Formation of primordial helium: a rapid and simple scheme of calculation

TL;DR

This paper introduces a quick and straightforward computational scheme for modeling the cosmological recombination of helium, utilizing Coulomb Green's functions and Hartree-Fock wavefunctions to calculate transition probabilities.

Contribution

It presents a novel, simplified method for calculating helium recombination processes using integral forms and nonrelativistic Coulomb Green's functions, improving computational efficiency.

Findings

Free-bound transition probabilities are weakly affected by deviations from Coulomb fields.

Transition probabilities are highly sensitive to the choice of bound electron wavefunctions.

The scheme effectively models helium recombination with reduced computational complexity.

Abstract

A rapid and relatively simple scheme of calculation is elaborated and applied to cosmological recombination of helium. Employing the nonrelativistic Coulomb Green's function, a wavefunction of a colliding electron is represented in an integral form applicable for calculations. Bound electrons of helium are described by the Hartree-Fock wavefunctions. The free-bound transition probabilities into excited states of helium, and the probabilities of bound-bound transitions in helium are calculated in different modes. It is revealed that free-bound transition probabilities weakly depend on to what extent a field experienced by a colliding electron deviates from the purely Coulomb field with charge Z=1, whereas these probabilities strongly depend on the choice of a wavefunction of a bound active electron involved in recombination.