  Spin-orbit mediated phonon relaxation in a two-dimensional quantum dot is
investigated using different confining potentials. Elliptical harmonic
oscillator and cylindrical well results are compared to each other in the case
of a two-electron GaAs quantum dot subjected to a tilted magnetic field. The
lowest energy set of two-body singlet and triplet states are calculated
including spin-orbit and magnetic effects. These are used to calculate the
phonon induced transition rate from the excited triplet to the ground state
singlet for magnetic fields up to where the states cross. The roll of the cubic
Dresselhaus effect and the positioning of "spin hot-spots" are discussed and
relaxation rates for a few different systems are exhibited.
