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mv 0

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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mv 0

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  1. mvf  mv0 ( ) mvf recoil momentum of target (mv) = - mv0 • large impact parameterb • and/or • large projectile speedv0 • vf  vo For small scattering (  )

  2. mvf  /2 p  /2 mv0 Together with: Recognizing that all charges are simple multiples of the fundamental unit of the electron charge e, we write q1 = Z1e q2 = Z2 e

  3. Z2≡Atomic Number, the number of protons (or electrons) q2=Z2e q1=Z1e

  4. Recalling that kinetic energy K = ½mv2 = (mv)2/(2m) the transmitted kinetic energy (the energy lost in collision to the target) K = (Dp)2/(2mtarget)

  5. For nuclear collisions: mtarget 2Z2mproton

  6. For nuclear collisions: mtarget 2Z2mproton For collisions with atomic electrons: mtarget melectronq1 = e Z2 times as many of these occur! Z2

  7. mproton= 0.0000000000000000000000000016748kg melectron = 0.0000000000000000000000000000009kg The energy loss due to collisions with electrons is GREATER by a factor of

  8. Notice this simple approximation shows that Why are a-particles “more ionizing” than b-particles?

  9. energy loss speed

  10. the 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')2

  11. P  1 / (E')2 Charged 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 b Note: The (mean) energy loss involves logarithms of energy extremes

  12. -dE/dx = (4pNoz2e4/mev2)(Z/A)[ln{2mev2/I(1-b2)}-b2] I = mean excitation (ionization) potential of atoms in target ~ Z10 GeV Hans Bethe NOTE: a function of only incoming particle’s  (not mass!) so a fairly universal expression Felix Bloch 103 102 101 100 Range of dE/dx for proton through various materials xx dx dx defines effective depth through material dE/dx ~ 1/b2 dE/d( x) r H2 gas target Pb target Logarithmic rise E (MeV) 101 102 104 105 106

  13. 103 102 101 100 Range of dE/dx for proton through various materials dE/dx ~ 1/b2 dE/d( x) r H2 gas target ~constant for several decades of energy ~4.1 MeV/(g/cm2) Pb target ~1 MeV/(g/cm2) typically 1.1-1.5 MeV(g/cm2) for solid targets 101 102 104 105 106 E (MeV) minimum at ~0.96, E~1 GeV for protons

  14. g b Muon momentum [GeV/c] Particle Data Group, R.M. Barnett et al., Phys.Rev.D54 (1996) 1; Eur.Phys.J. C3 (1998)

  15. D. R. Nygren, J. N. Marx, Physics Today 31 (1978) 46 a p p d m dE/dx(keV/cm) e Momentum [GeV/c]

  16. 1911 Rutherford’s assistant Hans Geiger develops a device registering the passage of ionizing particles.

  17. Balloon Electroscope Electroscopes become so robust, data can be collected remotely (for example retreived from unmanned weather balloons)

  18. 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

  19. November 1935 Eastman Kodak plates carried aboard Explorer II’s record altitude (72,395 ft) manned flight into the stratosphere

  20. 1937 Marietta Blau and Herta Wambacher report “stars” of tracks resulting from cosmic ray collisions with nuclei within the emulsion 50mm

  21. 1937-1939 Cloud chamber photographs by George Rochesterand J.G. Wilson of Manchester University showed the large number of particles contained within cosmic ray showers.

  22. C.F.Powell, P.H. Fowler, D.H.Perkins Nature 159, 694 (1947) Nature 163, 82 (1949)

  23. Side View 3.7mdiameter Big European Bubble Chamber CERN (Geneva, Switzerland) Top View

  24. 2000 scintillator panels, 2000 PMTs, 500 low and power supplies at UNL CASA detectors’ new home at the University of Nebraska

  25. Read out by 10 stage EMI 9256 photomultiplier tube PMMA (polymethyl methacrylate) doped with a scintillating fluor 2 ft x 2 ft x ½ inch

  26. (from scintillator) Photocathode Schematic drawing of a photomultiplier tube Photons eject electrons via photoelectric effect Each incident electron ejects about 4 new electrons at each dynode stage Vacuum inside tube An applied voltage difference between dynodes makes electrons accelerate from stage to stage “Multiplied” signal comes out here

  27. PMT output viewed on an oscilloscope

  28. Spark Chambers + + - - - - + - - - - + - - - - + - - - - + + + + - + d • High Voltage across two metal plates, separated • by a small (~cm) gap can break down.

  29. 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.

  30. Incoming particle B Outgoing particles A C HV pulse Logic Unit

  31. M.Schwartzposes before theBrookhaven National Laboratory experiment which confirmed two distinct types of neutrinos.

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