will split
this discussion up

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in the interaction
of neutral particles

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and charged particles, and
we start with the photon.

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So the photon interacts
with detector material.

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With material in general, we
have three leading effects.

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The photo effect,
Compton scattering,

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and pair production.

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In the photo effect,
we have a photon

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interacting with an atom, and
then kicking out an electron.

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And then, your
detector has a chance

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to identify the energy and
the momentum of the electron.

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This concept is used in
photo multiplier tubes

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where then the kicked out
electron is further amplified.

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And that leads to a
shower of electrons

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which can be measured like
the photodiode [? species ?]

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effect.

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We have discussed the
Compton effect quite a bit.

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Here, the energy of
the scattered electron

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can be measured out of the
energy of the scattered photon.

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And then there's
pair production.

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Pair production
dominated high energies.

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And typically, it's
part of an initiation

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process of electromagnetic
showers in calorimeters.

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That's great.

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So what happens in
the calorimeter--

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and we'll talk about
this more later--

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is that an incoming photon or
electron causes this photon

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to convert into pairs of
electrons and positrons.

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And then there's this cascade
of electrons and positrons,

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and additional photons
being produced.

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In tracking detectors,
this is unwanted.

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So therefore, build tracking
detectors rather thin.

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We don't want to
have this confusion

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of additional charged
particles, and we

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try to measure the
energy of a proton.

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So this plot here shows you
the cross-section as a function

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of the photon energy.

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And you see here very
nicely those three effects

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contributing to the
total cross-section.

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So for low energies--

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in the range of some 100 keV,
the photo effect dominates.

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And there is this intermediate
range from about 100 keV

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to about 10 MeV where we see the
effect of Compton scattering.

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And everything above this is
dominated by pair production.

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And this here shows
you that there

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are some differences in what
kind of material you interact,

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of course.

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Photon or electron interaction.

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Again, the main
energy loss mechanism

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for high energy photons
and electrons in matter

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is through pair production,
and also bremsstrahlung.

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Bremsstrahlung is the effect
when an electron or positron

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radiates a photon.

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You can characterize
the materials

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by introducing a concept
of radiation length.

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And there's some
confusion sometimes.

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In the definition,
they are very similar,

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but they're not quite the same.

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Radiation length can be defined
as the length after which

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an electron loses about
1 over e of its energy

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by bremsstrahlung.

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And you often find
the definition

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through the mean
free path lengths.

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And in X0, the
radiation length is

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defined as 7/9 of the mean free
path length for pair production

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by a photon.

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So those are the
two definitions.

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And they're typically
used in the regime

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where the process is dominant.

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It's a very convenient
property because of quantity,

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because you don't have to worry
about when you're thinking

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about the interaction
of the detector,

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about the specific thickness
and what it means in terms

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of energy loss, and simply
know that your piece of lead

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is a fraction of a
radiation length.

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And that tells you how
many of your photons

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or how much of the photon
energy is being lost.

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Typically, when you
build detector concepts

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like a collider experiment
like ATLAS or CMS,

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you want the tracking volume
to be of low radiation length.

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And for ATLAS and
CMS, this depends

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on the rapidity or
the forward direction,

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but it varies between 30% and
200% of the radiation length.

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And for calorimeters, you
want that all the energy is

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deposited in the calorimeter.

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Nothing has leaked
out in the back,

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and therefore, you design
calorimeters typically

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with 20 or 30 radiation
lengths [INAUDIBLE]..

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So again, when me think about
how a photon or an electron

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leaves a footprint
in a calorimeter,

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you start from this first
electron and photon.

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And then, this particle evolves
in an electromagnetic shower.

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So there's this cascade
effect as the particle tries

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to move through this material.

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The shower maximum
is given here.

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Slightly depends on the energy.

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It uses logarithmic dependency.

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I introduce here the
critical energies.

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This is where the energy
loss through ionization

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is equal to the bremsstrahlung.

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And you see this
in this plot here--

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It's rather small--
as a function

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of energy and the energy loss.

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Again, you see, this effect
here is from ionization.

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And this effect here
is from bremsstrahlung.

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The critical energy is defined
as where those two energy loss

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mechanisms give you
the same result.

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So this is just a
normalization factor.

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But you see that there is
this logarithmic dependency

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of the energy loss.

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You can also wonder how wide
a shower actually becomes.

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And this is given by the width.

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The transverse
width of the shower

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is given by the Moliere radius.

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And that's approximate.

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You find 21 MeV over
the critical energy

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times the radiation
length gives you

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the size of the transverse
sides of your shower.

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And in this example,
this is 8 centimeters,

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compared to a shower
length of 46 centimeters.

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This is a very quick summary
of electromagnetic showers.

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You can also have nuclear
showers, of course.

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You have a neutron or a proton
entering your calorimeter.

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Here, the physics is a
little bit more complicated,

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but you can introduce
similar concepts.

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This concept of radiation
lengths for strong interactions

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of the hadron with the nuclei.

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So as for the
electromagnetic shower,

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there is this
cascade developing.

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However, if in the
cascade, for example,

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you would choose a neutron.

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That neutron can travel
without leaving an interaction

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for quite a distance.

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So you don't have
this continuous kind

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of flow of energy, and you have
little clusters of energies.

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And in those clusters, you have
not just nuclear interaction,

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but you can also
produce new pions.

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And those new pions decay
into a pair of photons.

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And then, the photons, they
leave electromagnetic showers.

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So hadronic showers have
typically two components--

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a hadronic part, which is
charged hadrons, pions, kaons,

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protons, neutrons, and an
electromagnetic part which

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is [INAUDIBLE] coming from
the decay of the neutrons.

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From the decay of the neutral
pions, which are photons.

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So here, just to give you a
feel four orders of magnitude,

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radiation length given--

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the nuclear and the
electromagnetic radiation

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is given as a function
of Z. And for a gas,

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we're talking about
hundreds of meters.

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For light material--
aluminum and silicon--

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we talk about 10 centimeters.

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And for heavy
material-- specifically

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lead-- we're talking about
sub-centimeter radiation

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length.

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Moving from the neutral
particles from the photons

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and electrons--

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sorry-- to the charged
particle interactions.

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Here again, just summarizing
or giving a summary first,

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and then going through
the individual components.

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The interaction mechanisms
are multiple scattering--

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elastic scattering
with the atoms.

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This is a process
which is not very

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much wanted because,
when you try

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to monitor the trajectory
of the particle,

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you don't want it to
scatter and change randomly

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its direction or momentum.

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Ionization is a basic mechanism
for tracking detectors.

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Photon radiation is
an important part

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through bremsstrahlung but
also through Cerenkov radiation

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or transition radiation.

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And then, in scintillators,
you can excite the material.

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And then, if you have a
wavelength shifting fiber

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material, you can cause
scintillation light

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to be shifted in wavelength.

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And then you can read
this out in order

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to gain information about
particles going through.

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All right.

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Let's start with
multiple scattering.

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So after passing a layer
of thickness with L,

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a particle with
some displacement r

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and some angle of deflection.

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So that is problematic
because you lose information

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through the random process.

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You see here this random
Gaussian-like distribution

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which is rather annoying.

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So the key here is to
minimize the radiation lengths

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of the particle going through.

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The next part is an ionization.

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Again, this is a primary
source of information

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we gained from in
tracking detectors.

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Typically, you have a number
of primary interactions

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per unit length which
are Poisson distribution.

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So it's a random
process whether or not

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the particle sees an
atom which it can ionize.

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And typically, in a
gas, you find about 30

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of those primary
interactions per centimeter.

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You have more in
denser materials.

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If you have kicked out an
electron in your ionization

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process, that electron
itself can again

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lead to secondary ionization.

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And once those electrons
reach sufficient energy,

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they're sometimes visible as
individual tracks themselves.

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They called delta electrons--

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new particles which are visible
in your tracking detector.

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Energy fluctuations can
be really, really large

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through ionization.

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Sometimes, you have a
really tough interaction

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and you transfer a lot of
energy to the electron,

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while the mean number
is well under control.

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So, interesting.

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Just to give you
a feel, again, you

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have about 30
primary interactions

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per centimeters in gas.

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The total ionization
energy you find

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is typically 3 times the
primary ionization energy.

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00:12:47,850 --> 00:12:51,840
So you cause those seeds of
ionization, and then the energy

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to move away from
this initial track.

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When you look at the
energy loss distribution,

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00:13:00,490 --> 00:13:03,070
this is a nice plot here
I made many, many years

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ago of the energy loss
in a piece of silicon

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of 100 gb pion.

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So this pion loses its energy
primarily through ionization.

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And this is a small piece of
silicon which we used here.

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So you see this
typical distribution.

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It's called the
Landau distribution

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with a most probable value
and then a very long tail.

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And this tail here is dominated
by those delta electrons

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I was talking about.

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In bubble chamber or
cloud chamber pictures,

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you see those delta
electrons here

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as little curls of ionization
along the main part

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of your particle leading
an ionization track.

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The energy loss of
charged particles

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can be calculated using
the Bethe-Bloch formula.

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And it's a very good
description in a specific energy

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range-- in the
energy range which

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is dominated by ionization.

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00:14:08,390 --> 00:14:10,370
And so, the formula
is given here.

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We discuss this some more
in our recitation section.

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But you see here in this
medium energy range,

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you are dominated with
Bethe-Bloch formula

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or by ionization where, when you
go into higher energies here,

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you find additional
energy loss--

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energy loss with radiation.

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So we can study the details
of this Bethe-Bloch formula.

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One interesting point is
the particle dependency

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of the energy loss-- and you
see this here shown for a muon,

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for a pion, and for proton.

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If you measure the energy
loss of a specific particle

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00:14:54,450 --> 00:14:56,640
in a reasonable
momentum range, you

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00:14:56,640 --> 00:14:58,290
can use that
information in order

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00:14:58,290 --> 00:15:03,030
to learn which particle
travels through your detector.

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00:15:03,030 --> 00:15:12,040
So you can use energy loss
in some cases in combination

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00:15:12,040 --> 00:15:17,170
with the momentum measurement
in order to identify particles.

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00:15:17,170 --> 00:15:20,300
Last but not least,
more radiation effects.

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00:15:20,300 --> 00:15:22,420
Cerenkov radiation is
a very neat feature

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00:15:22,420 --> 00:15:25,142
to also measure
particles as they

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go through a specific material.

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00:15:27,850 --> 00:15:31,580
They can also be used in order
to identify particles again.

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So the idea here is
that Cerenkov radiation

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00:15:35,170 --> 00:15:37,480
is emitted when
a particle passes

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00:15:37,480 --> 00:15:41,290
through a dielectric medium with
a speed larger than the speed

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00:15:41,290 --> 00:15:42,700
of the light in that medium.

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00:15:42,700 --> 00:15:45,610
And that causes
a radiation cone.

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00:15:45,610 --> 00:15:50,410
It's like a sonic boom when
you have airplanes passing by.

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And the simple picture is one
of the classical pictures.

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00:15:54,010 --> 00:15:59,810
It's one of this wave front
cone under a specific Cerenkov

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angle.

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00:16:03,020 --> 00:16:07,080
And then, last but not
least, transition radiation.

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00:16:07,080 --> 00:16:10,445
This is a process which
were predicted by Ginzburg

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00:16:10,445 --> 00:16:13,670
and Frenck in the 1940s.

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00:16:13,670 --> 00:16:17,090
His idea is that a
photon is emitted

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00:16:17,090 --> 00:16:20,660
when a charged particle
transfers through the boundary

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00:16:20,660 --> 00:16:21,780
of two mediums.

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00:16:21,780 --> 00:16:23,780
And so, if you
have a medium here

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00:16:23,780 --> 00:16:29,590
in a vacuum, for example, if the
particle travels through here,

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00:16:29,590 --> 00:16:32,980
it polarizes the
medium when it exits.

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00:16:32,980 --> 00:16:37,060
And that polarization then
leads to an electric dipole

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00:16:37,060 --> 00:16:38,560
which then starts to radiate.

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00:16:38,560 --> 00:16:42,590
And you get a photon from
this type of radiation.

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00:16:42,590 --> 00:16:44,980
So if you measure this
type of radiation,

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00:16:44,980 --> 00:16:47,680
you might be able to identify
that the particle traveling

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00:16:47,680 --> 00:16:50,395
through the transition of two
materials was an electron.

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00:16:54,170 --> 00:16:55,150
All right.

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00:16:55,150 --> 00:16:57,660
So this is the first
introduction to the topic.

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00:16:57,660 --> 00:17:00,110
So in the next part, we
now have to understand

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00:17:00,110 --> 00:17:04,270
how we use those phenomena
in order to build detectors.