Detecting Particles: How to “see” without seeing…. Interactions of Particles with Matter: Electromagnetic and Nuclear Interactions. Prof. Robin D. Erbacher University of California, Davis. References : R. Fernow, Introduction to Experimental Particle Physics, Ch. 2, 3
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Interactions of Particles with Matter:
Electromagnetic 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
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
Incoming particle: charge z
Target nucleus: charge Z
Elastic cross section:
(valid: spin 0, small angles low )
Cross section diverges for <>=0.
For very small angles (large impact b), get screening:
At =0 cross section goes to a constant.
Rutherford Scattering Formula
We can estimate min by localizing the incident trajectory to within x ~ atomic radius rafor 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 .
For any observed angle of a particle, we don’t 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.
Expectation of :
X0 = “radiation length”
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 (me<<mN) for energy loss]
Ne: electron density
If are in the right range, we get ionization.
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 A~2Z)
If m=me and z2=1 for e,
M=Amp and z2=Z for n:
Total energy lost by incident particle per unit length:
characteristic orbital frequency for
the atomic electron. This classical form
Is an approximation.
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.
Want average differential energy loss .
Energy loss at a single encounter with an electron:
Number of encounters proportional to
electron density in medium:
Plot of signal pulse height made
using 300-m-thick Si strip detector
σx = ~10 μm
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
Bremsstrahlung cross section for a relativistic particle.
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.
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
Scattering an incident photon with an atomic electron.
Wavelength difference between incoming and outgoing photon:
Frequency of Scattered
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:
Will discuss more when we talk about calorimetry…
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).
Next Monday, finish up with nuclear interactions.