Multiple quantum NMR of spin-carrying molecules in nanopores: high order corrections to the two-spin/two-quantum Hamiltonian

This paper is devoted to multiple quantum (MQ) NMR spectroscopy in nanopores filled by a gas of spin-carrying molecules (s = 1/2) in a strong external magnetic field. It turns out that the high symmetry of the spin system in nanopores yields a possibility to overcome the problem of the exponential growth of the Hilbert space dimension with an increase in the number of spins and to investigate MQ NMR dynamics in systems consisting of several hundred spins. We investigate the dependence of the MQ coherence intensities on their order (the profile of the MQ coherence intensities) for a spin system governed by the standard MQ NMR Hamiltonian (the nonsecular two-spin/two-quantum Hamiltonian) together with the second order correction of average Hamiltonian theory. It is shown that the profile depends on the value of this correction and varies from an exponential to a logarithmic one.