sequence is due to the scalar coupling interaction only. The initial 90x
pulse generates the Iy operator from the equilibrium operator Iz
(the similarSspin term is omitted for clarity). The coupling develops
duringt,
Iy )
2 JISIzSzt
IycosðJIStÞþ 2 IxSzsinðJIStÞ: ½ 2 : 275 The 180 8 pulse, regarded as a 180 8 pulse on one spin followed by a 180 8
pulse on the other spin, yields
IycosðJIStÞþ 2 IxSzsinðJIStÞ!
Ix
IycosðJIStÞþ 2 IxSzsinðJIStÞ
!
Sx
IycosðJIStÞ 2 IxSzsinðJIStÞ:
½ 2 : 276 The 180xpulse applied to theIspin does not affect theSspin and
vice versa. Evolution during the second delay,t, yields
IycosðJIStÞ 2 IxSzsinðJIStÞ
)
2 JISIzSzt
Iycos^2 ðJIStÞ 2 IxSzsinðJIStÞcosðJIStÞ
2 IxSzcosðJIStÞsinðJIStÞIysin^2 ðJIStÞ, ½ 2 : 277 which, using the identities cos(2)¼cos^2 – sin^2 and sin(2)¼
2 sincos, reduces to
IycosðJIStÞ 2 IxSzsinðJIStÞ
)
2 JISIzSzt
Iycosð 2 JIStÞ 2 IxSzsinð 2 JIStÞ:½ 2 : 278 The overall effect of the –t– 180x–t– pulse sequence on the initialIy
magnetization is given by
Iy )
tðÞIxþSx t
Iycosð 2 JIStÞ 2 IxSzsinð 2 JIStÞ: ½ 2 : 279 The density operator has evolved under the scalar coupling Hamiltonian
for the entire spin echo period, 2t. The result obtained for initialSz
magnetization is obtained by exchangingIandSoperators in [2.279].
Setting the delay,t, to be equal to 1/(4JIS) generates the purely anti-
phase term 2IxSz, while havingt¼1/(2JIS) serves to produceIy. The
generation of an antiphase state by this method is a common feature in
many pulse sequences.
If the two scalar coupled spins belong to different nuclear species, or
if sufficiently selective rf pulses can be obtained (see Chapter 3,
2.7 PRODUCTOPERATORFORMALISM 95