Nuclear quadrupole resonance in the interaction representation

Abstract

Using the interaction representation, the transient pulsed response of an ensemble of nuclei with spin I=3/2 experiencing electric quadrupole couplings is calculated, both in zero field and in the presence of a weak, applied static field. It is found that, in this representation, the evolution of the density operator depends, to a good approximation, on a time-independent effective hamiltonian.

For the response to a solitary, resonant 90° pulse, the prediction is made of the existence of two transient decay signals, 90° out of phase with each other, one being determined by the even moments of the absorption line (as in the ordinary N.M.R. case) and the other being determined by the odd moments. This second signal will be present in the N.Q.R. case, since here the effect of dipole-dipole couplings seems to be, in general, to broaden the resonance line at ω₀ asymmetrically, and while the first moment can be proved to be always zero, this is not, in general, true of the higher odd moments. Expressions are derived from which, in principle, any even or odd moment may be calculated.

As another example of the use of the interaction representation in N.Q.R., the effect of a weak applied static magnetic field is considered and it is shown that the response to a single 90° pulse is modulated by two frequencies associated with the known splitting of the c.w. absorption line into two pairs of satellites.

Using the interaction representation formalism, the response of the ensemble to the Slichter-Holton and Lee-Goldburg pulse sequences (considered previously by the author) is also investigated.

Lastly, it is shown how a two-pulse sequence, identical to that previously used by other investigators for the same purpose in N.M.R., may be used to overcome the ‘dead-time’ problem associated with pulsed work and enable one, to a good approximation, to observe the N.Q.R. free induction decay from an effective time zero.