The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter The volume occupied by matter is due primarily to it’s A) electron cloud 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 The volume of matter is due primarily to it’s A) electron cloud B) protons C) nuclei D) other The mass of matter is due primarily to the A) electron cloud B) nuclei C) other The answer to the first question is (A). Atoms comprise matter and most of the space in an atom is due to the electron cloud. The nucleus occupies only a very small volume (about %) of the total space of the atom. The electron cloud is not easily compressed which is why matter is really mostly empty space. The answer to the second question is (B). Although the nucleus occupies a very small volume, it is very massive. One proton is equal in mass to about 2000 electrons. Thus the electrons contribute only about 0.05% of the mass of an atom.

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 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 answer is (A). Whenever two atoms overlap, their electrons repel each other strongly. The atomic orbitals are not easily compressed, or squeezed down. If the atoms in your shoe try to push through the floor, the electrons in the atoms of the floor repel it, supporting it with an upward “normal” force that keeps the shoe’s atoms from getting too close.

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 Number density, n : number of individual atoms (or scattering centers!) per unit volume n=  N A / A where N A = Avogadro’s Number A = atomic weight (g)  = density (g/cc) n= (11.3 g/cc)(6.02  /mole)/(207.2 g/mole) = 3.28  /cm 3 w

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  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 Swimmer 4.5 mph Long Distance 10 mph Runner Sprinter 22 mph 100 yd dash (1980) human-powered Vector 63 mph Cheetah 65 mph automobile 140 mph piston-engine dragster 244 mph commercial jet airliner 600 mph speed,sound 740 mph SSC jet-car 763 mph

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter SR-71 Blackbird reconnaissance jet 2200 mph GPS orbitting satellite 8700 mph auto 140 mph dragster 244 mph commercial jet airliner 600 mph speed,sound 740 mph SSC jet-car 763 mph

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter Blackbird 2200 mph GPS satellite 8700 mph Orbitting space shuttle 17,000 mph Voyager 1 38,600 mph (launched 1977)

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter space shuttle 17,000 mph Voyager 38,600 mph 100,000 mph 200,000 mph 300,000 mph 400,000 mph 500,000 mph 600,000 mph 700,000 mph 800,000 mph 900,000 mph 1,000,000 mph 2,000,000 mph 3,000,000 mph 4,000,000 mph 5,000,000 mph 6,000,000 mph 7,000,000 mph 8,000,000 mph 9,000,000 mph 10,000,000 mph

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter 1,000,000 mph 2,000,000 mph 3,000,000 mph 4,000,000 mph 5,000,000 mph 6,000,000 mph 7,000,000 mph 8,000,000 mph 9,000,000 mph 10,000,000 mph 20,000,000 mph 30,000,000 mph 40,000,000 mph 50,000,000 mph 60,000,000 mph 70,000,000 mph 80,000,000 mph 90,000,000 mph 100,000,000 mph 200,000,000 mph 300,000,000 mph 400,000,000 mph 500,000,000 mph 600,000,000 mph 700,000,000 mph 800,000,000 mph 900,000,000 mph 1,000,000,000 mph LIGHT

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 bowling ball and ping-pong ball are rolling towards you with the same momentum. If you exert the same force in stopping each, which takes a longer time to bring to rest? A) the bowling ball A) the bowling ball B) the ping pong ball B) the ping pong ball C) same time for both C) same time for both

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. If you exert the same force in stopping each, for which is the stopping distance greater? A) the bowling ball A) the bowling ball B) the ping pong ball B) the ping pong ball C) same distance for both C) same distance 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 heavy truck and light car have a head-on collision bringing them to a sudden stop. Which vehicle experienced the greater force of impact? the greater impulse? the greater change in momentum? the greater acceleration? A) the truck B) the car C) both the same

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter A heavy truck and a light car have a head-on collision bringing them to a sudden stop. Which vehicle experienced the greater force of impact? the greater impulse? the greater change in momentum? the greater acceleration? 1) the truck 2) the car 3) both the same Since forces are equal and opposite, both experience the same force. Since both experience the same force in the same time, they both have the same impulse. Since they both have the same impulse, they both must have the same change in momentum. Since they both experience the same force, the less massive car has a greater acceleration, since a = F/m.

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 moving cue ball hits an identical mass, but stationary, billiard ball head on. The collision is elastic. Describe the motion of both balls just after their collision. V V

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

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 BeforeAfter Two billiard balls undergo the glancing (not head-on) collision shown above ( some spin must have been placed on the cue ball, but you don’t have to worry about that detail ). What is the direction of the target ball after the collision? mv

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter The answer is (D). Even without numbers, the vector arrows representing momentum = mv, are enough! As usual, the momentum before and after collision must remain the same. After the collision, there are two balls moving, so their momentum must add up to the same total momentum observed before collision. The question becomes, what momentum vector, when added to the vector gives the vector ? Recall how to add vectors: place the tail end of one to the head of the other. The answer must be (4), as shown in the figure below: BeforeAfter Two billiard balls undergo a glancing (not head-on) collision shown above. What is the direction of the target ball after the collision? mv resultant white ball momentum black ball momentum

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 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 stick together. Neglecting friction Which of the arrows best represents the direction the combined wreck travels? The answer is (A). Momentum is conserved, so the total momentum before the collision must equal the total momentum after. But momentum is a vector, so we have to add the vector arrows (by sliding them and placing them head to tail). The momentum of car A is mass  velocity = 9000 kg m/s in the direction of east. The momentum of car B is mass  velocity = kg m/s north. Draw these vectors, making sure to make the lengths proportional to the momenta. 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 fromand 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

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

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 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 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

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

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter mv + M(0) = mv mv = mv 1 + Mv 2 Conservation of Momentum: The initial momentum Must equal the final momentum ½mv 2 + ½M(0) 2 = ½mv 2 ½mv 2 = ½mv ½Mv 2 2 Conservation of Energy: The initial energy must equal the final energy

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter mv = mv 1 + Mv 2 ½mv 2 = ½mv ½Mv 2 2 both equations must be satisfied together mv  mv 1 = Mv 2 m(v  v 1 ) = Mv 2 2  ½mv 2 = 2  (½mv ½Mv 2 2 ) mv 2 = mv Mv 2 2 m(v 2  v 1 2 ) = Mv 2 2

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter m(v  v 1 ) = Mv 2 m(v 2  v 1 2 ) = Mv 2 2 m(v  v 1 ) = Mv 2 m(v 2  v 1 2 ) = Mv 2 2 Divide the top equation by the bottom equation (v  v 1 ) = v 2 (v 2  v 1 2 ) = v 2 2 (v  v 1 ) (v  v 1 ) = v 2 2 (v  v 1 ) = v 2

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter m(v  v 1 ) = Mv 2 m(v 2  v 1 2 ) = Mv 2 2 (v  v 1 ) = v 2 m(v  v 1 ) = M(v + v 1 ) mv  mv 1 = Mv + Mv 1 mv  Mv = mv 1 + Mv 1 (m  M)v = (m + M)v 1 (m  M) (m + M) v = v 1

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter (m  M) (m + M) v 1 = v 2m (m + M) v 2 = v If M = m:v 1 = v 2 = If M = 10m :v 1 = v 2 = If M = 100m: v 1 = v 2 = If M>>100m: v 1 

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

The Cosmic Ray Observatory Project High Energy Physics Group The University of Nebraska-Lincoln Interaction of Charged Particles with Matter V (m  M) (m + M) v 1 = v 2m (m + M) v 2 = v

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)