A Simple Numerical Matrix Method for Accurate Triplet-1s2s 3S1 Energy Levels of Some Light Helium-like Ions

Abstract

Triplet-1s2s 3S1 energy levels of some light Helium-like ions (Li+ to Ne8+) were numerically calculated using a truncated-matrix method implemented in a simple Mathematica code. The two-electron wave functions were expanded in finite number of basis states consisting of hydrogenic s-orbitals. Here, the Hamiltonian matrix used was of size 15×15, 25×25 and 35×35. From the results, triplet-1s2s 3S1 energies of the ions were in good agreement with other advanced and highly accurate calculations in the literature. Comparisons with one of the most accurate calculations in the literature showed that our results were very accurate with the largest error in energy being only 0.135 % for Li+ ion and the smallest one being approximately 0.018 % for Ne8+ ion energy, when 35 basis states were used in our calculations. Errors from our calculations were also much lower than those from the geometrical model.