Method of Complex Coordinates for Three-Body Calculations above the Breakup Threshold

Abstract

A method is proposed for calculating elastic and inelastic three-particle scattering amplitudes in the breakup region using a coordinate-space variational approach, with each coordinate multiplied by a complex phase factor. The trial wave functions have relatively simple asymptotic forms. The method applies to short-range potentials analytic in coordinate space. A numerical example indicates that the method works well for two-particle scattering.

Quantum Scattering with the Driven Schrödinger Approach and Complex Scaling

“…Rescigno et al [9] have recently explored this method [7] combined with exterior complex scaling [8] (ECS) in several electron-atom (molecule) scattering studies.…”

“…With given boundary conditions, including ECS we can compute the scattered wave for an arbitrary energy E. Following [7] one can use complex scaling to obtain zero boundary condition at infinity if the potential there decreases exponentially or faster. Rescigno et al [9] realized, without presenting rigorous arguments, that this method could be extended to long-range potentials.…”

“…In a well quoted short paper Nuttal and Cohen [7] propose the use of the driven Schrödinger equation combined with complex scaling [8] to compute quantum cross sections for short range potentials. Rescigno et al [9] have recently explored this method [7] combined with exterior complex scaling [8] (ECS) in several electron-atom (molecule) scattering studies.…”

“…The idea in [7] was to consider the Schrödinger equation and split the wave function into an incoming in and a scattered scat part, = in + scat . As the incoming wave satisfies the free Schrödinger equation, we find…”

Solving the Coulomb scattering problem using the complex-scaling method

“…They become even more complicated for the long-range case when the Coulomb potential is present in the interaction [2]. Therefore, a method which allows the problem to be solved without explicit use of the asymptotic form of the wave function is of great interest from both the theoretical and computational points of view.One of such methods was proposed by Nuttal and Cohen [3]. The approach is based on the complex scaling theory [4].…”