The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter The volume occupied by any lump of matter is due primarily to it’s atoms’ A) electron clouds B) protons C) nuclei D) other

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter The mass of matter is due primarily to it’s A) electron cloud B) nuclei C) other

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter If atoms are mostly empty space, why don’t we just fall through the floor? A) electrical forces B) magnetic forces C) gravitational forces D) nuclear forces E) atoms are not mostly empty space

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter EarthMoon

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter EarthMoon

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter In a solid interatomic spacing: 1  5 Å (1  5  m) nuclear radii: 1.5  5fm (1.5  5  m) for some sense of spacing consider the ratio orbital diameters central body diameter ~ 10s for moons/planets ~100s for planets orbiting sun the ratio orbital diameters central body diameter ~ 66,666 for atomic electron orbitals to their own nucleus A basketball scale nucleus would have its family of electrons stretching 10s of miles away

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter Carbon 6 C Oxygen 8 O Aluminum 13 Al Iron 26 Fe Copper 29 Cu Lead 82 Pb What about a single, high energy, charged particle?

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter A solid sheet of lead offers how much of a (cross sectional) physical target (and how much empty space) to a subatomic projectile? 82 Pb 207 n=  N A / A where N A = Avogadro’s Number A = atomic “weight” (g)  = density (g/cc) w Number density, n: number of individual atoms (or scattering centers!) per unit volume n= (11.3 g/cc)(6.02  /mole)/(207.2 g/mole) = 3.28  /cm 3

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter 82 Pb 207 For a thin enough layer n  ( Volume )  ( atomic cross section ) = n  (surface area,A  w)(  r 2 ) as a fraction of the target’s area: = n  (w)  -13 cm) 2 w  -15 m

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter 82 Pb 207 For a thin enough layer n  (w)  -13 cm) 2 w For 1 mm sheet of lead: cm sheet of lead:

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter Actually a projectile “sees” nw nuclei per unit area but Znw electrons per unit area!

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter We’ve named 3 forms of natural terrestrial radiation  How did these rank in ionizing power?

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter We’ve named 3 forms of natural terrestrial radiation  How did these rank in ionizing power? in penetrability(range)? 1 2 3

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter We’ve named 3 forms of natural terrestrial radiation  How did these rank in ionizing power? in penetrability(range)? Can you suggest WHY there is this inverse relationship between ionization and penetrability? “ionizing” radiation

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter m proton = kg m electron = kg

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter Momentum is inertia of motion Easy to start Hard to start While inertia depends on mass Momentum depends on mass and velocity Easy to stop Hard to stop v v v v m m m m momentum = mass  velocity “Quantity of motion”

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter To change velocity  Force To change momentum  Impulse Impulse = force × time   p = F  t F t =  p (doesn’t break) F t =  p (breaks) Ft  pFt  p Ft  pFt  p

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter A bowling ball and ping-pong ball are rolling towards you with the same momentum. Which ball is moving toward you with the greater speed? A) the bowling ball B) the ping pong ball C) same speed for both

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter A fast moving car traveling with a speed v rear-ends an identical model (and total mass) car idling in neutral at the intersection. They lock bumpers on impact and move forward at A) 0 (both stop). B) v /4 C) v /2 D) v v

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter A heavy truck and light car both traveling at the speed limit v, have a head-on collision. If they lock bumpers on impact they skid together to the A) right B) left Under what conditions would they stop dead?

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter A 100 kg astronaut at rest catches a 50 kg meteor moving toward him at 9 m/sec. If the astronaut manages to hold onto the meteor after catching it, what speed does he pick up? A) 3 m/sec B) 4.5 m/sec C) 9 m/sec D) 15 m/sec E) 18 m/sec F) some other speed

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter v v mvmv mvmv (m+m)v mvmv mvmv

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter A B C Car A has a mass of 900 kg and is travelling east at a speed of 10 m/sec. Car B has a mass of 600 kg and is travelling north at a speed of 25 m/sec. The two cars collide, and lock bumpers. Neglecting friction which arrow best represents the direction the combined wreck travels? 900 kg 10 m/sec 600 kg 25 m/sec

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter q2q2 q1q1 b b “impact” parameter A light particle of charge q 1 encounters (passes by, not directly hitting) a heavy particle of charge q 2 at rest,

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter q2q2 q1q1 b b “impact” parameter A light particle of charge q 1 encounters (passes by, not directly hitting) a heavy particle of charge q 2 at rest,

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter q2q2 q1q1 b b “impact” parameter A light particle of charge q 1 encounters (passes by, not directly hitting) a heavy particle of charge q 2 at rest,

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter q2q2 q1q1 b b “impact” parameter A light particle of charge q 1 encounters (passes by, not directly hitting) a heavy particle of charge q 2 at rest, and follows a HYPERBOLIC TRAJECTORY F F'F'

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter q2q2 q1q1 b A light particle of charge q 1 encounters (passes by, not directly hitting) a heavy particle of charge q 2 at rest, and follows a HYPERBOLIC TRAJECTORY F F'F' For an attractive “central” force the heavy charge occupies the focus of the trajectory like the sun does for a comet sweeping past the sun (falling from and escaping back to distant space).

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter q2q2 q1q1 b A light particle of charge q 1 encounters (passes by, not directly hitting) a heavy particle of charge q 2 at rest, and follows a HYPERBOLIC TRAJECTORY F F´F´  

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter q2q2 q1q1 b   Larger deflection m q v 0 b smaller much smaller smaller larger

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter q2q2 q1q1 Relaxing the “light”, “heavy” requirement simply means BOTH will move in response to the forces between them. Recoil of target

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter q2q2 q1q1 Relaxing the “light”, “heavy” requirement simply means BOTH will move in response to the forces between them. Recoil of target q1q1

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter What about the ENERGY LOST in the collision? the recoiling target carries energy some of the projectile’s energy was surrendered if the target is heavy the recoil is small the energy loss is insignificant Reminder:  1/ (3672  Z)

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter mv 0 mv f A projectile with initial speed v 0 scatters off a target (as shown) with final speed v f. The direction its target is sent recoiling is best represented by ATAT B C DEDE G F

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter mv 0 mv f A projectile with initial speed v 0 scatters off a target (as shown) with final speed v f. The sum of the final momentum (the scattered projectile and the recoiling target) must be the same as the initial momentum of the projectile! F

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter  mv 0 mv f mv 0 mv f

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter  mv 0 mv f mv 0 mv f  (mv) =  recoil momentum of target ( )

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter mv 0 mv f pp If scattering (  ) is small large impact parameter b and/or large projectile speed v 0 v f  v o  /2 A B C  Recall sin  = B/C

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter mv 0 mv f pp  /2 Together with:

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter Recognizing that all charges are simple multiples of the fundamental unit of the electron charge e, we can write q 1 = Z 1 eq 2 = Z 2 e

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter q1=Z1eq1=Z1e q2=Z2eq2=Z2e Z 2 ≡Atomic Number, the number of protons (or electrons)

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter 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 )

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter For nuclear collisions: m target  2Z 2 m proton For collisions with atomic electrons: m target  m electron q 2 = 1e for an encounter with 1 electron

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter For nuclear collisions: m target  2Z 2 m proton For collisions with atomic electrons: m target  m electron q 1 = 1e Z 2 times as many of these occur!

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter The energy loss due to collisions with electrons is GREATER by a factor of

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter Notice this simple approximation shows that Why are  -particles “more ionizing” than  -particles?

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter energy loss speed

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter 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 ~ Z  10 eV Felix BlochHans Bethe

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter Particle Data Group, R.M. Barnett et al., Phys.Rev. D54 (1996) 1; Eur. Phys. J. C3 (1998) Muon momentum [GeV/c]  

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter D. R. Nygren, J. N. Marx, Physics Today 31 (1978) 46    p d e Momentum [GeV/c] dE/dx(keV/cm)