Delves Principle Applied to Helium Using a Numerical Excited Hartree Basis

Abstract

Expectation values for [Formula: see text], n = 2, 1, −1, −2, and 1/r12 for the 1S state of helium have been calculated using numerical Hartree orbitals. These were then modified by use of the Delves principle, approximating the auxiliary vector of the Delves formalism with a nine-term basis formed from the numerical excited orbitals of the ground state Hartree operator. The modified expectations were then compared with the essentially exact calculations of Pekeris. Results are mixed: excellent for n = 1,2, modest for 1/r12, and poor for n = −1, −2. It is conjectured that the latter results are due to a deficiency of s orbitals in the basis used engendering a poor approximation to the auxiliary vector for these operators.