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The transmission phase through a quantum dot with few electrons shows acomplex, non-universal behavior. Here we combine configuration-interactioncalculations ---treating rigorously Coulomb interaction--- and the Friedel sumrule to provide a rationale for the experimental findings. The phase evolutionfor more than two electrons is found to strongly depend on dot's shape andelectron density, whereas from one to two the phase never lapses. In theCoulomb (Kondo) regime the phase shifts are significant fractions of pi (pi/2)for the second and subsequent charge addition if the dot is stronglycorrelated. These results are explained by the proper inclusion in the theoryof Coulomb interaction, spin, and orbital degrees of freedom.

Exchange and correlation effects in the transmission phase through a few-electron quantum dot