Correlation–polarization effects in electron/positron scattering from acetylene: A comparison of computational models

doi:10.1016/j.nimb.2007.12.019

Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms

Volume 266, Issue 3, February 2008, Pages 425-434

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Abstract

Different computational methods are employed to evaluate elastic (rotationally summed) integral and differential cross sections for low energy (below about 10 eV) positron scattering off gas-phase C₂H₂ molecules. The computations are carried out at the static and static-plus-polarization levels for describing the interaction forces and the correlation–polarization contributions are found to be an essential component for the correct description of low-energy cross section behavior. The local model potentials derived from density functional theory (DFT) and from the distributed positron model (DPM) are found to produce very high-quality agreement with existing measurements. On the other hand, the less satisfactory agreement between the R-matrix (RM) results and measured data shows the effects of the slow convergence rate of configuration-interaction (CI) expansion methods with respect to the size of the CI-expansion. To contrast the positron scattering findings, results for electron–C₂H₂ integral and differential cross sections, calculated with both a DFT model potential and the R-matrix method, are compared and analysed around the shape resonance energy region and found to produce better internal agreement.

Introduction

The increase of interest in high-quality measurements involving antimatter has attracted,in recent years, the attention of experimentalists and theoreticians in the field of molecular physics [1], [2], [3], [4], [5]. This has generated a wealth of new information on the nanoscopic behavior of a broad variety of molecular systems when they are made to interact with beams of positrons at thermal and near-thermal energies. To understand the interaction of positron beams with matter, it becomes important to also be able to distinguish to what extent the additional features of positron interaction with molecules (e.g. Ps formation and positron annihilation) are related to positron dynamics and to positron–electron correlation features. The study of even the simplest of such observables, e.g. the elastic scattering integral and differential cross sections occurring below the thresholds of Positroniun (Ps) formation in polyatomic gases, already provides a very useful testing ground for the theoretical and computational models which are currently employed to analyze positron-matter dynamics [2].

While the electrostatic interaction can in principle be described exactly by an essentially repulsive potential due to the molecular network of ( electrons + nuclei), different approximations for correlation–polarization effects – the $V_{pcp}$ potential – play an essential role in deciding the quality of the adopted theoretical model over the whole range of relevant distances between target and the positron projectile. As the projectile nears the target, in fact, the repulsive Coulombic core further slows it down while the attraction from the bound electrons increases and strongly modifies its motion in the intermediate range of distances via a correlation mechanism reminiscent of multiple scattering effects [6]. This short-range effect should therefore be energy-dependent and nonlocal and would asymptotically give rise to charge-induced polarization effects, the leading term of which will be given via the dipole-polarizability of the target molecule [6]. The evaluation of the $V_{pcp}$ contribution to positron–molecule interaction is therefore central to theoretical scattering calculations and its correct evaluation within cross section modelling studies is one of the stumbling blocks to the quantitative interpretation of existing experimental findings.

In the present paper we therefore carry out a detailed comparison of the results of different theoretical approximations for the correlation–polarization forces by using the acetylene molecule as a benchmark system, in view of the availability of good quality experimental data on this system and of its relatively simple structure as a polyatomic target.

The structure of the paper shall be the following: in the next Section 2 we will report in some detail an outline of the methods employed to generate correlation–polarization and static potentials while Section 3 will give and discuss our results for the elastic (rotationally summed) integral cross sections. The differential cross sections will also be given by Section 3, while our conclusions will be collected in Section 4.

Section snippets

Scattering equations and interaction forces

In order to carry out our comparison between different treatments of correlation–polarization forces, we have tested three different approaches: we have employed the single-center-expansion (SCE) treatment of the scattering problem and included the $V_{pcp}$ potential in two different ways, i.e. the Density functional modelling (DFT), used by us before [7] and the distributed positron model (DPM) also introduced earlier on [8] and employed within the SCE treatment. We have then tested a

Low-energy positron scattering from C₂H₂ targets

As mentioned in the Introduction, the present study intends to select gaseous C₂H₂ as a benchmark system for an extended comparison of methods. Some of the earlier work on this molecule, both for positron and electron scattering studies, has been carried out by some of the present authors [24], [25], [26]. Therefore, the present work employs the same molecular geometry to describe the equilibrium structure of the target, the same quality of Hartree-Fock basis set and, whenever necessary, the

Present conclusions

In the present work we have tried to analyze in some detail the relative performances of different computational treatments for obtaining low-energy scattering observables (integral cross sections and angular distributions in the elastic channels) associated with both positron and electron low-energy collisions with a specific polyatomic target: the C₂H₂ molecule at its equilibrium geometry.

In particular, we have first made sure that both methods are comparable when the interaction forces are

Acknowledgements

J.F., J.T. and K.L.B. acknowledge funding from both EPSRC and the Royal Society through their India–UK exchange program. J.F. thanks the EIPAM network of the European Science Foundation (ESF) for the award of a fellowship at the beginning of the present work. F.A.G. further thanks the CASPUR Consortium for the availability of computational time for the present project. This work was also supported by the Robert A. Welch Foundation (Houston, TX) under grant A-1020.

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Correlation–polarization effects in electron/positron scattering from acetylene: A comparison of computational models

Abstract

Introduction

Section snippets

Scattering equations and interaction forces

Low-energy positron scattering from C2H2 targets

Present conclusions

Acknowledgements

Nucl. Instr. Meth. B

Phys. Rep.

Ann. Phys. NY

Radiat. Phys. Chem.

Nucl. Instr. and Meth. B

Computer Phys. Comms.

Nucl. Instr. and Meth. B

Comp. Phys. Comms.

Comput. Phys. Commun.

Nucl. Instr. and Meth. B

Positron Physics

Rev. Mod. Phys.

Adv. Chem. Phys.

J. Phys. B

J. Phys. F

Phys. Rev. A

J. Phys. B

Phys. Rev. A

J. Phys. B: At. Mol. Opt. Phys.

J. Phys. B

Phys. Rev.

Low-energy positron scattering from C₂H₂ targets