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We determine the contributions from the direct Coulomb and exchange interactions to the total interaction in semiconductor artificial atoms. We tune the relative strengths of the two interactions and measure them as a function of the number of confined electrons. We find that electrons tend to have parallel spins when they occupy nearly degenerate single-particle states. We use a magnetic field to adjust the single-particle state degeneracy, and find that the spin-configurations in an arbitrary magnetic field are well explained in terms of two-electron singlet and triplet states.

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