Calculation of the K $4s,7s,$ and $4p$ photoabsorption near threshold

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$$\to$$nl$ optical oscillator strengths, and compared with recent experimental and theoretical data.