INTERACTION OF RADIATION WITH MATTER
1

CHARGED PARTICLES IN MATTER
Charged particles interact mostly with the electronic cloud
Alpha
Small energy loss, but very frequent collisions
2

CHARGED PARTICLES IN MATTER
Classical, non-relativistic collision s of charged particles with electrons v
α
Conservation of energy and mom
Before collision v
α v
α v
α α v
α
After c ollision v
α v’
α≈ v
α
E =
1
2 m e v
2 e
=
1
2 m e
(2 v
↵
)
2
= 4 m m e
↵
E
↵ v e ≈ 2 v α
E
↵ m
↵ v
2 α v
Charged particle looses a tiny fraction of its original energy v v e e ≈ 2 v v
α
α E m e
!
= 4 ⌧ 1 v e v
2 α
α 2 α
3

COULOMB INTERACTION
4

STOPPING POWER
Integrate over all impact parameters b
Lower bound (closest approach max energy lost):
Upper bound: Bohr radius (from ionization energy)
5

STOPPING RANGE
1. Thousands of events (collisions) are needed to effectively 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 SCATTERING
ANIMATION
7

RUTHERFORD SCATTERING
Classical x-section: d 2 ⇡ bdb
= d ⌦ d ⌦
Momentum change: p = 2 mv
0 sin
✓
2 b v
α
Conservation of angular momentum
Coulomb interaction: dp =
~ t =
4 ⇡✏
0
| r 2 | dt
ϑ p=mv
0
∆ p r d r min ϑ
Nucleus
γ d
δ p
ϑ
Nucleus
( π−ϑ )/2 x
8 x
ϑ p=mv
0
∆ p

COULOMB SCATTERING
Cross-section: d d ⌦
=
✓ zZe 2
◆
2
4 ⇡✏
0
(4 T a
) 2 sin
4
2
0 p
4 p
2
3 p
4
Why Rutherford used Gold in the experiment?
9 p

MIT OpenCourseWare http://ocw.mit.edu
22.02 Introduction to Applied Nuclear Physics
Spring 2012
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