Quadrupole Allowed Transitions in Nitrogen Fourteen

The 14N nucleus is not spherical but rather is ellipsoidal; hence, it has a quadrupole moment. The spin of 14N is 1 so that the application of a magnetic field splits the doubly degenerate quadrupole levels, mI=±1. Normally, transitions are allowed only if /Δm/=1. For this case transitions with /Δm/=2 are possible; that is, transitions from mI=1 to mI=1 have nonzero probabilities since the mI=±1 states are coupled by the magnetic field to the mI=O state. This is what the experiment will attempt to observe. The analytical problems were solved in the following steps: a) Quadrupole Hamiltonian with cylindrically symmetric field gradient b) Quadrupole Hamiltonian with non-axial field gradient c) Magnetic field alone d) Magnetic field as a perturbation to the Hamiltonian in case a) e) Magnetic field plus the Hamiltonian in case a) f) Magnetic field plus the Hamiltonian in case b). An energy correlation diagram and intensities for the quadrupole allowed transitions as a function of magnetic field strength varying between the limits of pure quadrupole field to pure magnetic field will be calculated by computer.