โ Scribed by Allan C.G. Mitchell
No coin nor oath required. For personal study only.
A GENERAl. wave-mechanical theory of FOUNDATION collisional processes has been developed by Com~,,~c,tionNo. 3S. Born 1 and applied by \Ventzel 2 to the scattering of alpha-particles by heavy atoms, and by Elsasser 3 to collisional processes in atomic hydrogen. Recently Sommerfeld 4 has applied the method to the scattering of electrons in argon and has found agreement with the experimental results.
To carry out the calculation it is necessary to know the potential of the atom v(r) as a function of the distance from the nucleus. Wentzel first assumed the potential of an atom of atomic number Z to be given by the Coulomb law v(r) = Ze/r, neglecting the effect of the electrons around the nucleus but found that this led to integrals which would not converge. On assuming the potential function to be v(r) = Ze/re -T/R, where R is of the order of magnitude of an atomic radius, he was able to obtain a scattering formula which, for alpha-particles, agreed with the Rutherford scattering law. On the other hand Elsasser found the potential of the hydrogen atom in terms of its eigenfunctions, the potential for the hydrogen atom in its normal state being similar to that used by Wentzel, thus ]ustifying his assumption, and showed that a scattering law for atomic hydrogen could be obtained. Finally, Sommerfeld considered scattering from other atoms by treating all the electrons of the atom as united in the K-shell without mutually influencing each other. "The action of these electrons toward the outside would then
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