Nonperturbative distorted-wave approach for asymptotic solutions of coupled-channel scattering problems

We developed and implemented a numerical method using distorted waves for coupled-channel scattering problems. Solutions of the full problem are expressed as ${\bf F=A}(r)f+{\bf B}(r)g$, where $f$ and $g$ are solutions of the single-channel problem including the full diagonal potential. The `unperturbed' distorted-waves $f$ and $g$ are obtained using our newly developed scheme for Milne's phase-amplitude method. The differential equations for ${\bf A}(r)$ and ${\bf B}(r)$ are recast in the new variable $x=1/r$, and are solved using a spectral integration method based on Chebyshev polynomials. Our approach takes advantage of the fact that Milne's phase and amplitude, as well as ${\bf A}(r)$ and $\textbf{B}(r)$, are slowly varying functions. Moreover, the simple change of variable $x=1/r$ allows one to take fully into account the infinite tail of the potentials in a very efficient way.