The physics of quadrupole interactions in crystals. Quadrupole interactions observed in the 1+ → 0+γ-ray transition

For many people the nuclear interaction with the electric quadrupole is not as easily understood as the magnetic dipole interaction. This is partly due to the use of Racah algebra in conventional quadrupole interaction calculations. Although this is a powerful technique that provides a neat summation over the m-substates of both the initial nuclear state and the emitted radiation, the formalism does tend to 'hide' some of the details and interesting features of the interaction. Therefore, to improve our understanding of these processes with an emphasis on the physical characteristics, these notes will detail the calculation of quadrupole interactions with both polarised and aligned nuclei without using Racah algebra. To make these calculations manageable only the 1+→ 0+γ-ray transition is considered. The Jπ =1+ state has only 3 substates (m = -1,0,+1), and the parity and angular momentum selection rules allow only M1 magnetic dipole transitions. The calculation has led to some explanations of the difference between the aligned and polarized quadrupole interactions, which is the orientation of the quantization axis with respect to the equatorial plane