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and the electron-nucleus distances are, respectively, ri = R(ï + y) r2 = R(? + y') (199)

The electron-electron repulsive potential can be written as a series expansion in products of associate Legendre polynomials

where fmu n=,pr(?')Qm(?) ?>? fl 1 PT(rnm(z ) ?<?

em is Neumann's factor: e0= 1, en= 2 (n = 1, 2, 3,...) [116].

If the atom is enclosed in an impenetrable prolate spheroidal box defined as

{£ = £0 - 1 < y < 1 0 < p < 2w} (202)

then the wavefunctions must fulfill the requirements

To obtain the ground state energy of a helium atom by using the direct variational method, the ansatz wavefunc-tion is constructed as a product of two hydrogenic functions, namely, ft(£, y, p; £, y', p') = A exp[-aR(£ + y)] x exp[-aR(£' + y')] x (£ - £))(£' - £0) (204)

where A is a normalization constant, and a is a varia-tional parameter to be determined after minimizing the energy functional with the additional constrictions imposed by Eq. (203). To satisfy the latter, two auxiliary functions

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