Detection of particles Flashcards
How are interacting particles detected?
Interacting particles are (relatively stable) particles have a large enough lifetime that can go through some substantial amount of our detector and create signals.
For example Photons, Protons, Neutrons, Muon, charged/neutral pions
What are the important properties in interacting particles?
- Charged vs. uncharged
- rest mass
- particles type /possible interactions
How do particles interact?
Charged particles: - Ionisation - Scattering - Energy loss by radiation, Bremsstrahlung (electron/positions) - Emitting -Cherenkov radiation *Neutral particles need to convert to charged particles to be detected Photons: - Pair production - Photoelectric effect - Compton scattering
How do you detect charged particles that interact with atomic electrons?
Interaction with the
atomic electrons. The
incoming particle loses energy in lab frame) and the atoms are excited or ionized.
The mean rate of energy loss by moderately relativistic charged heavy particles is described by the “Bethe
equation” which is valid in the region 0.1 < βγ < 1000 between this region the energy loss initially decreases with increasing energy and then rises logarithmically with energy.
How do you find the energy lose per centimetre ,=?
Inorder to get the energy loss per centimetre you will need to multiply with the density of the
material.
What does the graph of the Bethe formula tell us (the mean energy loss for charged particles in different media as a function of βγ?
Valid in the region 0.1 < βγ < 1000
Low velocity regime: Energy loss
decrease like β^-2 (precise dependence ~ β^-5/3)
MIP: at βγ =4-5
the energy loss falls as a function of βγ and
reaches a minimum which is quite important. the minimum ionisation
Relativistic rise : Energy loss increases like ln(βγ)2 (relativistic extension of electric field). The electric field from the primary charged particle flattens and so allows collisions with more distant atoms
This rise does not go to infinity, and this is what the term delta in our formula
does, because at some stage atomic electrons that are in a large distance from our travelling
particle are getting “screened”
What does the Bethe formula depend on?
- Material dependence
- Function of βγ but type of particle enters via its mass
We need to convert from βγ to momentum and vice versa
βγ = p/Mc
Calculating energy loss using the material dependence empirical
approximation?
minimum ionization energy loss for different materials _min =2.35 – 0.28ln(Z) came up with this ability line
where Z is the atomic number
What do detectors do?
Helping us reconstruct charged particle trajectories
are based on “seeing” the produced ionization. The detectors we will see depend on the particle interacting with their medium and producing some amount of ionization. Then we get signals and then we try to figure out the
properties of the particle
How do you detect charged particles that interact with the atomic nucleus?
Interaction with the atomic
nucleus. The particle is deflected causing multiple scattering of the particle in the material. During this scattering, a Bremsstrahlung photon can be emitted.
What is multiple scattering?
A charged particle traversing matter will be scattered by the electric field potentials of nuclei and
electrons.
Multiple-scattering processes are dominated by deflections in the electric field of nuclei.
Does not cause energy loss but alters the direction of the particle.
This leads to the particle being deflected by many small-angle scatters.
The result is that the particle will exit the material with a small angle θ_0 with respect its initial direction
The fact that it introduces “noise” is another reason we want “thin” detector when following a particle’s trajectory.
How can multiple scattering be described?
Considering many identical particles, one gets a distribution of their angles θ that follows a Gaussian distribution
A Gaussian distribution approximately describes the projected angular distribution.
θ_0=13.6MeV/βcpzsqrt(x/X_0)[1+ 0.038ln(xz^2/X_0β^2)
p,βc, and z are the momentum, velocity, and charge number of the incident particle,and x/X0 is the thickness of the scattering medium in radiation lengths.
Why do we want tracking detectors to be thin?
Multiple scattering is needs to accounted for the trajectories of charged particles (amount of material expressed in radiation lengths)
thin units of radiation length
we must minimize the use of high-Z material.
How are photons detected?
“indirectly” via interactions producing charged particles which are detected through their subsequent ionisation in our detectors
What happens to photons in pair production?
High energy photon interact with matter mainly via pair production , where they are “converted” to an
electron-positron pair.
Pair production can not happen in vacuum . We need material , recoil for energy and momentum conservation. P_γ=P_e+ + P_e- + P_R
What is photon conversion caused by?
caused by interaction with the electric field of the nucleus. For
materials with low atomic number Z pair production can happen via interactions with electric field of the
atomic electrons.
What is the cross-section for high-energy photons?
σ=7A/9N_AX_0
Where the ratio of atomic weight A and Avogadro’s number NA denotes the number of atoms per gram of
material, and X0 is in units g cm-2
What is the mean free path for high energy photons?
The average distance between interactions for particle travelling through material is called the
mean free path.
It related to the cross section and the number density of atoms
λ_γ= 9/7 X_0
.
What is the cross-section for high-energy photons?
σ=7A/9N_AX_0
Where the ratio of atomic weight A and Avogadro’s number NA denotes the number of atoms per gram of
material, and X0 is in units g cm-2
What is the attenuation length?
the distance where
the intensity of the beam has dropped to approximately 37%(1/e) of the initial one, meaning that
approximately 63% of the particles have been stopped.
What is the photoelectric effect?
The atom absorbs a photon and emits an electrons. At low energies this is the most likely process to occur.
What is the cross-section for photons in the photoelectric effect?
Cross section is strongly dependent on the available number of electrons and therefore on the Z value of theabsorber material. (Z^n
with n between 4 and 5).
Furthermore, depends on the energy as E^-3, so it loses its importance as the energy increases.
σ=const x Z^n/E^3
What is the photoelectric effect?
The atom absorbs a photon and emits an electrons. At low energies this is the most likely process to occur.
plays a role in low energies many photons
are absorbed in a sequence of Compton scattering processes . The photon energy is reduced in a
number of steps down to the point where the final absorption happen via the photoelectric effect. In this
process the angular preference for the direction of the initial photon is lost, photon end up isotropically
distributed. This fact can affect the design of “calorimeters
What is Compton Scattering?
In compton scattering a photon is scattered by an atomic electron with transfer of momentum and
energy to the recoiled electron that is sufficient to put that electron in an unbound state.
Except for the highest Z absorber materials, Compton Scattering is by far the most likely process to
occur for photons in the energy range between a few hundred KeV and 5 MeV
What is the scattering angles of the electron φ and
the photon θ relate as?
cot(ϕ)=(1+ζ)tan(θ/2)
Where ζ = Εγ/ (me) i.e energy of photon in
terms of electron mass.
