Sturmian theory of three-body recombination: application to the formation of H$_2$ in primordial gas

TL;DR

This paper introduces a Sturmian theoretical framework for three-body recombination, enabling comprehensive quantum mechanical calculations of H$_2$ formation in primordial gas, which improves astrophysical models of star formation.

Contribution

It develops a unified Sturmian approach for three-body recombination, incorporating bound, quasi-bound, and continuum states for reactive systems.

Findings

Numerical rate constants for H$_2$ formation with H and He are provided.

The theory accounts for metastable states and non-equilibrium effects.

Results help refine astrophysical simulations of primordial star formation.

Abstract

A Sturmian theory of three-body recombination is presented which provides a unified treatment of bound states, quasi-bound states, and continuum states. The Sturmian representation provides a numerical quadrature of the two-body continuum which may be used to generate a complete set of states within any desired three-body recombination pathway. Consequently, the dynamical calculation may be conveniently formulated using the simplest energy transfer mechanism, even for reactive systems which allow substantial rearrangement. The Sturmian theory generalizes the quantum kinetic theory of Snider and Lowry [J. Chem. Phys. 61, 2330 (1974)] to include metastable states which are formed as independent species. Steady-state rate constants are expressed in terms of a pathway-independent part plus a non-equilibrium correction which depends on tunneling lifetimes and pressure. Numerical results are presented for H$_2$ recombination due to collisions with H and He using quantum mechanical coupled states and infinite order sudden approximations. These results may be used to remove some of the uncertainties that have limited astrophysical simulations of primordial star formation.