QMGreensite_merged

witht¼1/(4JIS), is called the spin-state-selective coherence transfer
(S^3 CT) sequence element ( 19 ). The propagator corresponding to this
sequence is given by

U¼exp 
i



2

Sy



expðÞ
iIx expðÞ
iHt exp½Š
iðIxþSxÞ

expðÞ
iHt exp 
i



2

Sx



¼exp 
i



2

Sy



expðÞ
iSx exp
i



2

2 IzSz



exp
i



2

Sx



¼exp 
i



2

Sy



expi



2

Sx



expi



2

Sx



exp 
i



2

2 IzSz



exp 
i



2

Sx



¼exp 
i



2

Sy



expi



2

Sx



exp
i



2

2 IzSy



¼exp 
i



2

Sz



exp 
i



2

Sy



exp
i



2

2 IzSy



:

½ 2 : 293 Š

This propagator can be expressed using single transition basis
operators as

U¼exp 
i



2

Sz



exp 
i



2

Sy



exp
i



2

2 IzSy



¼exp 
i



2

Sz



exp 
i

1

2

ðSyþ 2 IzSyÞ



¼exp 
i



2

Sz



exp
iI^ Sy



: ½ 2 : 294 Š

Ignoring thez-rotation, which can be compensated by phase shifting
subsequent pulses in an actual experiment, the propagator corresponds
to a selective inversion across thej i$j itransition in the two-spin
energy level system (Fig. 2.4). In contrast, a conventional 180 8 pulse
corresponds to simultaneous inversion across both thej i$j iand
thej i$j itransitions. The effect of this sequence element on theSz
operator can be described in either the Cartesian or the single-transition
operator bases by

Sz )

I^ Sy


 2 IzSz,

I^ þI^



Sz )

I^ Sy


I^ þI^



Sz:

½ 2 : 295 Š

100 CHAPTER 2 THEORETICALDESCRIPTION OFNMR SPECTROSCOPY