Chemistry Reference
In-Depth Information
1.2 Application to the Material Research
Previous discussion on the nuclear levels is for the point nucleus or for the bare
nucleus. But the nucleus has a finite charge radius and surrounded by the atomic
electron clouds. The interaction with the electron clouds leads the shift and/or split
of the nuclear levels, which is called as the hyperfine interactions. When the
nucleus has a magnetic dipole moment, the magnetic interactions with the
magnetic field due to the atom's own electrons lifts all of their (2j ? 1)-fold
degeneracy of the nuclear levels which is called as the nuclear Zeeman effect.
Coulomb interactions between electron charge clouds and the proton charge dis-
tribution within the nucleus make a shift and/or split of the nuclear levels. From
the observation of these shift and split, it is possible to determine the electronic
states of the Mössbauer active atom, using nuclear parameters like a charge radius
and electromagnetic moments of the nucleus.
Soon after its discovery the application of the Mössbauer effect has been made
by the fact that the energy of electromagnetic radiation can be measured with very
great precision. Using this characteristic feature, study on gravitational red shift
has been performed [ 21 ], but details concerning this type of the experiment are not
described here. Atomic motion and lattice vibration of solid are also important
research subjects using Mössbauer effect. However, the Mössbauer effect is fun-
damentally concerned only with processes in which the quantum state of the lattice
remains unchanged. The information concerning the motion of the lattice atoms is
less obtained in an experiment where only recoilless c-rays are observed.
A development of synchrotron radiation facility made possible to perform the
nuclear resonant scattering with synchrotron radiation. Elastic scattering is iden-
tical, in principle, to the Mössbauer resonance by c photons from radioactive
nuclei. From the inelastic scattering one can observe the scattering involved
phonon
annihilation
and
creation
in
solid.
Nuclear
resonant
scattering
with
synchrotron radiation will briefly described in final part of this chapter.
1.2.1 Hyperfine Interactions
Coulomb interactions between electron charge clouds and the proton charge dis-
tribution within the nucleus is given by
E el ¼ ZZ q e ð r e Þ q N ð r N Þ
r e r N
dr e dr N ;
j
j
and
j ¼ 4p X
X
1
k
r k \
r k þ 1
[
1
r e r N
1
2k þ 1
Y km ð _ e Þ Y km ð _ N Þ:
ð 1 : 24 Þ
j
k ¼ 0
m ¼ k
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