1. Compton Effect
Compton performed an experiment which supported this idea
directed a beam of x-rays of wavelength  onto a carbon target
x-rays are scattered in different directions  ` 
` has 2 peaks
 = 71.1 pm (10-12 m)

3. Compton Scattering Wavelength ` of scattered x-rays has two peaks
these occur at  and  + 
 >0 is the Compton shift
classical physics predicts  =0
Quantum picture:
a single photon interacts with electrons in the target
light behaves like a ‘particle” of energy E=hf=hc/ and momentum p=h/  => a collision

4. Compton Scattering Conservation of energy E = E` + K
E=hf=hc/
E`=hf `=hc/`
K=mec2(-1)
Conservation of energy E = E` + K
=> E` < E => f ` < f => ` > 
X-ray momentum p=h/ p`= h/`
electron momentum pe = mev

5. Compton Scattering Conservation of energy E = E` + K
E=hf=hc/
E`=hf `=hc/`
K=mec2(-1)
Conservation of energy E = E` + K
=> E` < E => f ` < f => ` > 
X-ray momentum p=h/ p`= h/`
electron momentum pe = mev

6. X-ray scattering Energy and momentum are conserved
Momentum is a vector! F=dp/dt=0 => p = constant

8. X-ray Scattering 3 equations in 5 variables: , `,v,,
eliminate the electron variables v,  => find (v)
` -  =(h/mec) (1 - cos)
= c (1 - cos) c is Compton wavelength of the electron

9. Compton Scattering ` -  =  c (1 - cos) =0 ==> ` = 
= ==> ` = 
=/2 ==> ` =  + c
=  ==> ` =  + 2 c
why are there two peaks?

10. Compton Scattering
“loosely” bound electrons in Carbon are ejected and the x-rays are scattered
` -  =(h/mec) (1 - cos)
“tightly” bound electrons are not ejected => photon interacts with entire carbon atom
mass ~ 22,000 me =>  reduced by this factor

11. Problem
An x-ray beam of wavelength 0.01 nm strikes a target containing free electrons. Consider the xrays scattered back at 1800
Determine (a) change in wavelength of the xrays (b) change in photon energy between incident and scattered beams (c) the kinetic energy transferred to the electron (d) the electron’s direction of motion

12. Solution X-ray beam has =.01 nm = 10 pm =1800
` -  =(h/mec) (1 - cos)
= c (1 - cos) c is Compton wavelength of the electron
(a) =(h/cme)(1-cos(180))= 2h/cme =2(6.63x10-34)/[(3x108)(9.11x10-31)] =2(2.43 pm)= 4.86 pm
(b) E={ hc/ ` -hc/} =(6.63x10-34)(3x108){1/ /10}/(10-12) =-.65x10-14 J = -.41x105 eV = -41 keV

13. Solution (c) K (electron) = 41 keV (d) direction of electron?
Momentum conserved => electron moves forward p

14. Photons Revealed
Can we devise an experiment where both the wave and photon characteristics of light are involved?
Photon has 50% chance of being transmitted or reflected at B
reduce light beam energy to that of a single photon
if photon picture is correct we get anticoincidences
experiments were not convincing

15. Designated Photons
1986 Grangier, Roger, Aspect replaced source S by beam of calcium ions
Calcium excited by a laser and emits two photons
trigger photon turns detectors on and off (emitted and absorbed!)
designated photon demonstrated anticoincidences!
Supported the photon picture! - no wave interpretation possible
other modifications are possible to demonstrate both wave and photon properties of light - see section 45-6

16. Slowing Atoms by Photon Bombardment
A gas of atoms at room temperature is in constant motion
for argon gas at T=3000K, vrms = (3kT/m)1/2 = 430 m/s !
How can we use photons to slow these atoms down?
Consider that the atom absorbs a photon with p=h/
Typically a change of few cm/s
due to a single photon
Atoms moving in the same direction as the laser are speeded up => no net slowing down

17. Laser Cooling
When a photon is absorbed, the atom moves from the ground state to an excited state
excited state does not have a well defined energy since it only exists for a short time => uncertainty principle
Probability of absorption by atom at rest
Atom illuminated by two beams
laser greater than peak value
Photons absorbed from L slow it down and
those absorbed from R speed it up => do these effects cancel?

18. Laser Cooling Doppler effect:
L01 Mar 8/02
Laser Cooling
Doppler effect:
atom detects L as a higher f or lower L < laser
atom detects R as a lower f or higher R > laser
probabilities are not the same!
net reduction in speed results
experiments use 6 laser beams
trap