from a surface S defines the current passing through. The oriented element of S is
indicated by ds. If S is closed, I
B vanishes, which constitutes the integral form of
the continuity equation
r Á J
B
¼ 0:
7.2.2 Current Density Tensor and Current Susceptibility
Vector
The current density second-rank tensor [3, 15, 71, 75] associated with the
magnetic-field induced current density J
B
a is a function of position defined all over
the molecular domain by the derivative
J
B b
a ðrÞ ¼
@J
B
a ðrÞ
@B b
:
ð7:45Þ
An analogous definition has been proposed for the current density J
m I
a induced
by a nuclear magnetic dipole [16, 51, 52, 62, 63]
J
m I b
a ¼
@J
m I
a
@m I b
:
ð7:46Þ
The diamagnetic and paramagnetic contributions to J
B b
a , Eq. (7.45), are obtained
from Eqs. (7.8) and (7.10), respectively,
J
B b
da ðrÞ ¼ À
e
2
2m e
abc r c c
ð0Þ
ðrÞ;
ð7:47Þ
J
B b
pa ðrÞ ¼ À
ne
m e
Z
dx 2 . . .dx n
 W
B b Ã
a ðr; x 2 ; . . .x n Þ^ p a W
ð0Þ
a ðr; x 2 ; . . .x n Þ
h
þ W
ð0ÞÃ
a ðr; x 2 . . .x n Þ^ p a W
B b
a ðr; x 2 ; . . .x n Þ
i
:
ð7:48Þ
The contributions to J
m I b
a , Eq. (7.46), obtained from current density terms
corresponding to a given Ramsey mechanism, e.g., the diamagnetic and paramagnetic contributions from the nuclear spin/electron orbit terms, Eqs. (7.12) and
(7.14), are, respectively,
162
P. Lazzeretti