  Spin-flip rates in GaAs quantum dots can be quite slow, thus opening up the
possibilities to manipulate spin states in the dots. We present here
estimations of inelastic spin-flip rates mediated by hyperfine interaction with
nuclei. Under general assumptions the nucleus mediated rate is proportional to
the phonon relaxation rate for the corresponding non-spin-flip transitions. The
rate can be accelerated in the vicinity of a singlet-triplet excited states
crossing. The small proportionality coefficient depends inversely on the number
of nuclei in the quantum dot. We compare our results with known mechanisms of
spin-flip in $GaAs$ quantum dot.
