Neutron Spin Echo Spectroscopy (NSE)

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Neutron Spin Echo Spectroscopy(NSE)
Dobrin P. Bossev, Steven Kline, Nicholas Rosov
NCNR, NIST Gaithersburg, MD 20899
E-mail dbossev_at_nist.gov Internet http//www.nc
nr.nist.gov/
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Why precession?

• Goal ?E 10-5 10-2 meV (very small !!!)
• We need low energy neutrons. Cold neutrons ?
  5 12 Å, E 0.5 3.3 meV
• The problem neutron beam wavelength spread
  ??/? 5 20,
• ?E/E 10 40, ?E 0.05 0.2 meV
• ?E 0.05 0.2 meV gtgt ?E 10-5 10-2 meV
• In fact, to measure neutron energy
• we need to measure the neutron velocity
• E mV2/2 ? V l/t ? t?
• The solution We need neutron precession in
  magnetic field. We are going to attach internal
  clock for each neutron. Thus, we can observe very
  small velocity changes of a neutron beam,
  regardless of the velocity spread

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Neutrons in magnetic fields Precession
Mass, mn 1.675?10-27 kg Spin, S 1/2 in units
of h/(2?) Nuclear g number, gn ?n/?N
-1.9130 where (?N 5.0508?10-27
J/T) Gyromagnetic ratio g ?n/S?h/(2?)
1.832?108 s-1T-1 (29.164 MHz T-1)
B
?L
The neutron will experience a torque from a
magnetic field B perpendicular to its spin
direction. Precession with the Larmor
frequency ?L gB The precession rate is
predetermined by the strength of the field only.
S
N
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Spin flippers
?/2 flipper
Precession
? flipper
?L
B
S
n
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NSE Spectrometer schematic
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Monochromatic beam
elastic scattering inelastic
scattering
?/2 flipper
?/2 flipper
sample
B
B
S
Analyzer measures cos( ??)
of cycles
2N?? 2N??
-(2N??) -(2N??)??
0 ??
0
2N??
J field integral At NCNR Jmax 0.5 T.m N
(?8Å) 3?105
!
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Polychromatic beam
?/2 flipper
?/2 flipper
sample
B
B
?lt?0
?0
S
f(?)
?gt?0
The analyzer projects out the spin component
parallel to the beam, cos(??(?))
Energy change
Neglect 2nd order terms for small asymmetries or
quasielastic scattering.
Asymmetry between coil field integrals
Neglected
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Intensity at the detector
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How to deal with the resolution?
In the time domain the deconvolution is simply a
division.
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Measuring I(Q,t)
The difference between the flipper ON and
flipper OFF data gives I(Q,0) The echo is fit
to a gaussian-damped cosine.
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Experimental system
AOT
Surfactant molecule
Hydrophilic head
Hydrophobic tail
Experiment I Diffusion of AOT micelles in
C10D22 (5.4 vol. fraction)
Experiment II Shape fluctuations
in AOT/D2O/C10D22 microemulsion (5.4/4.6/90
vol. fraction)
Inverse microemulsion droplet
Inverse spherical micelle
Shape fluctuations
D2O
25 AOT
Translational diffusion
AOT
C10D22
C10D22
Translational diffusion
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Data analysis
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Summary of data analysis
?2 the damping frequency frequency of
deformation lta2gt mean square displacement of
the 2-nd harmonic amplitude of deformation p2
size polydispersity, measurable by SANS or DLS