- S,l sin p
s, = S,! S, =
$ 1
sin p
+ S,t cos p
where we have assumed axial symmetry. The angle y is then arbitrary and we have set it equal to 0”. The expressions for I,, I,, and I, may be obtained by replacing the S’s by Z’s, and p by p’. The spin Hamiltonian then becomes
x
+ (gll cos e sin p + g , sin e cos p)S,J} +
= p H o { ( g l cos l
e cos p
- g, sin e sin p)s,!
( D / 2 ) { [ S z t 2- l/&S
S,)(S+/
+ 4
(35) M. E. Rose, “Elementary Theory of Angular Momentum,” Wiley, New York, N . Y . , 1957, p 65.
+ l)] x
+
p’ -
A , sin p’ cos p’)[(S+t
+ S-t)I,t]
by making the usual substitution of raising and lowering operators for x and y operators. One additional constraint we have applied is that the coefficient of the term in S,tZ,t should be zero, as previously mentioned. This condition leads t o a relationship between p and p‘, namely A tan p‘ = B tan p, but no general expression is available to relate 0 to p or 0’. The spin Hamiltonian derived in this way is almost of the same form as that found when D
