Neutron Scattering

sample size of cm and a detection position uncertainty of some mm in the detectors l° . If
all timing uncertainties are lumped into At, a classical TOF instruments bas the following
resolution :
Ow -- ()WOt) 2 + (OW 0A)2 (10 .14)
From Eqns . 10 .2 - 10 .5 follows :
Ow (
2
~t3 Ot) 2 +
(m~~3 0A)2 (10 .15)
n
Because A' a 1/v' oc t and close to the elastic line (Y ~ A) it follows that Ow oc 1 /,\ 3 , i .e .
the most efficient measure to increase the "elastic" resolution is the use of a long neutron
wavelength/ For a matched setup the relative timing uncertainty Ot/t o and the relative
wavelength width 0A/A should be about equal .
Egn .10 .15 shows in addition that the
timing uncertainty term oc Ot dominates the resolution width for short time t, i .e . large
energy gain of the neutron .
If path uncertainties AL are treated separately, Ot represents
only the chopper opening and Eqn . 10 .15 reads :
( mnLOL)2 + (maL Ot)2 + ( 47 2 1i oa)2 (10 .16)
Ät~t 2
3 mn\3
For the inverted spectrometer the expressions stay the saine except for the exchange of A
and Y .
10.4 .1 Intensity
The available neutron sources are rather weak compared to sources of electromagnetic
radiation (laser,
synchrotron), they emit neutrons in form of a thermalized gas with a
broad distribution of velocities and into all directions . Preparation of collimated and
monochromatic beams is only possible by selection, i .e . removing all unwanted neutrons .
The resulting beams -even ai high flux reactors- contain only relatively few neutrons . 11
For this reason the available neutrons have to be utilized as efficient as possible .
Even
"For sample in form of thin plates the path uncertainty due to scattering position in the Sample may
be reduced for (only) one scattering angle (region) to the plate thickness .
"The typical neutron flux in front of the chopper of a classical TOP instrument is in the order of
10 °n/cm2 s, after chopping only 1O sn/cm2 s hit the sample and are available for scattering . In comparison
a beam of a small 1 mW HeNe laser is strictly collimated and monochromatic and represents an integral
flux of 3 x 10 15Photonen/s with a cross section of maybe lmm 2 , i .e . 3 x 10 17photons/cm 2s .
10-2 1