  We present an analysis of the appearance of the Cooper Minimum in singly
ionized argon in both the photoionization cross-section (PICS) and
high-harmonic generation (HHG) spectrum. We employ two computational approaches
based on the same R-matrix technique to provide a coherent description of the
atomic structure of the Ar+ system, finding that the PICS and HHG spectrum are
affected differently by the inclusion of additional residual ion states and the
improved description of correlation effects. Both the PICS and HHG spectrum
possess a clear minimum for all atomic structure models used, with the centre
of the minimum at 55 eV in the PICS and 60 eV in the HHG spectrum for the most
complete description employed. The HHG minimum is systematically shifted to
higher energies with respect to the PICS minimum. We also find that the initial
magnetic alignment (magnetic quantum number) of the Ar+ system does not affect
substantially the position and shape of the HHG minimum (given a sufficiently
detailed atomic structure description), but the harmonic yield is enhanced by
two-orders of magnitude for M_L = 1 over M_L = 0. We also perform similar
calculations for neutral argon, finding that this system is more sensitive to
enhancements in the atomic structure description.
