Hyperspherical approach to atom--dimer collision with the Jacobi boundary condition

TL;DR

This paper presents a hyperspherical method combined with R-matrix and smooth variable discretization to accurately analyze atom-dimer scattering, demonstrating reliable results and computational efficiency for specific scattering processes.

Contribution

The study introduces a novel hyperspherical approach with Jacobi boundary conditions and R-matrix propagation, improving accuracy and efficiency in atom-dimer scattering calculations.

Findings

The method accurately computes scattering lengths for helium and lithium systems.

The approach shows good convergence and computational savings over previous methods.

It reliably models elastic scattering processes in atom-dimer collisions.

Abstract

In this study, we investigate atom--dimer scattering within the framework of the hyperspherical method. The coupled channel Schr\"odinger equation is solved using the R-matrix propagation technique combined with the smooth variable discretization method. In the matching procedure, the asymptotic wave functions are expressed in the rotated Jacobi coordinates. We apply this approach to the elastic scattering $^{3}$He(T$\uparrow$) + $^{4}$He$_{2}$ and H$\uparrow$ + H$\uparrow$Li processes. The convergence of the scattering length as a function of the propagation distance is studied. We find that the method is reliable and can provide considerable savings over previous propagators.