  We revisit the photoabsorption from the ground state of K, ending below and
above the ionization threshold, with special emphasis on the shape of the
photoionization cross section around the Cooper minimum. The present treatment,
including core polarization effects and dynamic core polarizability matches
very well the most accurate measurements resolving an older question about the
width of the Cooper minimum. The photoabsorption from the excited $7s$ and $4p$
states is also calculated, along with $4p$$\rightarrow $$nl$ optical oscillator
strengths, and compared with recent experimental and theoretical data.
