Nuclear Forward Scattering


Coherence Aspects


The nuclear forward scattered intensity depends strongly
on the coherence of the scattered radiation.

  • For coherent superpositions
    the scattering
    amplitudes have to be averaged.
  • For incoherent superpositions
    the individual scattering
    intensities are averaged.

The reason to take for some cases coherent superpositions and for others incoherent superpositions into account is the different magnitude of the longitudinal and transversal coherence length for Nuclear Resonance Scattering on 57Fe.

The coherence length

is the distance between two points, where the radiation, coming from a source, still has a defined phase relation. Considering two points along the propagation axis the longitudinal coherence length has to be regarded and perpendicular to the propagation axis the transversal coherence length.

The longitudinal coherence length

is a function of the monochromaticity of the radiation
ll
µ
 l2

Dl
= l· æ
è
 DEg

Eg
ö
ø
-1
 
 
where Dl (DEg) is the FWHM of the distribution of the wavelength (energy) around l (Eg). For the iron resonance the longitudinal coherence length is more than 30 m.


This large longitudinal coherence length is for example
used to measure the isomer shift of one sample against an other:
    • In case of conventional MS the isomer shift leads to a shift of the lines, the reference sample is the radioactive source itself (with its sharp energy line).
    • In NFS the radiation from the source is broadly distributed in energy, therefore no energy shift between the target and the source can be detected. In order to measure an energy shift, one has to place a reference sample in the beam and measure it together with the sample under investigation. This can be far away from the sample of interest because of the large longitudinal coherence length. As reference samples one normally uses single line absorbers such as stainless steel.

The transversal coherence length

is, in contrast to the longitudinal coherence length, a function of experimental quantities like
    • source size,
    • detector acceptance,
    • illuminated target area and
    • the distances between
      the source, detector and target.
For typical NFS experiments at ID18
the dependence can be approximated by
lt
»
 l S

2p s
where S denotes the distance between detector and sample and s the detector acceptance. The transversal coherence length for typical conditions at ID18 (S » 1 m and s » 0.5 mm) was determined to be about 300 Å. This small transverse coherence length can be used to investigate e.g. spatial distributions in the target.

Based on the PhD thesis
of Alessandro Barla, Herdecke 2001
and Hanne Grünsteudel, Lübeck 1998

Last modified 11/06/02 06:29 PM by Ernst Schreier