mv0

mvf(mv) =

recoilmomentum

of target( )

mv0

mvf

•large impact parameter band/or

•large projectile speed v0

vf vo

For small scattering ( )

mv0

mvf

p /2

/2

2sin2 0

mvp

2

0

212sin2tanbmv

qq Together

with:

0

212

0

210

22

bv

qq

bmv

qqmvp

Recognizing that all charges are simplemultiples of the fundamental unit of the electron charge e, we write

q1 = Z1e q2 = Z2 e 0

2212

bv

eZZp

0

2212

bv

eZZp

q1=Z1e

q2=Z2e

Z2≡Atomic Number, the number of protons (or electrons)

ettett mvb

eZZ

m

p

arg2

02

422

21

arg

2

2

4

2

)(

Recalling that kinetic energy

K = ½mv2 = (mv)2/(2m) the transmitted kinetic energy(the energy lost in collision to the target)

K = (p)2/(2mtarget)

proton

protonettloss

mvb

eZZ

mvbZ

eZZ

m

pKE

20

2

42

21

20

22

422

21

arg

2

4

4

2

)(

For nuclear collisions: mtarget 2Z2mproton

proton

lossmvb

eZZKE 2

02

42

21

For nuclear collisions: mtarget 2Z2mproton

electron

lossmvb

eZKE 2

02

4212

For collisions with atomic electrons:

mtarget melectron q1 = e

Z2 timesas manyof theseoccur!

Z2

The energy loss due to collisions withelectrons is GREATER by a factor of

22 3672

2Z

m

mZ

electron

proton

mproton =

0.000 000 000 000 000 000 000 000 001 6748 kg

melectron =0.000 000 000 000 000 000 000 000 000 0009 kg

ett

lossmvb

eZZKE

arg2

02

422

21

2

4

Notice this simple approximation

shows that2

0

21

v

ZKEloss

Why are -particles “more ionizing”

than -particles?

20

21

v

ZKEloss

energyloss

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

emvE

Zeb 2

0

42

emvE

EdZedbb 2

02

4

2

Or

P (E, E' ) dE' dx = dx

E

Ed

vAm

eZN

e

A22

0

42

P 1 / (E')2

( 2b db ) ( dx NA 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

dx'dE'EE'E ),(P dxE

E

min

maxln[''

]

involves logarithms of energy extremes

E (MeV)

Range of dE/dx for proton through various materials

Pb target

H2 gas target

dE/dx ~ 1/2

Logarithmic rise

103

102

101

100

101 102 104 105 106

-dE/dx = (4Noz2e4/mev2)(Z/A)[ln{2mev2/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

xxdx dx

defineseffective

depththroughmaterial

E (MeV)

Range of dE/dx for proton through various materials

Pb target

H2 gas target

dE/dx ~ 1/2

103

102

101

100

101 102 104 105 106

~constant for severaldecades of energy

~4.1 MeV/(g/cm2)

~1 MeV/(g/cm2) typically1.1-1.5

MeV(g/cm2)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

50m

1937 Marietta Blau andHerta Wambacher

report “stars” of tracks resulting from cosmic

ray collisions with nuclei within the emulsion

1937-1939

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.PerkinsNature 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 incidentelectron ejectsabout 4 newelectrons at eachdynode stage

Vacuum insidetube

“Multiplied” signalcomes out here

An applied voltagedifference betweendynodes makeselectrons acceleratefrom 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 Laboratoryexperiment which confirmed two distinct types of neutrinos.