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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“Tilted” Fields for Diffraction: SANS<br />
d<br />
B<br />
χ<br />
χ<br />
B<br />
θ<br />
π/2 π<br />
π/2<br />
• <strong>An</strong>y unscattered neutron (θ=0) experiences the same precession angles<br />
(φ 1 and φ 2) before and after scattering, whatever its angle of incidence<br />
• Precession angles are different for scattered neutrons<br />
KBd<br />
φ1<br />
= and<br />
k sin χ<br />
P<br />
=<br />
∫<br />
φ 1<br />
φ<br />
2<br />
k sin( χ + θ )<br />
⎡ KBd cos χ ⎤<br />
dQ.<br />
S(<br />
Q).<br />
cos⎢<br />
Q<br />
2 2 ⎥<br />
⎢⎣<br />
k sin χ ⎥⎦<br />
=<br />
KBd<br />
Spin Echo Length,<br />
φ 2<br />
⎡ KBd cos χ ⎤<br />
⇒ cos( φ1<br />
−φ<br />
2)<br />
≈ cos⎢<br />
θ<br />
2 ⎥<br />
⎢⎣<br />
k sin χ ⎥⎦<br />
Polarization proportional <strong>to</strong><br />
Fourier Transform of S(Q)<br />
r =<br />
KBd cos χ /( k sin χ)<br />
2
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