  We consider the hyperfine-mediated transition rate between Zeeman split spin
states of the lowest orbital level in a GaAs quantum dot. We separate the
hyperfine Hamiltonian into a part which is diagonal in the orbital states and
another one which mixes different orbitals. The diagonal part gives rise to an
effective (internal) magnetic field which, in addition to an external magnetic
field, determines the Zeeman splitting. Spin-flip transitions in the dots are
induced by the orbital mixing part accompanied by an emission of a phonon. We
evaluate the rate for different regimes of applied magnetic field and
temperature. The rates we find are bigger that the spin-orbit related rates
provided the external magnetic field is sufficiently low.
