Effective adiabatic approximation in the problem of three bodies coupled via short-range potentials

The effective adiabatic approximation is constructed for the problem of thr ee bodies on a straight line that are coupled via short-range attractive de lta-function potentials. It is shown that, in this system, there arise a no nlocal momentum-dependent long-range effective potential and a polarization potential. A lower bound on the binding energy of the system is obtained t o a relative precision of about 10(-6). It is shown that, to. within 0.03%, this approximation yields a correct asymptotic behavior of solutions and a correct behavior of the phase shift for elastic scattering at relative mom enta below the three-body-breakup threshold. A local convergence of the adi abatic expansion in a finite interval of the radial variable is demonstrate d. (C) 2001 MAIK "Nauka/Interperiodica".