High-precision eigenvalues for the 1s2p^1P and ^3P states of helium

The double basis set method in Hylleraas coordinates described previously [ Nucl. Instrum. MethodsB31, 7 ( 1988)] is applied to the calculation of high-precision eigenvalues for the 1s2p1P and 3P states of helium. Convergence to a few parts in 1014 is obtained for the nonrelativistic energies. The new wave functions are used to calculate mass-polarization, relativistic, relativistic reduced mass, and quantum-electrodynamic corrections. A comparison of the P-state energies, together with the previously calculated S- and D-state energies, with the experimental energy levels tabulated by Martin [ Phys. Rev A36, 3575 ( 1987)] yields well-defined discrepancies of the order of 0.001 cm−1, which can be attributed to higher-order relativistic and quantum-electrodynamic effects.