66
M. Seto et al.
Fig. 2.5 151 Eu SR-based Mössbauer spectra of Eu metal under high hydrogen pressure. The energy
reference substance was EuF 3 as the scatterer. Rectangles represent experimental data, and lines
represent fitting curves by Lorentzian shape. The upper panel shows the Eu 2+ valence under 2.3
GPa hydrogen, and the lower panel shows Eu 3+ valence under 14.3 GPa hydrogen (reproduced from
Matusoka et al. (2011) [25])
expression on these characteristics [26]. For simplicity, we assume the following
conditions: (1) the transmitter is a sample under study and includes only one chemical compound with one site and (2) the scatterer is an energy reference substance
and connected to the velocity transducer, as shown in Fig. 2.3. Our aim here is to
express the detected intensity as a function of the velocity of the scatterer. First,
the propagating coherent field amplitude of the transmitter E t as a function of the
dimensionless frequency of w, that is, in the unit of natural linewidth, is considered.
It corresponds to the absorption by electrons and nuclei in the transmitter and is
expressed as follows:
E t (w) = E 0t exp
−
μ et z t
2
exp
−i
m
α tm
μ nt z t
2(2(w − w tm ) + i)
.
(2.1)
Here, the amplitude of the radiation field at the entrance of the transmitter is
denoted as E 0t . The electronic absorption coefficient of the transmitter is denoted
as μ et . The thickness of the transmitter is denoted as z t . The linear absorption coefficient of radiation by the nuclei at resonance in the transmitter is denoted as μ nt .
The index for a nuclear transition is denoted as m. The probability and the nuclear
resonant energy of the mth transition at the transmitter are denoted as α tm and w tm ,
respectively. The hyperfine structure of the transmitter, which is described by isomer
shift, quadrupole splitting, and magnetic hyperfine field, is expressed as w tm . The
purpose of Mössbauer spectroscopy is to evaluate them. Here, μ nt z t corresponds to
Mössbauer effective thickness T t . Next, the propagating coherent field amplitude of
the scatterer E s as a function w is considered. It also corresponds to the absorption
by electrons and nuclei in the scatterer and is expressed as follows:
M. Seto et al.
Fig. 2.5 151 Eu SR-based Mössbauer spectra of Eu metal under high hydrogen pressure. The energy
reference substance was EuF 3 as the scatterer. Rectangles represent experimental data, and lines
represent fitting curves by Lorentzian shape. The upper panel shows the Eu 2+ valence under 2.3
GPa hydrogen, and the lower panel shows Eu 3+ valence under 14.3 GPa hydrogen (reproduced from
Matusoka et al. (2011) [25])
expression on these characteristics [26]. For simplicity, we assume the following
conditions: (1) the transmitter is a sample under study and includes only one chemical compound with one site and (2) the scatterer is an energy reference substance
and connected to the velocity transducer, as shown in Fig. 2.3. Our aim here is to
express the detected intensity as a function of the velocity of the scatterer. First,
the propagating coherent field amplitude of the transmitter E t as a function of the
dimensionless frequency of w, that is, in the unit of natural linewidth, is considered.
It corresponds to the absorption by electrons and nuclei in the transmitter and is
expressed as follows:
E t (w) = E 0t exp
−
μ et z t
2
exp
−i
m
α tm
μ nt z t
2(2(w − w tm ) + i)
.
(2.1)
Here, the amplitude of the radiation field at the entrance of the transmitter is
denoted as E 0t . The electronic absorption coefficient of the transmitter is denoted
as μ et . The thickness of the transmitter is denoted as z t . The linear absorption coefficient of radiation by the nuclei at resonance in the transmitter is denoted as μ nt .
The index for a nuclear transition is denoted as m. The probability and the nuclear
resonant energy of the mth transition at the transmitter are denoted as α tm and w tm ,
respectively. The hyperfine structure of the transmitter, which is described by isomer
shift, quadrupole splitting, and magnetic hyperfine field, is expressed as w tm . The
purpose of Mössbauer spectroscopy is to evaluate them. Here, μ nt z t corresponds to
Mössbauer effective thickness T t . Next, the propagating coherent field amplitude of
the scatterer E s as a function w is considered. It also corresponds to the absorption
by electrons and nuclei in the scatterer and is expressed as follows: