Chemistry Reference
In-Depth Information
57
Co
Fig. 1.5
Decay of
57
Co
57
270 d
to
Fe
Electron Capture
−
5
2
136.3
8.9 ns
−
3
2
14.4
98 ns
14.4 keV
γ
-ray
−
1
2
57
Fe
where suffixes e and g denote the excited state and ground state, respectively. It is
known that any 2
L
pole multipole radiation field carries angular momentum L and
z-component of angular momentum M. The parity p of a multipole field is (-1)
L
or (-1)
L-1
for EL or ML radiation, respectively [
16
].
For the
57
Fe Mössbauer level whose parent nucleus is
57
Co, the decay scheme is
shown in Fig.
1.5
. Spin and parity of the first excited state are 3/2 and -. For the
ground state, spin and parity are 1/2 and -. Because of no parity change the
multipole radiation field of the c-ray emission decaying from excited state to
ground state is M1 and E2 radiation. Higher order multipolarity is less expected
and known as negligible small like 0.0006 % for the 14.4 keV c radiation from the
first excited state of
57
Fe [
17
]. For c-ray, the distribution function F
L
ð
h
Þ
can be
found by calculating the energy flow (Poynting vector) as a function of h for
multipole radiation characterized by the quantum numbers L and M. For dipole
radiation, one obtains
F
1
ð
h
Þ¼
3 sin
2
h
;
F
1
1
ð
1
:
20
Þ
ð
h
Þ¼
3
2
ð
1
þ
cos
2
h
Þ:
Usually
57
Co source for the
57
Fe Mössbauer experiment is doped into the metal
like Rh matrix and distributed uniformly without self-absorption showing a rather
sharp single Lorentzian energy distribution. Absorber is a specimen to study by the
Mössbauer effect and has a finite thickness containing multiple phases of resonant
nuclei
57
Fe. As shown in Fig.
1.4
, the c transition of nucleus from excited state to
ground state or vice versa shows the radiation field depending on the quantum
numbers of L, M, j
e
,m
e
,j
g
and m
g
. That is, the transition probability between
nuclear levels depends on Dm = m
e
-m
g
and the angular h dependence of the
emitting or absorbing radiation depends on the L and M given by (
1.20
).
