Compact and accurate integral-transform wave functions. II. The2S1,2S3,2P1, and2P3states of the helium-like ions from He throughMg10+

The method of the preceding paper is used to construct compact and accurate integral-transform wave functions for the four lowest excited states of the helium-like ions. Convergence studies of the energy and various expectation values are presented for the $2{}_{}{}^1{}_{}{}^{}S$, and $2{}_{}{}^3{}_{}{}^{}S$, states of the helium atom. Parallelotope parameters and energies are given for the $2{}_{}{}^1{}_{}{}^{}S$, $2{}_{}{}^3{}_{}{}^{}S$, $2{}_{}{}^1{}_{}{}^{}P$, and $2{}_{}{}^3{}_{}{}^{}P$ states of the ions from He through ${\mathrm{Mg}}^{10+}$. A brief discussion of the prospects for extending the method to many-electron systems is included.