Abstract:

Based on Rayleigh-Ritz variational and configuration interaction methods as well as Hylleraas coordinates, energies for the highly excited states of helium were calculated, and accuracy of the results reaches 10^-4. Specifically, when $L$ is small, the results are close to Drake's results, and when L becomes larger, the results are matched with the theoretical expectation. Besides, if choosing L=10 as an example, the energy converges when Hylleraas coordinates increase, therefore, the results are reliable. Finally, $L=10$ was chosen as an example to observe the correlation and energy contribution of partial waves. As a result, the largest contribution belongs to the (0, L) L partial wave but the contribution of other partial waves is very small. In conclusion, configuration interaction methods can be applied to calculate the highly excited states of  helium.

Key words: spectroscopy, helium, highly excited states, variational
method