  The time evolution of $\ell$-spin reduced density operators is studied for a
class of Heisenberg-type quantum spin models with long-range interactions. In
the framework of the quantum Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY)
hierarchy, we introduce an unconventional representation, different from the
usual cluster expansion, which casts the hierarchy into the form of a
second-order recursion. This structure suggests a scaling of the expansion
coefficients and the corresponding time scales in powers of $N^{1/2}$ with the
system size $N$, implying a separation of time scales in the large system
limit. For special parameter values and initial conditions, we can show
analytically that closing the BBGKY hierarchy by neglecting $\ell$-spin
correlations does never lead to equilibration, but gives rise to quasi-periodic
time evolution with at most $\ell/2$ independent frequencies. Moreover, for the
same special parameter values and in the large-$N$ limit, we solve the complete
recursion relation (the full BBGKY hierarchy), observing a superexponential
decay to equilibrium in rescaled time $\tau=tN^{-1/2}$.
