Energies of confined helium and isoelectronic ions

We now consider the extension [33] of our results to helium and isoelectronic ions, in terms of effective screening. We begin by considering the scaling properties of the hydrogenic system. 

The Schrodinger equation for the hydrogenic system confined to a sphere can be written in the form 

the energies for the general case of nuclear charge Z are related to the energies of a hydrogen atom with scaled radius ZR. 

The two-electron atom or ions confined to a sphere of radius R, are described by the Hamiltonian H, 

The complications due to the 1 /r 2 term are greatly simplified by simulating it with a screening of the nuclear charge. 

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