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We consider the hyperfine-mediated transition rate between Zeeman split spinstates of the lowest orbital level in a GaAs quantum dot. We separate thehyperfine Hamiltonian into a part which is diagonal in the orbital states andanother one which mixes different orbitals. The diagonal part gives rise to aneffective (internal) magnetic field which, in addition to an external magneticfield, determines the Zeeman splitting. Spin-flip transitions in the dots areinduced by the orbital mixing part accompanied by an emission of a phonon. Weevaluate the rate for different regimes of applied magnetic field andtemperature. The rates we find are bigger that the spin-orbit related ratesprovided the external magnetic field is sufficiently low.Comment: 8 pages, 3 figure

Hyperfine-mediated transitions between a Zeeman split doublet in GaAs quantum dots: The role of the internal field