  We calculate the spin relaxation rates in a parabolic InSb quantum dots due
to the spin interaction with acoustical phonons. We considered the deformation
potential mechanism as the dominant electron-phonon coupling in the
Pavlov-Firsov spin-phonon Hamiltonian. By studying suitable choices of magnetic
field and lateral dot size, we determine regions where the spin relaxation
rates can be practically suppressed. We analyze the behavior of the spin
relaxation rates as a function of an external magnetic field and mean quantum
dot radius. Effects of the spin admixture due to Dresselhaus contribution to
spin-orbit interaction are also discussed.
