  Decoherence with recurrences appear in the dynamics of the one-body density
matrix of an $F = 1$ spinor Bose-Einstein condensate, initially prepared in
coherent states, in the presence of an external uniform magnetic field and
within the single mode approximation. The phenomenon emerges as a many-body
effect of the interplay of the quadratic Zeeman effect, that breaks the
rotational symmetry, and the spin-spin interactions. By performing full quantum
diagonalizations very accurate time evolution of large condensates are
analyzed, leading to heuristic analytic expressions for the time dependence of
the one-body density matrix, in the weak and strong interacting regimes, for
initial coherent states. We are able to find accurate analytical expressions
for both the decoherence and the recurrence times, in terms of the number of
atoms and strength parameters, that show remarkable differences depending on
the strength of the spin-spin interactions. The features of the stationary
states in both regimes is also investigated. We discuss the nature of these
limits in the light of the thermodynamic limit.
