1 Historical Developments and Future Perspectives …
25
1.4.1 Absorption
The cases of the SMS and SRMS resemble closely the “classical” Mössbauer spectroscopy (see e.g. [10] and as well in various chapters of this book). Set-up, experimental details as well as the data evaluation are the same as in classical Mössbauer
spectroscopy. The only difference is the source with its special properties such as
lineshape, 100% linear polarization, and 100% resonant quanta, which is discussed
in Sects. 1.3.1 and 1.6.1.3.
1.4.2 Dynamical Beats
For samples with a large effective thickness, t eff = n MB d σ 0 f LM , with n MB the
density of Mössbauer nuclei, d the geometrical thickness, σ 0 the resonant Mössbauer
cross section, and f LM the Lamb-Mössbauer factor, a speed-up effect is observed
and dynamical beats (Bessel beats) show up in the time spectra of NFS.
In Fig. 1.8 the situation is shown for Mössbauer and NFS spectra. For a thin
sample, t eff = 1, we have a single Lorentzian line in the Mössbauer spectrum, which
corresponds to an exponential decay in the NFS spectrum (Fig. 1.8a, b, dotted lines).
Increasing the effective thickness (t eff = 25) the Mössbauer line becomes much
wider and non-Lorentzian (Fig. 1.8a, solid line). In the NFS spectrum (Fig. 1.8b, solid
line) we observe two features: (1) a speed-up, showing up as an acceleration of the
initial decay rate accompanied by an increase in intensity at early times (from 10
7 to
10
9 units in the present example) and (2) a dynamical beat structure is superimposed
to the decay. From this beat structure the effective thickness and correspondingly
f LM can very precisely be determined.
1.4.3 Quantum Beats
As it is well known, hyperfine interactions might shift and split the nuclear levels.
This is described by the Hamiltonian H as:
H = H 0 + E 0 + M 1 + E 2 + . . .
(1.25)
with H 0 representing all terms, which do not include hyperfine interactions and cause
no shift or splitting, E 0 the Coulombic interactions, i.e., the electric monopole term
(isomer shift), M 1 the magnetic dipole and E 2 the electric quadrupole interaction. A
detailed discussion might be found in [10] and will be mentioned in more detail as well
in other chapters of this book. In the energy domain such as Mössbauer spectroscopy
several absorption lines reveal this splitting whereas in the time domain such as NFS
and SRPAC an interference pattern, the quantum beat structure, shows up.
25
1.4.1 Absorption
The cases of the SMS and SRMS resemble closely the “classical” Mössbauer spectroscopy (see e.g. [10] and as well in various chapters of this book). Set-up, experimental details as well as the data evaluation are the same as in classical Mössbauer
spectroscopy. The only difference is the source with its special properties such as
lineshape, 100% linear polarization, and 100% resonant quanta, which is discussed
in Sects. 1.3.1 and 1.6.1.3.
1.4.2 Dynamical Beats
For samples with a large effective thickness, t eff = n MB d σ 0 f LM , with n MB the
density of Mössbauer nuclei, d the geometrical thickness, σ 0 the resonant Mössbauer
cross section, and f LM the Lamb-Mössbauer factor, a speed-up effect is observed
and dynamical beats (Bessel beats) show up in the time spectra of NFS.
In Fig. 1.8 the situation is shown for Mössbauer and NFS spectra. For a thin
sample, t eff = 1, we have a single Lorentzian line in the Mössbauer spectrum, which
corresponds to an exponential decay in the NFS spectrum (Fig. 1.8a, b, dotted lines).
Increasing the effective thickness (t eff = 25) the Mössbauer line becomes much
wider and non-Lorentzian (Fig. 1.8a, solid line). In the NFS spectrum (Fig. 1.8b, solid
line) we observe two features: (1) a speed-up, showing up as an acceleration of the
initial decay rate accompanied by an increase in intensity at early times (from 10
7 to
10
9 units in the present example) and (2) a dynamical beat structure is superimposed
to the decay. From this beat structure the effective thickness and correspondingly
f LM can very precisely be determined.
1.4.3 Quantum Beats
As it is well known, hyperfine interactions might shift and split the nuclear levels.
This is described by the Hamiltonian H as:
H = H 0 + E 0 + M 1 + E 2 + . . .
(1.25)
with H 0 representing all terms, which do not include hyperfine interactions and cause
no shift or splitting, E 0 the Coulombic interactions, i.e., the electric monopole term
(isomer shift), M 1 the magnetic dipole and E 2 the electric quadrupole interaction. A
detailed discussion might be found in [10] and will be mentioned in more detail as well
in other chapters of this book. In the energy domain such as Mössbauer spectroscopy
several absorption lines reveal this splitting whereas in the time domain such as NFS
and SRPAC an interference pattern, the quantum beat structure, shows up.