Nuclear Forward Scattering


Kinematical Approximation / Thin scatterer

Let us first consider elastic forward scattering of a g-ray by

one bound nucleus with only one transition line.

The amplitudes and phases of the relevant spectral components of incident E i(w) and scattered Es(w) radiation are related

Es(w) = Ei(w) ·a(w)  .
via the complex scattering amplitude
a0(w) = |a0(w)| ·eif(w) .
which can be expressed in terms of
  • the modulus |a0(w)| and
  • the phase shift F(w)

of the scattered radiation component
obtained in forward scattering


The kinetics i.e. the time response or response function a0(t) of an individual nucleus to a d-like excitation (the synchrotron radiation pulse) is given by the Fourier transformation:
a0(t)
=
 1

2p
¥
ó
õ
-¥ 
a(w) eiwt dw
=
- i  1

8p
   1

t0
   s0   · fLM · exp é
ë
iw0t -  t

2t0
ù
û
of the elastic forward scattering amplitude a0(w) [Hyp.Int.97/98(1996)551]
a0(w)
=
-  k

8p
·s0·  G0/(h/2p)

w-w0 - iG0/2(h/2p)
· fLM
(8)
with w0 the frequency of a resonance
s0 the maximum resonance cross section (5)
t0=(h/2p)/G0 the mean life time of the nuclear state
fLM the Lamb-Mössbauer factor of the target

In general the time response of the whole system is a convolution of the incident wave packet and the response function of the scatterer.


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

Last modified 28/03/02 10:20 AM by Ernst Schreier