28
R. Rüffer and A. I. Chumakov
the two m = + 1 and the two m = − 1 transitions interfere independently giving
now rise to left and right hand circular polarization (Fig. 1.9c). Finally, for H E all
m = ± 1 transitions interfere giving rise to a more complicated spectrum which
is sigma polarized (Fig. 1.9b). The slow overall modulation is caused by dynamical
beats due to the finite effective thickness. In case of the SMS the two cases with
m = ± 1 transitions are indistinguishable in a simple absorption experiment and
the resulting spectra resemble four-line absorption spectra (Fig. 1.9 lower right).
1.5 Structural Dynamics
Structural dynamics is accessible via quasi-elastic scattering techniques in the energy
domain by RSMR or directly in the time domain by TDI and NFS/SRPAC measuring
translational and rotational dynamics and via inelastic scattering techniques, NIS and
IXSNRA, in the energy domain giving access to the phonon density of states.
1.5.1 Quasi-elastic Dynamics
Nuclear quasi-elastic scattering measures structural dynamics on a ps to μs time
scale. The coherent and the incoherent channel can be utilized. In the first case, the
coherent channel, the Lamb-Mössbauer factor has to be greater than zero (f LM > 0).
The set-up is the same as in NFS (see Fig. 1.7). The incoming x-ray pulse creates a
coherent collective nuclear state which decays in the static case in forward direction.
Dynamics, e.g. the jump of a Mössbauer nucleus from one atomic site to another
(in space and angle, see e.g. [88]), destroys this state. As a consequence no x-ray
is scattered in forward direction, i.e., the measured intensity in the NFS detector is
decreased at later times. We will get an ‘accelerated decay’ or a ‘damping’ of the
NFS intensity I N F S (t), which might be described in a simplified picture by:
I (t) ∝ I NFS (t) e
−2λ t t e
−λ r t
.
(1.28)
The first exponential is related to the van Hove self-intermediate function [89] with λ t
being the translational relaxation rate and the second one to the rotational correlation
function with λ r being the rotational relaxation rate.
In the second case, the incoherent channel, the scattering is independent of the
Lamb-Mössbauer factor. The set-up is the same as in SRPAC (see Fig. 1.7). The
incoming x-ray pulse selectively excites a single nucleus, which decays in the static
case with an angular distribution according to the anisotropy parameter, A 22 . Dynamics, e.g. rotational motion monitored by the electric hyperfine interaction Ω,
changes this distribution and gives rise to a damping of the intensity signal.
The perturbation factor G 22 in the scattering intensity I S R P AC (see Eq. 1.24)
reduces in the slow approximation to
R. Rüffer and A. I. Chumakov
the two m = + 1 and the two m = − 1 transitions interfere independently giving
now rise to left and right hand circular polarization (Fig. 1.9c). Finally, for H E all
m = ± 1 transitions interfere giving rise to a more complicated spectrum which
is sigma polarized (Fig. 1.9b). The slow overall modulation is caused by dynamical
beats due to the finite effective thickness. In case of the SMS the two cases with
m = ± 1 transitions are indistinguishable in a simple absorption experiment and
the resulting spectra resemble four-line absorption spectra (Fig. 1.9 lower right).
1.5 Structural Dynamics
Structural dynamics is accessible via quasi-elastic scattering techniques in the energy
domain by RSMR or directly in the time domain by TDI and NFS/SRPAC measuring
translational and rotational dynamics and via inelastic scattering techniques, NIS and
IXSNRA, in the energy domain giving access to the phonon density of states.
1.5.1 Quasi-elastic Dynamics
Nuclear quasi-elastic scattering measures structural dynamics on a ps to μs time
scale. The coherent and the incoherent channel can be utilized. In the first case, the
coherent channel, the Lamb-Mössbauer factor has to be greater than zero (f LM > 0).
The set-up is the same as in NFS (see Fig. 1.7). The incoming x-ray pulse creates a
coherent collective nuclear state which decays in the static case in forward direction.
Dynamics, e.g. the jump of a Mössbauer nucleus from one atomic site to another
(in space and angle, see e.g. [88]), destroys this state. As a consequence no x-ray
is scattered in forward direction, i.e., the measured intensity in the NFS detector is
decreased at later times. We will get an ‘accelerated decay’ or a ‘damping’ of the
NFS intensity I N F S (t), which might be described in a simplified picture by:
I (t) ∝ I NFS (t) e
−2λ t t e
−λ r t
.
(1.28)
The first exponential is related to the van Hove self-intermediate function [89] with λ t
being the translational relaxation rate and the second one to the rotational correlation
function with λ r being the rotational relaxation rate.
In the second case, the incoherent channel, the scattering is independent of the
Lamb-Mössbauer factor. The set-up is the same as in SRPAC (see Fig. 1.7). The
incoming x-ray pulse selectively excites a single nucleus, which decays in the static
case with an angular distribution according to the anisotropy parameter, A 22 . Dynamics, e.g. rotational motion monitored by the electric hyperfine interaction Ω,
changes this distribution and gives rise to a damping of the intensity signal.
The perturbation factor G 22 in the scattering intensity I S R P AC (see Eq. 1.24)
reduces in the slow approximation to