[Paper Review] Mutual neutralization in low energy H^+ + H^- collisions

Michael Stenrup, Åsa Larson+1 more|ArXiv.org|Feb 11, 2009

High-Energy Particle Collisions Research3 citations

TL;DR

This study presents a fully quantum mechanical ab initio investigation of mutual neutralization in low-energy H⁺ + H⁻ collisions using a molecular close-coupling approach with full treatment of nuclear quantum effects and nuclear identity. The work computes state-resolved and total neutralization cross sections for H(1) + H(n), n=1,2,3, finding good agreement with prior theoretical studies but a factor of two to three lower than the experimental cross section from Moseley et al. (1970), suggesting possible overestimation in that measurement at low energies.

ABSTRACT

The mutual neutralization of H^+ and H^- ions at low collision energies is studied by means of a molecular close-coupling approach. All degrees of freedom are treated at the full quantum level taking into account also the identity of the nuclei. The relevant ^1Sigma_g,u^+ electronic states and their associated nonadiabatic radial couplings are calculated for internuclear distances between 0.5 and 50 a_0. Following a transformation into a strictly diabatic basis, these quantities enter into a set of coupled equations for the motion of the nuclei. Numerical solution of these equations allows the cross sections for scattering into the H(1)+H^*(n), n=1,2,3 channels to be calculated. In the present paper, results are reported for the collision energy region 0.001 to 100 eV, with special emphasis on the important energy region below 10 eV. The low temperature rate coefficient is obtained from a parametrization of the calculated neutralization cross section and is estimated to be valid in the range 10 to 10 000 K.

Motivation & Objective

• To provide a benchmark-quality quantum mechanical study of the simplest ion-ion reaction: H⁺ + H⁻ → H(1) + H(n), for accurate theoretical validation.
• To resolve discrepancies between low-energy experimental cross sections (Moseley et al., 1970) and prior theoretical predictions, particularly in the 0.001–10 eV energy range relevant to astrophysical environments.
• To rigorously account for nuclear quantum effects, electronic non-adiabatic couplings, and nuclear identity (spin statistics) in the scattering calculation.
• To compute state-specific and total neutralization cross sections and derive a low-temperature rate coefficient valid from 10 to 10,000 K for use in astrochemical modeling.

Proposed method

• Employ a molecular close-coupling approach with full quantum treatment of all nuclear and electronic degrees of freedom, including nuclear spin and identity.
• Calculate adiabatic potential energy curves and non-adiabatic radial coupling matrix elements for 1Σg⁺ and 1Σu⁺ electronic states across internuclear distances from 0.5 to 50 a₀ using ab initio electronic structure methods.
• Transform the adiabatic representation into a strictly diabatic basis to enable accurate solution of the coupled nuclear Schrödinger equations.
• Solve the resulting coupled equations numerically to obtain scattering amplitudes and cross sections for neutralization into H(1) + H(n), n=1,2,3.
• Combine gerade and ungerade symmetry contributions using proper nuclear spin statistics to account for identical particle exchange.
• Derive the low-temperature rate coefficient via parametrization of the calculated cross sections, valid over 10–10,000 K.

Experimental results

Research questions

• RQ1 What is the accurate state-resolved neutralization cross section for H⁺ + H⁻ collisions at low energies (0.001–10 eV), particularly for H(n) final states with n=1,2,3?
• RQ2 How do non-adiabatic couplings and nuclear quantum effects influence the mutual neutralization dynamics in this prototypical ion-ion reaction?
• RQ3 Why is there a discrepancy between the low-energy experimental cross section of Moseley et al. (1970) and theoretical predictions, and which is more reliable?
• RQ4 To what extent does the inclusion of nuclear identity (spin statistics) affect the total cross section, especially at low collision energies?
• RQ5 What is the low-temperature rate coefficient for this reaction, and how does it compare with experimental and theoretical estimates?

Key findings

• The calculated total neutralization cross section is in good agreement with previous theoretical studies by Bates and Lewis (1955), Fussen and Kubach (1986), and Eerden et al. (1995) in the 0.001–10 eV range.
• The present results are consistently a factor of two to three lower than the experimental cross section reported by Moseley et al. (1970), suggesting possible overestimation in that measurement.
• For collision energies below a few eV, the majority of neutral products are formed in the H(n=3) final state, consistent with conventional expectations.
• The weighting of gerade and ungerade symmetry contributions is only significant for n=2 formation at low energies, where cross sections are small.
• The low-temperature rate coefficient is parametrized and estimated to be valid over the astrophysically relevant range of 10 to 10,000 K.
• The study confirms that nuclear identity effects are negligible for total cross sections at low energies, except in minor contributions to n=2 formation.