Irreducible Tensor Operators and Multiple-Quantum NMR.

The aim of the work detailed in this thesis, is to provide a concise, and illuminating, mathematical description of multiple quantum nuclear magnetic resonance (MQNMR) experiments, on essentially isolated (non-coupled) nuclei. The treatment used is based on irreducible tensor operators, which form an orthonormal basis set. Such operators can be used to detail the state of the nuclear ensemble (density matrix) during every stage, preparation, evolution and detection, of a MQNMR experiment. Moreover, such operators can be also used to provide a rigorous analysis of pulsed NMR experiments, on oriented nuclei at low temperatures, where the initial density matrix is far from trivial. The specific topics dealt with in this thesis are as follows. In the first place the properties of irreducible tensor operators are discussed in some detail. In particular, symmetric and anti-symmetric combinations of tensor operators are introduced, to reflect the Hermitian nature of the nuclear Hamiltonian and density matrix. Secondly, the creation of multipolar nuclear states using hard, non-selective rf pulses, is detailed for spin I = 1, 3/2, 2 and 5/2 nuclei, subject to an axially symmetric quadrupole interaction. Results are also given for general I. Thirdly, some experimental results, verifying the production of a triple quantum NMR state, for the I = 3/2 ^{23}Na nuclei in a single crystal of NaIO_4 are presented and discussed. Fourthly, the treatment of MQNMR experiments is extended to the low temperature regime where the initial density matrix includes Fano statistical tensors other than rank one. In particular, it is argued that MQNMR techniques could be used to enhance the anisotropy of gamma-ray emission from oriented nuclei at low temperatures. Fifthly, the effect of a more general quadrupole Hamiltonian (including an asymmetry term) on MQNMR experiments is considered for spins I = 1 and 3/2. In particular, it is shown that double quantum states evolve to give longitudinal NMR signal, oscillating at twice the Larmor frequency, in the presence of an asymmetry term. Finally, results are presented for the evolution of I = 1 and 3/2 nuclear systems under the action of soft or intermediate strength rf pulses. These results are subsequently used to discuss a range of MQNMR experiments involving soft rf pulses.