  We estimate the spin relaxation rate due to spin-orbit coupling and acoustic
phonon scattering in weakly-confined quantum dots with up to five interacting
electrons. The Full Configuration Interaction approach is used to account for
the inter-electron repulsion, and Rashba and Dresselhaus spin-orbit couplings
are exactly diagonalized. We show that electron-electron interaction strongly
affects spin-orbit admixture in the sample. Consequently, relaxation rates
strongly depend on the number of carriers confined in the dot. We identify the
mechanisms which may lead to improved spin stability in few electron (>2)
quantum dots as compared to the usual one and two electron devices. Finally, we
discuss recent experiments on triplet-singlet transitions in GaAs dots subject
to external magnetic fields. Our simulations are in good agreement with the
experimental findings, and support the interpretation of the observed spin
relaxation as being due to spin-orbit coupling assisted by acoustic phonon
emission.
