The importance of an accurate target wavefunction in variational calculations for (e⁺–H₂) scattering

Abstract

Abstract. Using the complex Kohn method, we have calculated variational values of phase shifts and the annihilation parameter, Z eff , for the elastic scattering of positrons by molecular hydrogen. Our results are sensitive to small changes in the accuracy of the wave function representing the target hydrogen molecule. We have developed a systematic approach to demonstrate that, at low positron energies, there are particular forms of the Kohn trial wave function for which the results of variational calculations are not reliable, even when the target wave function accounts for as much as 96.8% of the correlation energy of H 2 . We find that reliable results can be recovered if our calculations are extended to admit more sophisticated target wave functions accounting for 99.7% of the correlation energy. Remaining discrepancies between theory and experiment are briefly discussed.

Positron Scattering and Annihilation from the Hydrogen Molecule at Zero Energy

“…This is a significant achievement since the annihilation cross section presents a stringent test to the accuracy of the scattering wave function [7] and its successful prediction solves a previously intractable problem. Our calculations also show the existence of an unexpected virtual state at a H 2 inter-nuclear distance of R ≈ 3.4 a 0 .There have been a number of calculations of low energy e + -H 2 scattering and annihilation [7,8,9,10,11]. At present, all previous calculations significantly underestimate the low energy annihilation cross section.…”

“…At present, all previous calculations significantly underestimate the low energy annihilation cross section. The most sophisticated calculations are the Kohn variational calculations performed by Armour and colleagues at the University of Nottingham (UN) [9,11,12]. Their most recent calculations significantly underestimate the annihilation cross section at thermal energies.…”

Theory and application of explicitly correlated Gaussians

“…The strong electron-positron interactions mandate the use of a correlated basis. Calculations of the low-energy cross section with Hylleraas basis sets (Armour and Baker, 1986;Cooper, Armour, and Plummer, 2008) had not been able to achieve convergence due to difficulties in calculating the matrix elements. However, matrix element evaluation of the ECG basis did not pose any insuperable problems in a recent calculation of zeroenergy e þ -H 2 scattering.…”

Muon, positron and antiproton interactions with atoms and molecules

“…Details of the first calculations carried out without using the method of models are given in [22]. Earlier calculations by the generalised Kohn method used the method of models [23].…”

“…In a very recent, very accurate calculation of Z eff (k) at very low energies, Zhang et al [27] find similar behaviour to the behaviour we find using the method of models as R increases beyond 1.6a 0 . The more accurate value obtained by the method of models, despite using a less accurate target wave function, may be due to the better convergence behaviour that is obtained using this method [28,22].…”