Ground State Energy Calculations of Isoelectronic Series of He in Double-Zeta Approximation Using Coulomb Potential with Noninteger Indices

Using formulae for one- and two-electron integrals of Coulomb interaction potential f_k(r)=r^-k with non-integer indices k established by one of the authors with the help of complete orthonormal sets of ψ^α-exponential-type
orbitals (α=1,0,-1,-2...), we perform the calculations for isoelectronic series of the He atom containing nuclear charges from 2 to 10, where k=1-μ (-1<μ<0). For this purpose we have used the double-zeta approximation, the configuration interaction and coupled-cluster methods employing the integer-n Slater-type orbitals as basis sets. It is demonstrated that the results of
calculations obtained are better than the numerical Hartree--Fock values.