PHYS 3446 – Lecture #10AnnouncementsSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Wednesday, Oct. 11, 2006 PHYS 3446, Fall 2006Jae Yu1PHYS 3446 – Lecture #10Wednesday, Oct. 11, 2006Dr. Jae Yu1. Energy Deposition in Media•Charged Particle Detection•Ionization Process•Photon Energy LossWednesday, Oct. 11, 2006 PHYS 3446, Fall 2006Jae Yu2Announcements•Colloquium today at 4pm in SH103–Dr. R. Arnowitt of Texas A&M–Title: Cosmology, SUSY and the LHC–Extra credit•Quiz next Monday, Oct. 16–Covers CH4•Reading assignment: CH5Wednesday, Oct. 11, 2006 PHYS 3446, Fall 2006Jae Yu3•We have learned the discovery of two additional forces–Gravitational force: formulated through Newton’s laws–Electro-magnetic force: formulated through Maxwell’s equations–Strong nuclear force: Discovered through studies of nuclei and their structure–Weak force: Discovered and postulated through nuclear -decayForces in NatureWednesday, Oct. 11, 2006 PHYS 3446, Fall 2006Jae Yu4•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 energyForewordsWednesday, Oct. 11, 2006 PHYS 3446, Fall 2006Jae Yu5•The most ideal detector should–Detect particle without affecting them•Realistic detectors–Use electromagnetic interactions of particles with matter•Ionization of matter by energetic, charged particles•Ionization electrons can then be accelerated within an electric field to produce detectable electric current–Sometime catastrophic nuclear collisions but rare–Particles like neutrinos which do not interact through EM and have low cross sections, need special methods to handleForewordsWednesday, Oct. 11, 2006 PHYS 3446, Fall 2006Jae Yu6How does a charged particle get detected?IonizationCharged trackCurrent amplification+++++++++++- - - - - - - - - - - -Wednesday, Oct. 11, 2006 PHYS 3446, Fall 2006Jae Yu7CERN-open-2000-344, A. SharmaLarge amplification70m140mWednesday, Oct. 11, 2006 PHYS 3446, Fall 2006Jae Yu8•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 the matter) by ionizing the atoms in the path –Or by exciting atoms or molecules to higher states–What are the differences between the above two methods?•The outcomes are either electrons or photons•If the charged particle is massive, its interactions with atomic electrons will not affect the particles trajectory•Sometimes, the particle undergoes a more catastrophic nuclear collisions Charged Particle DetectionelectronsphotonsWednesday, Oct. 11, 2006 PHYS 3446, Fall 2006Jae Yu9•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 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. 11, 2006 PHYS 3446, Fall 2006Jae Yu10•What do you think the stopping power of the given medium depends on?–Energy of the incident particle•Depends very little for relativistic particles–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. 11, 2006 PHYS 3446, Fall 2006Jae Yu11•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 emissions, the relativistic corrections are substantial•Bethe-Bloch formula can be used in many media, 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. 11, 2006 PHYS 3446, Fall 2006Jae Yu12•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. 11, 2006 PHYS 3446, Fall 2006Jae Yu13•At low particle velocities, ionization loss is sensitive to particle energy. How do you see this?–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. 11, 2006 PHYS 3446, Fall 2006Jae Yu14•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 by Beth-Bloch formula–Energy
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