  We study the polarisation dependence of the homogeneously broadened nuclear
spin resonance in a crystal. We employ a combinatorial method to restrict the
nuclear states to a fixed polarisation and show that the centre of the
resonance is shifted linearly with the nuclear polarisation by up to the zero
polarisation line width. The width shrinks from its maximum value at zero
polarisation to zero at full polarisation. This suggests to use the line shape
as a direct measure of nuclear polarisation reached under dynamical pumping. In
the limit of single quantum of excitation above the fully ferromagnetic state,
we provide an explicit solution to the problem of nuclear spin dynamics which
links a bound on the fastest decay rate to the observable width of the
resonance line.
