The collision between two ortho-Positronium (Ps) atoms: a four-body Coulomb problem

TL;DR

This study models the elastic collision between two ortho-positronium atoms as a four-body Coulomb problem, using an ab-initio static-exchange approach to compute phase shifts and cross sections with high precision.

Contribution

It introduces a new coupled-channel SEM code that accurately treats all Coulomb interactions and includes higher partial waves, advancing the theoretical modeling of Ps-Ps collisions.

Findings

Calculated s-, p-, d-wave phase shifts and cross sections for spin states.

Determined scattering lengths and effective ranges using effective range theory.

Provided insights into ortho to para conversion and quenching cross sections.

Abstract

The elastic collision between two ortho-positronium (e.g. S=1) atoms is studied using 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. A coupled-channel methodology in momentum space is used to solve Lippman-Schwinger equation following the integral approach. A new SEM code is developed in which the Born-Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude adapting the partial wave analysis. The s-, p- and d- wave elastic phase shifts and the corresponding partial cross sections for the spin alignment S=0, i.e. singlet (+) and S=2, i.e. triplet (-) states are studied. An augmented-Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross section ( ), the quenching cross section ( ) and ortho to para conversion ratio ( ). The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The theory includes the non-adiabatic short-range effects due to exchange.