lecture 7 slides - mit opencourseware · lecture 7 slides author: cappellaro, paola created date:...
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Neutron Interferometry
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NIST Center for Neutron ResearchHome to a 20 MW reactor that provides neutrons for scien>fic researchDozens of instruments (most for Solid State applica>ons)Some instruments for the study of Fundamental Physics
Public domain image
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The Neutron Interferometer and Optics Facility
Isolated 40,000 Kg room is supported by six airspringsActive Vibration Control eliminates vibrations less than 10Hz Temperature Controlled to +/- 5 mK
Public domain image
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Inside the NCNRReactor Core
LH2
7 Neutron Guides
NIOF
Fuel Elements
Guide Hall
Public domain images4
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Wavepacket
p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 p x
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 k
Neutron coming out of the reactor is a wavepacket:Sum of many plane waves with different wavenumber k[not a stationary state: evolves (moves!) in time]
Fourier Transform Pair
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Monochromator
Monochromator selects a small range of momenta���������� ���� ������������������������������������������������������ ��������� �
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Wavepacket
p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 p x
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 k
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3-blade interferometer from single Si crystal
Neutron Interferometer
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5-blade interferometer from single Si crystal
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Wavepacket ➙ Plane wave
p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 p x
Wavepacket ∆x ≫ Interferometer ➞ consider ∆x =∞
or neutron = plane wave |ki = '
k
(x) =1p2⇡
e
ikx
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Momentum eigenfunctions
We can analyze the neutron interferometer looking only at the momentum eigenfunctions:STATIONARY SOLUTION (no time evolution)
|ki|ki
|-ki
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The neutron is a plain wave with k>0. The first blade is a beam splitter (50/50% probability of going up or down)
Interference(Calculations: 1)
| (0)i = |ki
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After the first blade, the state is a superposition.
Interference(Calculations: 2)
| 1i =1p2(|ki+ |-ki)
t1
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The second blade is a mirror, exchanging neutrons with positive and negative k
Interference(Calculations: 3)
| 2i =1p2(|-ki+ |ki)
t2
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Neutrons in the upper path (with negative momentum) go through the phase flag (an object)
Interference(Calculations: 4)
| 3i =1p2(ei' |-ki+ |ki)
t3
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The third blade recombines the beams and allows them to interfere.
' | i = cos' |ki+ sin' |-ki
Interference(Calculations: 5)
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The detector measure the neutron flux intensity (number of neutrons per unit time).
Interference
Detector
'
P (+k) = cos
2(')
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Interference
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Flux of particles
• Plane wave wavefunction is not properly normalized
• It is difficult to interpret as as the probability of finding a particle at position x.
• Interpret as a flux of particles
set
(x) = Ae
ikx
| (x)|2
v| (x)|2 = I
A =
rmI
~k 19
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Scatteringof Waves and Particles
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Transmission
Energy > Potential Step
H
E=T+V ➜ mv02/2 > mgH
Region I Region II21
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Transmission
Energy > Potential Step
H
E=T+V ➜ mv02/2 > mgH
Region I Region II22
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Reflection
Energy < Potential Step
H
E=T+V ➜ mv02/2 < mgH
Region I Region II23
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Reflection
Energy < Potential Step
H
E=T+V ➜ mv02/2 < mgH
Region I Region II24
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Reflection/Transmission
Incoming wave
Reflected wave Transmitted wave
eikx
e�ikx eikx
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Reflection/Transmission
Incoming wave
Reflected wave Transmitted wave
eikx
e�ikx eikx
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MIT OpenCourseWarehttp://ocw.mit.edu
22.02 Introduction to Applied Nuclear PhysicsSpring 2012 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
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MIT OpenCourseWarehttp://ocw.mit.edu
22.02 Introduction to Applied Nuclear PhysicsSpring 2012 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.