Pulse response in the presence of quadrupole splitting

A nucleus with nuclear spin I greater than has an electric quadrupole moment in addition to a nuclear magnetic moment. An electric quadrupole moment arises from an asymmetry of the distribution of the electrical charges in the nucleus and does not depend on the net charge. It is often viewed as two electric dipoles displaced from one another and 

The electric quadrupole moment becomes important only when the nucleus is in an electric field gradient (EFG), either static or dynamic. Any environment that does not 

In a stationary EFG, the quadrupole interaction shifts the Zeeman levels according to the square of the quantum number m to a first approximation. Thus, for 1=3/2, for example, m can be 3/2, 1/2, -1/2, or -3/2, and the m= 3/2 levels shift identically while the m= l/2 levels shift identically. 

The splitting shown below can be quite large and the irradiation and the detection of such transitions can be difficult, as discussed below. If, due to the molecular motion, the EFG at the nucleus is averaging rapidly and isotropically on the time scale of the experiment, for example, for nitrogen-14 in an ammonia molecule dissolved in water at room temperature, 

In Chapter I, we introduced the angular velocity of the magnetization around Hj in the rotating frame as u)j=yHj, in analogy with the Larmor frequency in the laboratory frame. This physical picture of the effect of Hj breaks down for 1 % when the non-zero quadrupole interaction makes the energy levels unequal. The basic principles are treated in Chapter VII, Section II.B.(c) of Abragam, 1961 (Appendix A) but our discussion relies on some lecture notes by Schmidt (1972). 

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