  Using the Algebraic Bethe Ansatz in conjunction with a simple Monte Carlo
sampling technique, we study the problem of the decoherence of a central spin
coupled to a nuclear spin bath. We describe in detail the full crossover from
strong to weak external magnetic field field, a limit where a large
non-decaying coherence factor is found. This feature is explained by
Bose-Einstein-condensate-like physics which also allows us to argue that the
corresponding zero frequency peak would not be broadened by statistical or
ensemble averaging.
