Coherent interactions of the polarized nuclear spins of gaseous atoms with the container walls

We have developed a general perturbative theory which describes how coherent wall interactions affect the NMR spectrum of nuclear-spin–polarized gases in containers of any shape. The important practical case of cylindrical containers with quadrupolar wall interactions has been worked out completely. The basic results are quite simple. The frequency shift and damping of the NMR spectrum depend on seven fundamental parameters: v, the mean thermal velocity of spin polarized atoms; λ, the mean-free path of spin-polarized atoms in the gas; l, a characteristic linear dimension of the container; A, an asymmetry parameter of the container; 〈θ〉, the mean twist angle experienced by the nuclear polarization of an atom as a result of a collision with the wall; 〈${\theta }^2$〉, the mean-squared twist angle experienced by the nuclear polarization of an atom as a result of a collision with the wall; and β, the angle between the symmetry axis of the container and the direction of the quantizing magnetic field.