RELATIONSHIP BETWEEN THE ADIABATIC HYPERSPHERICAL AND THE BORN-OPPENHEIMER APPROACH TO THE COULOMB 3-BODY PROBLEM

The relationship between the adiabatic hyperspherical (AHS) and the st andard adiabatic (Born-Oppenheimer) approach to the Coulomb three-body problem in which the three charges satisfy the conditions Z(1)>0, Z(2 )>0, and Z(3)<0 is studied, It is shown that, in the limit M-->infinit y [M=m(1)m(2)/(m(1)+m(2)), where m(1), m(2), and m(3) are the masses o f the three particles involved], each AHS term E-j(J lambda) reduces t o the corresponding term E-kqm Of the Coulomb two-center (CTC) problem . There is a one-to-one correspondence j reversible arrow{kqm} for eac h fixed set {J,lambda} that determines the CTC classification of AHS t erms. It is shown that the avoided crossings of AHS terms result from the perturbation of the exact crossings of CTC terms because of the fi niteness of M. The transition from the pure discrete AHS spectrum to t he compound (discrete plus continuous) CTC spectrum for M-->infinity i s traced. Theoretical conclusions are illustrated by the numerical cal culations for the mesic molecule dt mu.