The elastic collision of two H-like atoms including the exotic Ps and Mu

TL;DR

This paper presents a comprehensive ab-initio study of elastic collisions between H-like atoms, including exotic positronium and muonium, using a static-exchange model and coupled-channel methodology to analyze phase shifts and cross sections.

Contribution

It introduces an advanced SEM code for accurate calculation of elastic scattering, incorporating exchange effects and long-range van der Waals interactions for H-like atom systems.

Findings

Calculated phase shifts and cross sections for various H-like atom collisions.

Demonstrated the influence of long-range van der Waals forces on scattering lengths.

Showed dependence of scattering length on reduced mass and interaction strength.

Abstract

The elastic collision between two H-like atoms utilizing an ab-initio static-exchange model (SEM) in the center of mass (CM) frame considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly, is studied thoroughly. A coupled-channel methodology in momentum space is used to solve Lippman-Schwinger equation following the integral approach. The new SEM code [1-5] in which the Born-Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude using partial wave analysis, is utilized to study the s-, p-, d- wave elastic phase shifts and the corresponding partial cross sections. An augmented-Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross sections. The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The systems studied are Ps-Ps, Ps-Mu, Ps-H, Ps-D, Ps-T, Mu-Mu, Mu-H, Mu-D, Mu-T, H-H, H-D, H-T, D-D, D-T, T-T. The SEM includes the non-adiabatic short-range effects due to exchange. The MSEM code [1] is used to study the effect of the long-range van der Waals interaction due to induced dipole polarizabilities of the atoms in H(1s)-H(1s) elastic collision. The dependence of scattering length on the reduced mass of the system and the dependence of scattering length on the strength of long-range van der Waals interaction that varies with the minimum interatomic distance are observed [3].