A Computational Phase Function Method for $\alpha-\alpha$ Scattering: Wavefunction Construction from Single and Two-Term Morse Potentials

TL;DR

This paper introduces a novel application of the phase function method to directly construct scattering wavefunctions for the alpha-alpha system using Morse potentials, showing good agreement with existing methods and highlighting PFM's efficiency.

Contribution

It is the first to use PFM for explicit wavefunction construction in alpha-alpha scattering with Morse potentials, bypassing the need to solve the Schrödinger equation.

Findings

Wavefunctions constructed with PFM agree well with previous methods.

PFM provides a stable and efficient framework for cluster scattering problems.

Results are consistent with resonating-group method calculations.

Abstract

In this work, the phase function method (PFM) is employed for the first time to explicitly construct scattering wavefunctions for the $\alpha\alpha$ system using a single-term Morse potential. Unlike earlier PFM-based studies that primarily focused on reproducing scattering phase shifts, the present approach directly reconstructs radial wavefunctions for the $\ell = 0$, 2, and 4 partial waves without solving the Schr$\ddot{\text{o}}$dinger equation. For comparison, we adopt the interaction potential parameters reported by Sastri et al., who determined them using a two-term reference potential approach with genetic algorithm optimization to accurately reproduce the $\alpha\alpha$ scattering phase shifts. Without re-optimization, we construct the corresponding wavefunctions and find very good agreement with those obtained using our single-term Morse potential. The results also show excellent consistency with the resonating-group method calculations of Hiura \textit{et al.}.These findings demonstrate that PFM provides a numerically stable, efficient, and unified framework for scattering wavefunction construction in cluster-cluster systems.