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We discuss the problem of spin-orbit interaction in a 2D chaotic or diffusivequantum dot in the presence of exchange correlations. Spin-orbit scatteringbreaks spin rotation invariance, and in the crossover regime between differentsymmetries of the spin-orbit coupling, the problem has no closed solution. Aconventional choice of a many-particle basis in a numerical diagonalization isthe set of Slater determinants built from the single-particle eigenstates ofthe one-body Hamiltonian (including the spin-orbit terms). We develop adifferent approach based on the use of a good-spin many-particle basis that iscomposed of the eigenstates of the universal Hamiltonian in the absence ofspin-orbit scattering. We introduce a complete labelling of this good-spinbasis and use angular momentum algebra to calculate in closed form the matrixelements of the spin-orbit interaction in this basis. Spin properties, such asthe ground-state spin distribution and the spin excitation function, are easilycalculated in this basis.Comment: 14 pages, 3 figure

Spin-orbit interaction in quantum dots in the presence of exchange correlations: An approach based on a good-spin basis of the universal Hamiltonian