Nuclear Relaxation

Up until now we have only discussed some time-independent properties. In the formalism we used we mentioned only states which are (almost) eigenstates of a slightly perturbed Hamiltonian and we treated them as they would have infinite life time. We investigated these static properties by means of spectra. In order to exclude any dynamical effects in the measurement the repetition delay has to be choosen of the order of T₁ and the pulse delay in the echo sequence has to be shorter than T₂.

But NMR may also probe dynamical properties of matter such as spin-lattice (T₁^-1) and spin-spin relaxation rates (T₂^-1). T₂ denotes the characteristic time scale in which the spins reach thermal equilibrium among themselves; T₁ denotes the time scale in which the spins reach thermal equilibrium with the lattice. In equlibrium the populations of the single states are described by a Boltzmann distribution with the temperature of the lattice T_L. By means of the rf pulses we bring some excess energy to the spin system. This energy gets absorbed by the lattice due to relaxation processes. Since the energy of the lattice is in general much larger than the difference between the energy levels (¹¹B in a field of 5T: eV) we can savely treat the lattice as an infinite heat reservoir according to statistical mechanics.

Speaking about the spin-lattice relaxation one usually distinguishes between two different mechanisms. The magnetic relaxation is due to fluctuations in the local magnetic field and the so-called quadrupolar spin-lattice relaxation is due to fluctuations in the local electrostatic potential. Usually there is a contribution of both mechanisms but in metals or magnetic intermetallic systems clearly domintates.^3.2 In this section we want to discuss the spin-lattice relaxation and we will show how it is correlated with the magnetisation recovery which we can measure. We follow the derivations given in [#!slichter!#,#!kind!#,#!rhodes!#].

• Magnus Expansion and Relaxation
• Magnetization Recovery in a System described by more than one Temperature
• Relaxation Mechanisms