High-precision, variational, bound-state calculations in Coulomb three-body systems

The present study contains high-precision variational results for a number of bound states in various Coulomb three-body systems. In particular, we discuss the bound-state properties for the $2^{3}S$ state of the ${}^{\infty }\mathrm{He}$ atom, the bound $S(L=0\mathrm{})\mathrm{}$ and $P(L=1\mathrm{})\mathrm{}$ states in symmetric muonic molecular ions, and ground states in the ${}^3{\mathrm{He}}^{2+}{\mu }^{-}{e}^{-}$ and ${}^4{\mathrm{He}}^{2+}{\mu }^{-}{e}^{-}$ atoms. The accuracy achieved for the total energies in these systems is significantly higher than known from the previous works. These results have been obtained by using a package of FORTRAN programs and a pretranslator written by D.H. Bailey from NASA [D.H. Bailey, ACM Trans. Math. Softw. 21, 379 (1995)]. This multiprecision FORTRAN package can completely eliminate all problems related to numerical instabilities at large dimensions, which are crucial for high-precision, bound-state calculations in few-body systems. In fact, the multiprecision FORTRAN programs open another avenue in the study of bound states in few-body systems.