Chemistry Reference
In-Depth Information
wrote down a set of simplified phenomenological equations for the time evolution
of the magnetization as follows. The static external magnetic field has components
H
x
=
2
H
1
cos
ωt
H
y
=
0
(30)
H
z
=
H
0
where, by convention, the constant field is taken to be in the
z
-direction with
strength
H
0
and the rf field in the
x
-direction with amplitude 2
H
1
and angular
frequency
ω
. The resultant angular momentum vector,
A
, of all the nuclei contained
in a unit volume satisfies the classical torque equation,
d
A
dt
=
T
(31)
where
T
represents the total torque acting upon the nuclei and can be expressed
as:
T
=
M
×
H
(32)
Here the vector
M
is the nuclear magnetization, that is, the resultant nuclear mag-
netic moment per unit volume. For each nucleus we have the relation,
μ
e
=
γ
e
J
e
=
γI
(33)
with
μ
and
J
e
representing the magnitude of the magnetic moment and the angular
momentum, respectively, where
γ
is the gyromagnetic ratio and
I
is nuclear spin.
This relation can be extended to the resultant quantities
M
and
A
, such that
M
=
γ
A
(34)
By combining Eqs. (31), (32), and (34), an expression for the variation of magne-
tization with time can be obtained
d
A
dt
=
T
M
γ
A
=
that is,
d
M
dt
=
γ
[
M
×
H
]
(35)
Bloch [10] further imposed a number of conditions in order to solve this equa-
tion. He asserted that
H
0
>> H
1
, and that both fields are positive and spatially
