The rotating Morse potential model for diatomic molecules in the J-matrix representation: II. The S-matrix approach

TL;DR

This paper presents an improved S-matrix approach using the J-matrix method to accurately compute bound states and resonances in the rotating Morse potential for diatomic molecules, handling various potential types.

Contribution

It introduces a refined, highly accurate computational method for bound and resonance states in the rotating Morse potential using an infinite basis and the S-matrix approach.

Findings

Enhanced accuracy over previous methods

Effective for both regular and inverted Morse potentials

Handles analytic, non-analytic, and 1/r singular potentials

Abstract

This is the second article in which we study the rotating Morse potential model for diatomic molecules using the tridiagonal J-matrix approach. Here, we improve further the accuracy of computing the bound states and resonance energies for this potential model from the poles of the S-matrix for arbitrary angular momentum. The calculation is performed using an infinite square integrable basis that supports a tridiagonal matrix representation for the reference Hamiltonian, which is included in the computations analytically without truncation. Our method has been applied to both the regular and inverted Morse potential with favorable results in comparison with available numerical data. We have also shown that the present method adds few significant digits to the accuracy obtained from the finite dimensional approach (e.g. the complex rotation method). Moreover, it allows us to handle easily both analytic and non-analytic potentials as well as 1/r singular potentials.