mv 0 mv f  (mv) =  recoil momentum of target ( )  mv 0 mv f large impact parameter b and/or large projectile speed v 0 v f  v o For small scattering (  )

mv 0 mv f pp  /2 Together with: Recognizing that all charges are simple multiples of the fundamental unit of the electron charge e, we write q 1 = Z 1 e q 2 = Z 2 e

q1=Z1eq1=Z1e q2=Z2eq2=Z2e Z 2 ≡Atomic Number, the number of protons (or electrons)

Recalling that kinetic energy K = ½mv 2 = (mv) 2 /(2m) the transmitted kinetic energy (the energy lost in collision to the target) K = (  p) 2 /(2m target )

For nuclear collisions: m target  2Z 2 m proton

For collisions with atomic electrons: m target  m electron q 1 = e Z 2 times as many of these occur! Z2Z2

The energy loss due to collisions with electrons is GREATER by a factor of m proton = kg m electron = kg

Notice this simple approximation shows that Why are  -particles “more ionizing” than  -particles?

energy loss speed

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 Or P (E, E' ) dE'  dx = P  1 / (E') 2 ( 2  b db )  (  dx N A Z/A )

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 The (mean) energy loss involves logarithms of energy extremes

E (MeV) Range of dE/dx for proton through various materials Pb target H 2 gas target dE/dx ~ 1/  2 Logarithmic rise dE/dx = (4  N o z 2 e 4 /m e v 2 )(Z/A)[ ln {2m e v 2 /I(1-  2 )}-  2 ] I = mean excitation (ionization) potential of atoms in target ~ Z10 GeV Felix Bloch Hans Bethe NOTE : a function of only incoming particle’s  (not mass!) so a fairly universal expression x  x dx  dx defines effective depth through material

E (MeV) Range of dE/dx for proton through various materials Pb target H 2 gas target dE/dx ~ 1/  ~constant for several decades of energy ~4.1 MeV/(g/cm 2 ) ~1 MeV/(g/cm 2 ) typically MeV(g/cm 2 ) for solid targets minimum at  ~0.96, E~1 GeV for protons

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

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

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

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

1930s plates 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 Ag grains 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 1935 Eastman Kodak plates carried aboard Explorer II’s record altitude (72,395 ft) manned flight into the stratosphere

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

Cloud chamber photographs by George Rochester and 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.Perkins Nature 159, 694 (1947) Nature 163, 82 (1949)

3.7m diameter Big European Bubble Chamber CERN (Geneva, Switzerland) Side View Top View

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

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

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

PMT output viewed on an oscilloscope

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

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 triggered by external electronics that “recognize” the event topology of interest.

HV pulse Logic Unit A B C Incoming particle Outgoing particles

M.Schwartz poses before the Brookhaven National Laboratory experiment which confirmed two distinct types of neutrinos.