On the Transition Probability Between two States with Positive Energy in a Central Field

Abstract

By the aid of the hypergeometric function with two variables, the transition probability in the sense of the quantum mechanics between two states with positive energy in a central field due to nuclear charge $\mathrm{Ne}$ has been calculated. When the transition probability calculated is applied to the intensity of continuous x-rays, the spectral energy distribution, which is nearly independent of the frequency of the radiation emitted, has been obtained. As the result of the present computation, the dependence of the intensity for the isochromat $I_{\nu }$ on the applied voltage $V$ is somewhat flatter than the result expected from the law $I_{\nu }\sim \frac{1}{V}$. The isochromat experiments by Kuhlenkampff for the continuous x-rays emitted from a thin target show a good agreement with the values computed here. The polarization and the angular intensity distribution of continuous x-rays have been discussed.