Correlated wave functions for three-particle systems with Coulomb interaction: The muonic helium atom

A computational procedure for calculating correlated wave functions is proposed for ground and excited states of three-particle systems with Coulomb interaction. Calculations are performed for the muonic helium atom as an example. Hylleraas-type trial functions multiplied by appropriate angular factors are used as the basis of the correlated wave functions. The expansion coefficients and two nonlinear parameters are obtained variationally. Results for the states ${\mathrm{}\left(1s\right)\mathrm{}}_e{\mathrm{}\left(1s\right)\mathrm{}}_{\mu } {}_{}{}^{1,3}{}_{}{}^{}S$, ${\mathrm{}\left(1s\right)\mathrm{}}_e{\mathrm{}\left(2p\right)\mathrm{}}_{\mu } {}_{}{}^{1,3}{}_{}{}^{}P$, ${\mathrm{}\left(1s\right)\mathrm{}}_e{\mathrm{}\left(3d\right)\mathrm{}}_{\mu } {}_{}{}^{1,3}{}_{}{}^{}D$, ${\mathrm{}\left(1s\right)\mathrm{}}_e{\mathrm{}\left(4f\right)\mathrm{}}_{\mu } {}_{}{}^{1,3}{}_{}{}^{}F$, and ${\mathrm{}\left(1s\right)\mathrm{}}_e{\mathrm{}\left(5g\right)\mathrm{}}_{\mu } {}_{}{}^{1,3}{}_{}{}^{}G$ are listed.