Computed Transition Probabilities for X-Ray Continua of Potassium

Abstract

The rate of change of the oscillator strength at the $K$-edge of ionized potassium has been computed in a number of ways and a few computations have been made on the $L$-edge. The work has been carried through by using both hydrogenic and Hartree wave functions at the level of the single-electron approximation and Hartree and Hartree-Fock wave functions when the single-electron approximation was not used. Calcium wave functions both with with and without exchange have also been employed. The moment, momentum, and acceleration matrix elements have been computed. The momentum matrix element gives values most closely in agreement with experiment and is most stable with respect to changes in the wave functions. It is followed by the acceleration and the moment in that order. The single electron approximation gives good results. If the single-electron approximation is not used, it is essential that exchange effects be included by employing the determinant form of the wave functions, and the Hartree-Fock one-electron wave functions then give considerably better results than the ordinary Hartree functions. It also proves to be possible to substitute the wave functions of the unexcited ion of next higher atomic number, calcium, for the wave functions of potassium excited in an x-ray level without noticeable deterioration in the results.