Chemistry Reference
In-Depth Information
natural line width C is resonantly absorbed by the absorber nucleus to excite to the
first excited state apart 14.4 keV for
57
Fe from ground state that also has same
natural line width C. Spectrum obtained by the Mössbauer experiment as shown in
Fig.
1.1
consists of the c photon counts passing through the absorber as a function of
Doppler velocity v of the source. By the Doppler velocity v the photon energy E
0
is
changed by the first order Doppler effect DE
¼
c
E
0
. Finally Mössbauer spectrum
consists of c-ray count rate versus Doppler velocity v. Since source line shape is a
Lorentzian with width C and absorber line shape is also Lorentzian with width C, the
observed spectrum by transmission of the c-ray should have a Lorentzian with width
of 2C because of the convolution of source and absorber Lorentz functions. This is
an ideal case for the ideal source and very thin absorber. However, the real source
shows a little self-absorption of c photons and the absorber has a finite thickness
showing a thickness effect, although the resultant spectrum is very close to Lorentz
function [
17
,
18
].
A general expression for the fraction of zero phonon or recoilless process is
f
¼
exp
4p
2
x
2
k
2
¼
exp
j
2
x
2
;
ð
1
:
17
Þ
where k is the wavelength of the c-ray, j = 2p/k = E/hc, and x
2
is the com-
ponent of the mean square vibrational amplitude of the emitting nucleus in the
direction of the c-ray. In order to obtain a value of f close to unity, we require
j
2
x
2
1, which requires that the root mean square displacement of the nucleus
is small compared to the wavelength of the c-ray.
Emission of c-ray by the decay from excited state
ji
to ground state
ji
is
accompanied the conservation of energy and the angular momentum. Using the
quantities denoted in Fig.
1.4
, following conservation should be satisfied. For
energy conservation,
E
i
¼
E
f
þ
hx
Angular momentum and parity conservations give
L
j
e
þ
j
g
j
e
j
g
and L
6¼
0
ð
1
:
18
Þ
L and p
e
¼
p
g
p
;
jj¼
m
e
m
g
ð
1
:
19
Þ
Fig. 1.4 Initial and final
states of nuclear levels,
photon energy, their angular
momentums and parities
i
=
α
;
j
,
m
,
π
e
e
e
LM
,
,
π
f
=
β
;
j
,
m
,
π
g
g
g
