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

Abstract

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 infinityHe atom, the bound S(L=0) and P(L=1) states in symmetric muonic molecular ions, and ground states in the 3He2+&mgr;(-)e(-) and 4He2+&mgr;(-)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.