  The spin relaxation time due to the electron-acoustic phonon scattering in
GaAs quantum dots is studied after the exact diagonalization of the electron
Hamiltonian with the spin-orbit coupling. Different effects such as the
magnetic field, the quantum dot size, the temperature as well as the electric
field on the spin relaxation time are investigated in detail. Moreover, we show
that the perturbation method widely used in the literature is inadequate in
accounting for the electron structure and therefore the spin relaxation time.
