Multibox strategy for constructing highly accurate bound-state wave functions for three-body systems

Variational, multibox approach is proposed to construct extremely accurate, bound-state wave functions for arbitrary three-body systems. The high efficiency of our present approach is based on an optimal choice of nonlinear parameters in the exponential basis functions. The proposed method is very flexible, since the final wave function can also include a large number of separately optimized cluster fragments. The wave functions obtained are very compact and highly accurate. Such wave functions can be used to compute various bound state properties for different three-body systems. The proposed approach has been successfully tested on a large number of actual systems. It is shown that the present approach can be used to solve various three-body problems with, in principle, arbitrary precision. In particular, the long-standing problem of highly accurate determination of the weakly bound (1,1) states in the ddμ and dtμ muonic molecular ions has finally been solved. The determined binding energies are -1.9749880880±5×10^-10 eV and -0.66033874±1×10^-8 eV, respectively.