  NMR spin-spin relaxation in solids in strong magnetic fields is normally
described only with the help of the secular part of the full spin-spin
interaction Hamiltonian. This approximation is associated with the averaging of
the spin-spin interaction over the fast motion of spins under the combined
action of the static and the radio-frequency (rf) fields. Here we report a set
of conditions when the averaging over the above fast motion preserves some of
the non-secular terms entering the full interaction Hamiltonian. These
conditions relate the value of the static magnetic field with the frequency and
the amplitude of the rf field. When the above conditions are satisfied, the
effective recoupled spin-spin interaction Hamiltonian has an unconventional
form with tunable parameters. These tunable Hamiltonian offers interesting
possibilities to manipulate nuclear spins in solids and can shed new light on
the fundamental properties of the nuclear spin-spin relaxation phenomenon.
