Abstract
Fully correlated Hylleraas-type electronic wave functions and a biased-selection Monte Carlo method have been used to find a rigorous upper bound to the Born-Oppenheimer potential between two helium atoms. The potential agrees with the experimental results of Burgmans, Farrar, and Lee (BFL) to within 1.4 Monte Carlo standard deviations for all nuclear separation distances calculated ($4.5\ensuremath{-}15.0{a}_{B}$). At the potential minimum of $5.6{a}_{B}$ this bound (- 7.10\ifmmode\pm\else\textpm\fi{}0.30 Ry) is slightly below the BFL value of -6.70 Ry.
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