L L 2 = + 0 1 t v v Detector 1 0 THE VESUVIO SPECTOMETER - - PowerPoint PPT Presentation
Time of Flight Measurement Principle ( ) = 2 2 h 1 m v v L 0 0 1 2 ( ) = + 2 2 2 2 q m v v 2 v v cos 0 1 0 1 2 M q = L 1 y Moderator Sample q
L0 L1 Moderator Sample Detector Analyser Energy E1= ! mv1
2
Time of Flight Measurement Principle
1 1
v L v L t + =
( )
2 1 2 2 1
v v m − = ω h
( )
θ cos 2
1 2 1 2 2 2
v v v v m q − + = − = M q q M y 2
2
ω
THE VESUVIO SPECTOMETER
The Filter Difference Method
RESOLUTI ON COMPONENT ON VESUVI O
a Gaussian
a Gaussian and Lorentzian Au and U f oils
a 6. 7 eV, 20. 7 eV, 37 eV
a 0. 04 eV
a a 0. 11 eV
a a 0. 06 eV
DOUBLE DIFFERENCE TECHNIQUE Gold Foil U Foil
1-e-Ntσ=Nt σ as σ→ 0
Double Differenced and Single Differenced Pb Data taken with Au Foil
p r
q p r r +
M p
i
2 /
2
= κ
M q p
f
2 / ) (
2
r r + = κ
M p M q p 2 2 ) (
2 2
− + = r r ω
− = = M q q M q p y 2 ˆ .
2
ω r r
Energy transfer Momentum along q
ˆ
Momentum transfer
Impulse Approximation
Kinetic Energy of 4He Potential Energy of 4He
Quantum Correlations in H2O/D2O Mixtures
A Driesmann, et al PRL 79 2839 (1997)
∫
− = p d q p y p n y q J r r r r ) . ( ) ( ) , ˆ ( δ
) , ˆ ( ) , ( y q J q M q S = ω r
− = M q q M y 2
2
ω
Dynamic Structure Factor Radon Transform Longitudinal momentum component
∫
− = p d q p y p n y q J r r r r ) . ( ) ( ) , ˆ ( δ y
2
Reconstruction of Momentum Distribution from Neutron Compton Profile
∑
+
− =
m l n m l l n m l n
q Y y H a y y q J
, , , 2 , , 2
) ˆ ( ) ( ) exp( ) , ˆ ( π
) ˆ ( ) ( ) 1 ( ! 2 exp( ) (
2 2 / 1 , , , , 2 2 / 3 2
p Y p L p a n p p n
lm l n l m l n n m l n l n + +
− − =
∑
π r
Spherical Harmonic Hermite polynomial Laguerre polynomial
an,l,m is Fitting coefficient