  We investigate the relevance of multiple-orbital and multipole effects during
high-harmonic generation (HHG). The time-dependent configuration-interaction
singles (TDCIS) approach is used to study the impact of the detailed
description of the residual electron-ion interaction on the HHG spectrum. We
find that the shape and position of the Cooper minimum in the HHG spectrum of
argon changes significantly whether or not interchannel interactions are taken
into account. The HHG yield can be underestimated by up to 2 orders of
magnitude in the energy regio of 30-50 eV. We show that the argument of low
ionization probability is not sufficient to justify ignoring multiple-orbital
contributions. Additionally, we find the HHG yield is sensitive to the
nonspherical multipole character of the electron-ion interaction.
