A study of bound states of systems of helium and lithium using the method of discrete-variable representation

The systems of particles He$_{2}$, $^{6}$Li–He,$^{7}$Li–He, He$_{3}$, $^{6}$Li–He$_{2}$, and $^{7}$Li–He$_{2}$, the binding energies of which are small and the bound-state wave functions of which are widely distributed in space, are considered. Because the interaction potential is weak and rather localized compared to the characteristic sizes of wave functions of these systems, the problem of an accurate determination of binding energy and wave functions is complicated. Small changes in input parameters or an inaccuracy of calculations can lead to considerable deviations of calculated results from true values. An essential part of the study is the development and application of the discrete-variable representation method. This method is based on the determination of basis functions and the nodes and weights of a quadrature formula in such way that the values of a function are zero at all these nodes but one. With this representation the time required for calculating the Hamiltonianmatrix elements is reduced several times. The binding energies of several systems consisting of helium and lithium atoms were obtained using the method of discrete-variable representation. Thanks to the application of this approach, the calculation time was significantly reduced without loss in accuracy.