Photoionization Probabilities of Atomic Potassium

Abstract

Calculations of the absorption probabilities in the continuous spectrum of the potassium atom were made to investigate the possibility that the second maximum in the experimental photoionization curve is of atomic origin. The model for the $K$ atom is a single normal state valence electron moving in a non-Coulomb central force field. Two fields were used. The first was determined to satisfy the quantum conditions on the radial phase integrals for the x-ray and optical levels. This field is in error in the region of the deeper shells, and was replaced by Hartree's self-consistent field for the $K$ atom, corrected for polarization of the core to give the observed term values for the normal state and $3_3$ orbits as eigenvalues of the wave equation. The wave functions were obtained by numerical integration, and the matrix integrals for transition probabilities determined graphically. The resulting probability curve was found to decrease steadily from the series limit, with no hint of the experimental maximum. It further appears that no reasonable changes in the field will produce such a variation. The magnitude of the absorption coefficient at the series limit is about 2×${10}^{-20\mathrm{}}$ by our calculations, and $-\frac{\mathrm{df}}{d\epsilon }=\frac{1}{3}\frac{\nu }{R}{\mathrm{}\left[I\right]\mathrm{}}^2,$ where $I$ is the matrix integral, is 0.0024, much smaller than for lighter hydrogen-like atoms. From the percentage association of the vapor and $-\frac{\mathrm{df}}{d\epsilon }$ for the atom it is estimated that the second maximum could be attributed to molecules if $-\frac{\mathrm{df}}{d\epsilon }$ per valence electron at the molecular threshold were about 2. This value seems very large, but not impossibly so.