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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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detecting particles how to see without seeing

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

D. Green, The Physics of Particle Detectors, Ch. 5,6

http://pdg.lbl.gov/2004/reviews/pardetrpp.pdf

interactions of particles with matter
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

elastic scattering
Elastic Scattering

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

elastic scattering cross section
Elastic Scattering Cross Section

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 .

multiple scattering
Multiple Scattering

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.

Approximation:

Expectation of :

X0 = “radiation length”

detecting charges particles
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 (me<<mN) for energy loss]

Ne: electron density

If are in the right range, we get ionization.

classical de dx
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 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.

range of particles
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.

real ionization energy loss
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

bethe bloch formula for ionization
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!
energy loss distributions
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

silicon tracking detectors
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)

σx = ~10 μm

silicon pixel detectors
Silicon Pixel Detectors
  • we are presently building a detector for the LHC experiment CMS which uses 100x150 micron pixels
electrons and positrons
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.
bremsstrahlung
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.

positron annihilation
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.

photons and matter
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.
photon interactions
Photon Interactions
  • low energies (< 100 keV): Photoelectric effect
  • medium energies (~1 MeV):Compton scattering
  • high energies (> 10 MeV):e+e- pair production
  • Note that each of these processes leads to the ejection of electrons from atoms!
  • “electromagnetic showers”
photoelectric effect
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!

compton scattering
Compton Scattering

Compton Effect:

Scattering an incident photon with an atomic electron.

Wavelength difference between incoming and outgoing photon:

Frequency of Scattered

Photon:

conversions ugh
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:

electromagnetic showers
Electromagnetic Showers
  • a beam of electrons impinging on solid matter will have a linear absorption coefficient of1/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…

radiative energy loss
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).

nuclear interactions
Nuclear Interactions

Next Monday, finish up with nuclear interactions.