The Determination of Electron Distributions From Measurements of Scattered X-Rays

Abstract

A calculation based on classical electromagnetic theory is made of the intensity of the x-rays scattered by an atom in which the electrons are arranged with random orientation and with arbitrary radial distribution. Conversely an expression is derived for the radial distribution of the electrons in an atom, assuming that they have random orientation. This expression has the form of a Fourier integral, which can be evaluated from observed intensities of the scattered x-rays for different wave-lengths and angles.A comparison of this calculation with Wentzel's quantum theory of x-ray scattering suggests the introduction of a certain correction factor to express more nearly the intensity of the modified rays. It is also noted that the interpretation of $\stackrel{-}{\ensuremath{\psi}\ensuremath{\psi}}$ as a probability of the occurrence of an electron leads to the correct value for the intensity of total scattered x-rays.As an example of the application of the new method of calculation, Barrett's experimental data for the scattering of x-rays by helium are analyzed to give the distribution of the electrons in the helium atom. The resulting distribution is in close agreement with the value calculated by Pauling on the basis of wave mechanics, but differs by more than the probable experimental error from the electron orbits given by Bohr's theory.