Coulomb hole in some excited states of helium

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Abstract
The distribution function f(r12) of the interelectronic distance r12 in the 23S and 21S states of helium is calculated for several different wavefunctions. Mean values of positive and negative integral powers of r12 are reported. The dependence of f(r12) on the atomic number is shown to provide some additional physical insight into the excited states of helium. The Coulomb holes of the 23S and 21S states are calculated and found to be more complex than the Coulomb hole of the ground state. The effect of the Fermi hole in the triplet state is discussed. A new distribution function g(r12,r1) is introduced and is used to discuss the Coulomb hole in terms of the chosen position of electron 1. It is observed that when one electron is far from the nucleus the Coulomb hole is essentially centred on the nucleus, whereas at small distances from the nucleus the Coulomb hole follows the electron.

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