Nuclear Level Splitting Caused by a Combined Electric Quadrupole and Magnetic Dipole Interaction

The interaction of a static electric field gradient and a static magnetic field with the electromagnetic moments of a nucleus is considered in detail. The eigenvectors and eigenvalues of the interaction Hamiltonian are computed as a function of the angle $\beta$ between the electric field gradient and magnetic field directions, and as a function of the electric and magnetic interaction parameters ${\omega }_E$ and ${\omega }_H$. Numerical calculations of the eigenvectors and eigenvalues have been performed for nuclear spin values $I=1, \frac{3}{2}, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \mathrm{and} \frac{9}{2}$ and for a wide range of the parameters $\beta$, ${\omega }_E$, and ${\omega }_H$. The accuracy of the results is 0.001%. Representative numerical results are presented.