Interaction with External Fields
199
magnetic field produced by the electromagnet is gradually increased. As the
value of B passes through the critical value satisfying Eq. (6.96), an intense
absorption is observed. Since the experiments are done mostly for crystalline
or liquid paramagnetic substances in which the energy levels of the atoms are
perturbed by the internal fields, the resonance relation in Eq. (6.96) varies slightly
from atom to atom. As a result, the absorption curve for the intensity of the
transmitted radiation, as a function of B, has a finite width.
The nucleus of an atom has a magnetic moment given in Eq. (4.65),
µ N = N
p
e
g m
I
(6.99)
which is about 1000 times smaller than the magnetic moment of the electrons.
Under the influence of the external field, the nuclear level splits into (2I + 1)
Zeeman levels and resonance absorption is observed for the frequency ω,
ω =
N
p
e g B
m
(6.100)
For B = 10
4
G, this corresponds to a frequency of about 10
8
rad/s which is in
the radio-frequency range. Nuclear magnetic resonance is especially useful for
the study of atoms and molecules which may have zero electronic magnetic
dipole moment. These atoms generally have a nonzero nuclear magnetic moment
and can be studied by the nuclear magnetic resonance techniques.
The epr and nmr techniques can be used for identifying the presence of
certain elements, for determining the environment of the electron or the nucleus
(by noting the shift in the resonance frequency due to the environment), and
also for accurate measurement of magnetic fields.
Atomic and Molecular Beam Experiments
While magnetic resonance experiments are almost universal in their applications,
their accuracy is limited by the fact that they are based on the differential
population of nearby levels at thermal equilibrium and on the measurements of
changes in the radiation intensity. If the material is available in the form of
atomic or molecular beams, more accurate beam experiments can be performed.
Atomic and molecular-beam experiments are refinements of the SternGerlach experiment (Sec. 4.2) due to Rabi, incorporating the observation of
magnetic resonance. For simplicity, consider a beam of particles with the nuclear
angular momentum characterized by I = 1/2 and an associated magnetic moment.
In a typical set-up, the beam traverses three regions with magnetic fields B 1 , B 2
and B 3 produced by magnets 1, 2 and 3 respectively (see Fig. 6.7). The first
field B 1 is inhomogeneous with the gradient as shown, and splits the beam into
two components with M I = ± 1/2 one of which, say with M I = – 1/2 is eliminated
199
magnetic field produced by the electromagnet is gradually increased. As the
value of B passes through the critical value satisfying Eq. (6.96), an intense
absorption is observed. Since the experiments are done mostly for crystalline
or liquid paramagnetic substances in which the energy levels of the atoms are
perturbed by the internal fields, the resonance relation in Eq. (6.96) varies slightly
from atom to atom. As a result, the absorption curve for the intensity of the
transmitted radiation, as a function of B, has a finite width.
The nucleus of an atom has a magnetic moment given in Eq. (4.65),
µ N = N
p
e
g m
I
(6.99)
which is about 1000 times smaller than the magnetic moment of the electrons.
Under the influence of the external field, the nuclear level splits into (2I + 1)
Zeeman levels and resonance absorption is observed for the frequency ω,
ω =
N
p
e g B
m
(6.100)
For B = 10
4
G, this corresponds to a frequency of about 10
8
rad/s which is in
the radio-frequency range. Nuclear magnetic resonance is especially useful for
the study of atoms and molecules which may have zero electronic magnetic
dipole moment. These atoms generally have a nonzero nuclear magnetic moment
and can be studied by the nuclear magnetic resonance techniques.
The epr and nmr techniques can be used for identifying the presence of
certain elements, for determining the environment of the electron or the nucleus
(by noting the shift in the resonance frequency due to the environment), and
also for accurate measurement of magnetic fields.
Atomic and Molecular Beam Experiments
While magnetic resonance experiments are almost universal in their applications,
their accuracy is limited by the fact that they are based on the differential
population of nearby levels at thermal equilibrium and on the measurements of
changes in the radiation intensity. If the material is available in the form of
atomic or molecular beams, more accurate beam experiments can be performed.
Atomic and molecular-beam experiments are refinements of the SternGerlach experiment (Sec. 4.2) due to Rabi, incorporating the observation of
magnetic resonance. For simplicity, consider a beam of particles with the nuclear
angular momentum characterized by I = 1/2 and an associated magnetic moment.
In a typical set-up, the beam traverses three regions with magnetic fields B 1 , B 2
and B 3 produced by magnets 1, 2 and 3 respectively (see Fig. 6.7). The first
field B 1 is inhomogeneous with the gradient as shown, and splits the beam into
two components with M I = ± 1/2 one of which, say with M I = – 1/2 is eliminated