E.M. INTER A CTION WITH M A TTER

1

SC A TTERING of E.M. RADI A TION

T ype of scattering depends on t he e.m. energ y , ~ ω

wrt the electron energy: Ionization energy E I Rest-mass energy m e c 2

2

CLASSIC AL MODEL

E.M. wave interacting with an oscillating electron

Frequency of oscillation is given by Coulomb energy: ω 2

= k C /m e

e.m. field adds a driving force at e.m. frequency ω , F = — eE 0 sin( ω t )

Radiated power is related to the electron acceleration, a

2 e 2 1 e 2 2

P = a =

ω cE 2

3 c 3

3 m e c 2

( ω 2

— ω 2 ) 2 0

cE 2

The cross-section is then

σ = P /I 0 , I 0 = 0

8 π

8 π e 2 2

σ =

3 m e c 2

ω 2 2

2 — ω 2

3

R A YLEIGH SC A TTERING

At very low energy ω ⌧ ω 0 cross-section becomes:

8 π ✓ e 2

◆ 2 ✓ ω ◆ 4

σ =

3 m e c 2 ω 0

V ery strong depence on the frequency/wavelength

shorter wavelengths are scattered most

longer wavelengths travel in (almost) straight lines

Rayleigh scattering experiment?

4

R A YLEIGH SC A TTERING

Why is the sky blue?

The blue color of the sky is due to Rayleigh scattering. As light moves through the atmosphere, most of the longer wavelengths pass straight through. Little of the red, orange and yellow light is af fected by the air . However , much of the shorter wavelength light is absorbed by the gas molecules. The absorbed blue light is then radiated in dif ferent directions. It gets scattered all around the sk y . Whichever direction you look, some of this scattered blue light reaches you. Since you see the blue light from everywhere overhead, the sky looks blue.

Why is it paler close to the horizon?

As you look closer to the horizon, the sky appears much paler in color . T o reach you, the scattered blue light must pass through more air . Some of it gets scattered away again in other directions. Less blue light reaches your eyes. The color of the sky near the horizon appears paler or white.

Courtesy of Science Made Simple . Used with permission.

5

R A YLEIGH SC A TTERING

Why is the sky red at sunset?

As the sun begins to set, the light must travel farther through the atmosphere before it gets to you. More of the light is reflected and scattered. As less reaches you directl y , the sun appears less bright. The color of the sun itself appears to change, first to orange and then to red. This is because even more of the short wavelength blues and greens are now scattered. Only the longer wavelengths are left in the direct beam that reaches your eyes.

Courtesy of Science Made Simple . Used with permission.

Why are clouds white?

The water droplets that make up the cloud are much larger than the molecules of the air and the scattering from them is almost independent of wavelength in the visible range.

6

THOMSON SC A TTERING

Intermediate energy:

Higher than ionization energy (electron appears to be “free”) but not enough to impart relativistic speed:

~ ω 0

⌧ ~ ω ⌧ m e c 2

Simplify the cross-section: ω 2

2 — ω 2 ≈ — 1

7

HIGH-ENERGY

The classical picture fails at high energy (> ionization energy)

e.m. radiation can now be considered a “particle” (photon)

scattering = photon-electron collision

QM scattering theory

Quantized electromagnetic fi eld

Feynman Diagrams

8

HIGH-ENERGY

The classical picture fails at high energy (> ionization energy)

e.m. radiation can now be considered a “particle” (photon)

scattering = photon-electron collision

Photoelectric ef fect: photon absorbed, electron emitted

Compton Scattering

Pair production (E>1.022 MeV)

9

MIT OpenCourseWare http://ocw.mit.edu

22.02 Introduction to Applied Nuclear Physics

Spring 2012

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