# mv 0

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mv f. . mv 0. ( ). mv f. recoil momentum of target. ( mv ) = -. mv 0. large impact parameter b and/or large projectile speed v 0 v f  v o. For small scattering (  ). mv f.  /2.  p.  /2. mv 0. Together with:. Recognizing that all charges are simple
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mvf mv0( )mvfrecoilmomentumof target(mv) = -mv0
• large impact parameterb
• and/or
• large projectile speedv0
• vf  vo
• For small scattering (  ) mvf /2p /2mv0Together with:Recognizing that all charges are simplemultiples of the fundamental unit of the electron charge e, we writeq1 = Z1e q2 = Z2 eZ2≡Atomic Number, the number of protons (or electrons)q2=Z2eq1=Z1eRecalling that kinetic energyK = ½mv2 = (mv)2/(2m)the transmitted kinetic energy(the energy lost in collision to the target) K = (Dp)2/(2mtarget) For nuclear collisions: mtarget 2Z2mprotonFor nuclear collisions: mtarget 2Z2mprotonFor collisions with atomic electrons: mtarget melectronq1 = eZ2 timesas manyof theseoccur!Z2mproton=0.0000000000000000000000000016748kgmelectron =0.0000000000000000000000000000009kgThe energy loss due to collisions withelectrons is GREATER by a factor ofNotice this simple approximationshows thatWhy are a-particles “more ionizing”than b-particles?energylossspeedthe probability that a particle, entering a target volume with energy E“collides” within and loses an amount of energy between E'and E' + dE' P (E, E' ) dE'  dx( 2pb db )  ( dxNAZ/A)Or P(E, E')dE' dx =P  1 / (E')2P  1 / (E')2Charged particles passing through material undergo multiple collisions with atomic electrons shedding tiny fractions of their energy along the way.E' is a function of impact parameter bNote:The (mean) energy lossinvolves logarithms of energy extremes-dE/dx = (4pNoz2e4/mev2)(Z/A)[ln{2mev2/I(1-b2)}-b2] I = mean excitation (ionization) potential of atoms in target ~ Z10 GeVHans BetheNOTE: a function of only incoming particle’s (not mass!) so a fairly universal expressionFelix Bloch103102101100Range of dE/dx for proton through various materialsxxdx dxdefineseffectivedepththroughmaterialdE/dx ~ 1/b2dE/d( x)rH2 gas targetPb targetLogarithmic riseE (MeV)101 102 104 105 106103102101100Range of dE/dx for proton through various materialsdE/dx ~ 1/b2dE/d( x)rH2 gas target~constant for severaldecades of energy~4.1 MeV/(g/cm2)Pb target~1 MeV/(g/cm2)typically1.1-1.5 MeV(g/cm2)for solid targets101 102 104 105 106E (MeV)minimum at ~0.96, E~1 GeV for protonsgbMuon momentum [GeV/c]Particle Data Group, R.M. Barnett et al., Phys.Rev.D54 (1996) 1; Eur.Phys.J. C3 (1998) D. R. Nygren, J. N. Marx, Physics Today 31 (1978) 46 appdmdE/dx(keV/cm)eMomentum [GeV/c]1911 Rutherford’s assistant Hans Geiger develops a device registering the passage of ionizing particles.Balloon ElectroscopeElectroscopes become so robust, data can be collected remotely (for example retreived from unmanned weather balloons)1930splates coated with thick photographic emulsions
• (gelatins carrying silver bromide crystals)
• carried up mountains or in balloons clearly trace
• cosmic ray tracks through their depth when developed
• light produces spots of submicroscopic silver grains
• a fast charged particle can leave a trail of Aggrains
• 1/1000 mm (1/25000 in) diameter grains
• small singly charged particles - thin discontinuous wiggles
• only single grains thick
• heavy, multiply-charged particles - thick, straight tracks
• November 1935Eastman Kodak plates carried aboard Explorer II’s record altitude (72,395 ft) manned flight into the stratosphere 1937 Marietta Blau andHerta Wambacher report “stars” of tracks resulting from cosmic ray collisions with nuclei within the emulsion50mm1937-1939Cloud chamber photographs by George Rochesterand J.G. Wilson of Manchester University showed the large number of particles contained within cosmic ray showers. C.F.Powell, P.H. Fowler, D.H.PerkinsNature 159, 694 (1947)Nature 163, 82 (1949)Side View3.7mdiameterBig European Bubble ChamberCERN (Geneva, Switzerland)Top View2000 scintillator panels, 2000 PMTs, 500 low and power supplies at UNLCASA detectors’ new home at the University of NebraskaRead out by 10 stage EMI 9256photomultiplier tubePMMA (polymethyl methacrylate)doped with a scintillating fluor2 ft x 2 ft x ½ inch(from scintillator)PhotocathodeSchematic drawing of a photomultiplier tubePhotons eject electrons via photoelectric effectEach incidentelectron ejectsabout 4 newelectrons at eachdynode stageVacuum insidetubeAn applied voltagedifference betweendynodes makeselectrons acceleratefrom stage to stage“Multiplied” signalcomes out herePMT output viewed on an oscilloscopeSpark Chambers++----+----+----+----++++-+d
• High Voltage across two metal plates, separated
• by a small (~cm) gap can break down.
• If an ionizing particle passes through the gap producing ion
• pairs, spark discharges will follow it’s track.
• In the absence of HV across the gap, the ion pairs usually
• recombine after a few msec, but this means you can apply
• the HV after the ion pairs have formed, and still produce
• sparks revealing any charged particle’s path!
• Spark chambers (& the cameras that record what they
• display) can be triggeredby external electronics that
• “recognize” the event topology of interest.
• Incoming particleBOutgoing particles ACHV pulseLogic UnitM.Schwartzposes before theBrookhaven National Laboratoryexperiment which confirmed two distinct types of neutrinos.
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