An Introduction to Neutron Scattering - Spallation Neutron Source
An Introduction to Neutron Scattering - Spallation Neutron Source
An Introduction to Neutron Scattering - Spallation Neutron Source
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For Quasi-elastic <strong>Scattering</strong>, the Echo<br />
Polarization depends on Energy Transfer<br />
• If the neutron changes energy when it scatters, the precession<br />
phases before & after scattering, φ 1 & φ 2, will be different:<br />
1 2 2<br />
using hω<br />
= m(<br />
v1<br />
− v2<br />
) ≈ mvδv<br />
2<br />
2 3<br />
⎛ 1 1 ⎞ γBd<br />
γBdhω<br />
γBdm<br />
λ ω<br />
φ1<br />
−φ<br />
2 = γBd<br />
⎜ − ≈ δv<br />
≈ =<br />
2<br />
3<br />
2<br />
v1<br />
v ⎟<br />
⎝ 2 ⎠ v mv 2πh<br />
• To lowest order, the difference between φ 1 & φ 2 depends only<br />
on ω (I.e. v 1 – v 2) & not on v 1 & v 2 separately<br />
• The measured polarization, , is the average of cos(φ 1 - φ 2)<br />
over all transmitted neutrons I.e.<br />
P<br />
=<br />
∫∫<br />
I<br />
r<br />
λ)<br />
S(<br />
Q,<br />
ω)<br />
cos( φ1<br />
−φ<br />
) dλdω<br />
r<br />
I(<br />
λ)<br />
S(<br />
Q,<br />
ω)<br />
dλdω<br />
( 2<br />
∫∫
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