PHYS 3446 – Lecture #14Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Wednesday, Oct. 15, 2008 PHYS 3446, Fall 2008Andrew Brandt1PHYS 3446 – Lecture #14Wednesday, October 15, 2008Dr. Mark Sosebee1. Energy Deposition in Media•Charged Particle Detection•Ionization Process•Photon Energy LossWednesday, Oct. 15, 2008 PHYS 3446, Fall 2008Andrew Brandt2•Initially two forces–Gravitational force: formulated through Newton’s laws–Electro-magnetic force: formulated through Maxwell’s equations•We have learned about two additional forces–Strong nuclear force: Discovered through studies of nuclei and their structure–Weak force: Discovered and postulated through nuclear -decayForces in NatureWednesday, Oct. 15, 2008 PHYS 3446, Fall 2008Andrew Brandt3•Physics is an experimental science–Understand nature through experiments•In nuclear and particle physics, experiments are performed through scattering of particles•In order for a particle to be detected:–Must leave a trace of its presence deposit energyParticle PhysicsWednesday, Oct. 15, 2008 PHYS 3446, Fall 2008Andrew Brandt4•An ideal detector would–Detect particle without affecting them•Real detectors–Use electromagnetic interactions of particles with matter•Ionization of matter by energetic, charged particles•Ionized electrons can then be accelerated within an electric field to produce a detectable electric current–Sometime catastrophic nuclear collisions but rare–Particles like neutrinos, which do not interact through EM and have low cross sections, require special detection methodsDetecting ParticlesWednesday, Oct. 15, 2008 PHYS 3446, Fall 2008Andrew Brandt5CERN-open-2000-344, A. SharmaLarge amplification70m140mGas Electron Multiplier (GEM) detectorWednesday, Oct. 15, 2008 PHYS 3446, Fall 2008Andrew Brandt6How does a charged particle get detected?IonizationCharged trackCurrent amplification+++++++++++- - - - - - - - - - - -Wednesday, Oct. 15, 2008 PHYS 3446, Fall 2008Andrew Brandt7•What do you think is the primary interaction when a charged particle is traversing through a medium?–Interactions with the atomic electrons in the medium•If the energy of the charged particle is sufficiently high–It deposits its energy (or loses its energy in matter) by ionizing the atoms along its path –Or by exciting atoms or molecules to higher states–What are the differences between the above two methods?•In the former case you get electrons, for the latter photons•If the charged particle is massive, its interactions with atomic electrons will not affect the particles trajectory•Sometimes, the particle undergoes nuclear collisions Charged Particle DetectionelectronsphotonsWednesday, Oct. 15, 2008 PHYS 3446, Fall 2008Andrew Brandt8•Ionization properties can be described by the stopping power variable, S(T)–Definition: amount of kinetic energy lost by any incident object per unit length of the path traversed in the medium–Referred to as ionization energy loss or energy loss•T: Kinetic energy of the incident particle•nion: Number of electron-ion pair formed per unit path length• I : The average energy needed to ionize an atom in the medium; for large atomic numbers ~10Z eV.Ionization Process( )S T =Why negative sign?The particle’s energy decreases.dTdx- =ionn IWednesday, Oct. 15, 2008 PHYS 3446, Fall 2008Andrew Brandt9•What do you think the stopping power of the given medium depends on?–Energy of the incident particle–Electric charge of the incident particle•Since ionization is an EM process, easily calculable–Bethe-Bloch formula for relativistic particle–z: Incident particle atomic number–Z: medium atomic number–n: number of atoms in unit volume (=A0/A)–m: mass of the mediumIonization Process( )S T =( )222 2 222 242lnze e nZmcIm cpg bbb� �� �-� �� �� �� �� �Wednesday, Oct. 15, 2008 PHYS 3446, Fall 2008Andrew Brandt10•In natural -decay, the formula becomes–Due to its low kinetic energy (a few MeV) and large mass, relativistic corrections can be ignored•For energetic particles in accelerator experiments or beta emission, the relativistic corrections are substantial•Bethe-Bloch formula can be used in many media, for various incident particles over a wide range of energiesIonization Process( )S T =( )222 22 242lnze e nZmcIm cpbb� �� �� �( )222 2 222 242lnze e nZmcIm cpg bbb� �� �- �� �� �� �� �� �10Wednesday, Oct. 15, 2008 PHYS 3446, Fall 2008Andrew Brandt11•Why does the interaction with atomic electrons dominate the energy loss of the incident particle?–Interactions with heavy nucleus causes large change of direction of the momentum but little momentum transfer •Does not necessarily require large loss of kinetic energy–While momentum transfer to electrons would require large kinetic energy loss•Typical momentum transfer to electrons is 0.1MeV/c and requires 10KeV of kinetic energy loss•The same amount of momentum transfer to a gold nucleus would require less than 0.1eV of energy loss•Thus Bethe-Bloch formula is inversely proportional to the mass of the mediumIonization Process( )222 2 222 242( ) lnze e nZmcS TIm cpg bbb� �� �= -� �� �� �� �� �Wednesday, Oct. 15, 2008 PHYS 3446, Fall 2008Andrew Brandt12•At low particle velocities, ionization loss is sensitive to particle energy. How can you tell?–Stopping power decreases as v increases!!•This shows that the particles of different rest mass (M) but the same momentum (p) can be distinguished due to their different energy loss rate•At low velocities (~1), particles can be distinguishedIonization Process( )222 2 222 242( ) lnze e nZmcS TIm cpg bbb� �� �= -� �� �� �� �� �21( )S Tv� =2 22Mpg( )21cb=( )2 22MM cggb=Wednesday, Oct. 15, 2008 PHYS 3446, Fall 2008Andrew Brandt13•Stopping power decreases with increasing particle velocity independent of incident particle mass–Minimum occurs when ~3 •Particle is minimum ionizing when v~0.96c•For massive particles the minimum occurs at higher momenta–This is followed by a ln() relativistic rise (see Beth-Bloch formula)–Energy loss plateaus at high due to long range inter-atomic screening effect which is ignored in Beth-BlochProperties of Ionization ProcessPlateau due to inter-atomic
View Full Document
Unlocking...