74
M. Seto et al.
Fig. 2.9 Photograph of the detection system for nuclear resonant inelastic scattering measurement
using an eight-element avalanche photodiode (APD) detector. The sample in a cryostat chamber
can be cooled with the closed cycle refrigerator
σ a (E) = f L M
dτ
2π
exp(−iEτ )
exp(M(k, τ )) − 1
,
(2.7)
where
M(k, τ ) =
d E exp(iEτ )S(E, k),
(2.8)
S(E, k) = E R g(E, κ)
n + 1
E
,
(2.9)
f L M = exp(−M(k, 0)),
(2.10)
E R =
(k)
2
2M
,
(2.11)
¯
n = (exp(E/k B T ) − 1)
−1
.
(2.12)
In the above expressions, M is the mass of the resonant nucleus and k B is the
Boltzmann constant. Using Fourier transformation of the cross section corresponding
to the measured spectrum, g(E, κ) can be obtained through M(k,τ) and S(E,k), as
shown in Eqs. (2.7) and (2.8). However, before performing these procedures, the
subtraction of the elastic peak and the deconvolution of the monochromator widths
are required. Since the perfect deconvolution is impossible for the real measured