Finite terms Hylleraas- and Kinoshita-type variational wave functions are considered for three-body systems.
For calculation of the energies the stochastic variational method is applied. This approach leads to significant decrease of the number of terms present in the trial wave function.
In Coulombic case local properties of wave functions are restricted by the Kato's cusp conditions. It is showed that Kato's cusp conditions restrict the possible terms in variational calculations. Constraints for the linear expansion coefficients are also derived and a recursion type solution is given. Local and global properties of wave functions with correct cusp conditions are studied, finally the double-electron photoionization is considered.
In our latest study new sets of functions with arbitrary large finite cardinality are constructed for two-electron atoms. Functions from these sets exactly satisfy the Kato's cusp conditions. The new functions are special linear combinations of Hylleraas- and/or Kinoshita-type terms. Standard variational calculation, leading to matrix eigenvalue problem, can be carried out to calculate the energies of the system.
There is no need for optimization with constraints to satisfy the cusp conditions.