Quadrupolar interaction nuclear spin energy levels

Except for some quadrupolar effects, all the interactions mentioned are small compared with the Zeeman interaction between the nuclear spin and the applied magnetic field, which was discussed in detail in Chapter 2. Under these circumstances, the interaction may be treated as a perturbation, and the first-order modifications to energy levels then arise only from terms in the Hamiltonian that commute with the Zeeman Hamiltonian. This portion of the interaction Hamiltonian is often called the secular part of the Hamiltonian, and the Hamiltonian is said to be truncated when nonsecular terms are dropped. This secular approximation often simplifies calculations and is an excellent approximation except for large quadrupolar interactions, where second-order terms become important. 

Figure 2. Energy level scheme for an I = 1 nucleus (e.g., l N) weakly coupled to an S = 1/2 electron spin. For the case shown here, the nuclear quadrupolar interaction and the nuclear Zeeman interaction are of the same order. Interference between allowed transitions...

---