Accurate values for the nonrelativistic energies of the lowest singlet and triplet S-states of the4He-Isotop

Accurate lower and upper bounds for the nonrelativistic lowest energies¹ E ₀ and³ E ₀ of the singlet and triplet-system of the⁴He-Isotop are calculated with the linearized method of variance minimization. The same was done for¹ E ₁ the energy of the first excitedS-state 2¹ S. The results especially for¹ E ₀ and³ E ₀ in a.u. are −2.9033076997₅ ≤¹ E ₀ ≤ −2.9033076921₈ −2.1749324263₇ ≤³ E ₀ ≤ −2.1749324245₉ i.e. the values are determined with an absolute error smaller than 0.00167 cm⁻¹ for¹ E ₀ and 0.00039 cm⁻¹ for³ E ₀.