Transcript Physics 452 - BYU Physics and Astronomy

Physics 452
Quantum mechanics II
Winter 2011
Karine Chesnel
Phys 452
Homework
Today Mar 25: assignment # 19
10.3, 10.4, 10.5, 10.7
Wednesday Mar 30: assignment # 20
11.1, 11.2, 11.4
Friday Apr 1: assignment #21
11.5, 11.6, 11.7
Phys 452
Quiz 30a
A scattering process is isotropic
A. True
B. False
Phys 452
Scattering
From the sun light
Scattering pattern
from an obstacle
Phys 452
Scattering
Scattering at different scale of electromagnetic spectrum
Phys 452
Scattering
A tool for material science:
Phys 452
Scattering
A tool for material science:
crystallography
Bragg’s law
2d sin   n
Campbell et al.
Phys 452
Scattering
A tool for material science:
Electron scattering
Techniques:
LEED
RHEED
TEM
Phys 452
Magnetic Scattering
q=k’-k
XRMS
p’ e’
s’
p
e
Interaction
photon spin / magnetic moment
Sphoton
M
s

I (q ) 

iq rn
 fe
2
n
f  f non.res  f res
Electric dipolar transition E1 ( L2,3 : 2p 3d) edges)
f E1  (e '  e) F (0)  i (e '  e)  MF (1)  (e '  M )(e  M ) F (2)
charge
magnetism
Phys 452
Magnetic Scattering
Synchrotron Radiation Tool
L3 –Fe
edge
(708 ev)
• Energy selectivity
Soft X rays (~ 1-2 nm)
Hard X rays (< 1A)
• Polarization
• Coherence
Pinhole
20 mm
X
Circular polarization
Magnetic
stripes
100 nm
Phys 452
Magnetic Scattering
specular
Below edge
770 eV
Co L3 edge
780 eV
Structural peaks
Magnetic peaks
Pinhole
20 mm
Chesnel et al.
Phys 452
Coherent Magnetic Scattering
Detector
Magnetic
film
Pinhole
X-ray beam
X-ray Energy
Tuned to resonant edge
(ex Co L3 edge)
Coherent
illumination
Resonant
Scattering
Magnetic Speckle pattern
 = 2.48 nm (500 eV); d= 2.5 µm
Phys 452
Quiz 30b
Which one of these processes does generally NOT occur?
A. Electron scattered by electrons
B. Photon scattered by electrons
C. Electron scattered by photons
D. Neutron scattered by neutrons
E. Photon scattered by phonons
Phys 452
Scattering
A classical geometrical view
Scattering
solid angle
d
Scattering angle
ds
b
Incident
cross-section
Differential cross-section
ds
D   
d
Impact parameter
Phys 452
Scattering
Scattering
solid angle
A classical geometrical view
Scattering angle
ds
b
Incident
cross-section
Impact parameter
To be determined in specific situations
b db
D   
sin  d
s tot   ds   D  d 
Example: Hard-sphere scattering
b  R cos  / 2
s tot  p R 2
Phys 452
Quiz 30c
The hard-sphere scattering model is isotropic
A. True
B. False
Phys 452
Scattering
Pb 11.1 Rutherford scattering
1. Conservation of energy
2. Conservation of angular momentum
3. Change of variable to express r(f)
4. Integration: to find fmax in terms of b etc
5 Relationship between fmax and 
6 Final relationship
b
b
q1q2
tan 1  / 2 
8p 0 E
q1

r
f
q2