As part of a program aiming to determine all the observed term-values of two-electron atoms on the basis of the Schrödinger wave equation, we have evaluated the $1s\mathrm{ns}$ levels of helium up to $n=9\mathrm{}$, in both the singlet and the triplet states. Our previous method, using perimetric coordinates, was extended to allow for the asymmetry between the $1s$ and the excited electrons. The mass polarization and relativistic corrections were also determined. The difference between the ionization energies $J\left(220\right)\mathrm{}$, obtained by solving a determinant of order 220, and the experimental values, ranges from 3.6 ${\mathrm{cm}}^{-1\mathrm{}}$ for $3{}_{}{}^1{}_{}{}^{}S$ to 5.8 ${\mathrm{cm}}^{-1\mathrm{}}$ for $9{}_{}{}^1{}_{}{}^{}S$, and from 0.5 ${\mathrm{cm}}^{-1\mathrm{}}$ for $3{}_{}{}^3{}_{}{}^{}S$ to 5.7 ${\mathrm{cm}}^{-1\mathrm{}}$ for $9{}_{}{}^3{}_{}{}^{}S$. The extrapolated values indicate that with a faster computer than WEIZAC it should be feasible to determine all of the 31 observed $1s\mathrm{ns}$ levels ($n<~17$) of helium to within the experimental accuracy.

• Received 15 March 1962

DOI:https://doi.org/10.1103/PhysRev.127.509