  We derive a formula describing the adiabatically pumped charge through an
interacting quantum dot within the scattering matrix and Green's function
approach. We show that when the tunneling rates between the leads and the dot
are varied adiabatically in time, both in modulus and phase, the current
induced in the dot consists of two terms, the pumping current and a
rectification-like term. The last contribution arises from the time-derivative
of the tunneling phase and can have even or odd parity with respect to the
pumping phase \varphi. The rectification-like term is also discussed in
relation to some recent experiments in quantum-dots.
