SC A TTERING
INTERACTION OF RADIATION WITH MATTER
1
CHARGED P A R TICLES IN M A TTER
Charged particles interact mostly with the electronic cloud
Alpha
Small energy loss, but very frequent collisions
2
CHARGED P A R TIC LES IN M A TTER
Classical, non-relativistic collision s of charged particles with electrons
Conservation of energy and mom entum
Bef or e c ollision v
A f t er c ollision
v’ v
v e v
Charged particle looses a tiny fraction of its original energy
1
∆ E = m
v 2 =
1
m (2 v
) 2 = 4 m e E
! ∆ E
= 4 m e ⌧ 1
2 e e
2 e ↵
m ↵ ↵
E ↵ m ↵
3
COULOMB INTER A CTION
4
S T OPPING P O WER
Integrate over all impact parameters b
Lower bound (closest approach max energy lost):
Upper bound: Bohr radius (from ionization energy)
5
S T OPPING RANGE
1. Thousands of events (collisions) are needed to ef fectively slow down and stop the alpha particle
2. As the alpha particle is barely perturbed by individual collisions, the particle travels in a straight line.
3. The collisions are due to Coulomb interaction, which is an infinite-range interaction. Then, the alpha particle interacts simultaneously with many electrons, yielding a continuous slowing down a certain stopping range.
4. The electrons which are the collision targets get ionized, thus they lead to a visible trail (e.g. in cloud chambers)
6
RUTHERFORD SC A TTERING
ANIM A TION
7
RUTHERFORD SC A TTERING
Classical x-section:
d σ 2 π bdb
alp h a
v
b
r min
=
d ⌦ d ⌦
d Nucleus x
✓
Momentum change: ∆ p = 2 mv 0 sin 2
Conservation of angular momentum
~ zZ e 2 r ˆ
Coulomb interaction:
d p ~ = F d t =
4 ⇡✏ 0
| r 2 | dt
p
p=m v 0
p
r
d Nucleus
x
8
COULOMB SC A TTERING
Cross-section:
d σ 2 2
✓ zZ e ◆ ✓ θ ◆
= (4 T a ) — 2 sin — 4
d ⌦ 4 πϵ 0 2
0
p
p p 3 p
4 2 4
Why Rutherford used Gold in the experiment?
9
MIT OpenCourseWare http://ocw.mit.edu
22.02 Introduction to Applied Nuclear Physics
Spring 2012
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