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Physical Review A

Relativistic coupled-cluster-theory study for low-energy electron scattering with argon

Yongjun Cheng, Shi Liu, Song Bin Zhang, Yong-Bo Tang

Published Jul 30, 2020• 7 citations
Publisher

Abstract

In this work, we carry out an comprehensive study for the electron scattering with atomic argon in the framework of relativistic box-variational method. The phase shifts first are extracted from relativistic coupled-cluster-theory calculations. Then the properties including total elastic, momentum transfer, viscosity cross sections, and differential cross sections are evaluated and compared with available experimental and theoretical data. The validity and accuracy of present method are verified by the good agreement with experimental values, especially for the differential cross sections at small angle forward and backward scattering where obvious discrepancies exist between experiments and theories. The predicted scattering length of $\ensuremath{-}1.39 {a}_{0}$ for electron-argon system is only $2%$ larger in magnitude than the most recent experimental estimate. In addition, the role of electron correlation effect are also investigated in these properties.

DOI
10.1103/physreva.102.012824

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In this work, we carry out an comprehensive study for the electron scattering with atomic argon in the framework of relativistic box-variational method. The phase shifts first are extracted from relativistic coupled-cluster-theory calculations. Then the properties including total elastic, momentum transfer, viscosity cross sections, and differential cross sections are evaluated and compared with available experimental and theoretical data. The validity and accuracy of present method are verified by the good agreement with experimental values, especially for the differential cross sections at small angle forward and backward scattering where obvious discrepancies exist between experiments and theories. The predicted scattering length of \ensuremath−1.39a0\ensuremath{-}1.39 {a}_{0}\ensuremath−1.39a0​ for electron-argon system is only 22%2 larger in magnitude than the most recent experimental estimate. In addition, the role of electron correlation effect are also investigated in these properties.
We report results from new positron–argon total cross-section (TCS) measurements. Agreement with the corresponding recent data of Jones et al (2011 Phys. Rev. A 83 032701) is found to be very good, except at the lowest energies of common measurement. Excellent qualitative agreement is also found between our measurements and an improved convergent close-coupling (CCC) calculation which was undertaken as a part of this study. This level of accord between our experimental and theoretical TCSs has enabled us to determine an experimental scattering length ( a ) of a = −4.9 ± 0.7 au for the positron–argon system. That value is in excellent agreement with the relativistic polarized orbital optical potential approach result of Jones et al ( a = −4.7 au) and our CCC result of a = −4.3 au.
Results for elastic atom-atom scattering are obtained as a first practical application of RmatReact, a new code for generating high-accuracy scattering observables from potential energy curves. RmatReact has been created in response to new experimental methods which have paved the way for the routine production of ultracold (μK) atoms and molecules, and hence the experimental study of chemical reactions involving only a small number of partial waves. Elastic scattering between argon atoms is studied here. There is an unresolved discrepancy between different Ar2 potential energy curves which give different numbers of vibrational bound states and different scattering lengths for the Ar2 dimer. Depending on the number of bound states, the scattering length is either large and positive or large and negative. Scattering observables, specifically the scattering length, effective range, and partial and total cross-sections, are computed at low collision energies and compared to previous results. In general, good agreement is obtained, although our full scattering treatment yields resonances which are slightly lower in energy and narrower than previous determinations using the same potential energy curve.
Results for elastic atom-atom scattering are obtained as a first practical application of RmatReact, a new code for generating high-accuracy scattering observables from potential energy curves. RmatReact has been created in response to new experimental methods which have paved the way for the routine production of ultracold (μK) atoms and molecules, and hence the experimental study of chemical reactions involving only a small number of partial waves. Elastic scattering between argon atoms is studied here. There is an unresolved discrepancy between different Ar2 potential energy curves which give different numbers of vibrational bound states and different scattering lengths for the Ar2 dimer. Depending on the number of bound states, the scattering length is either large and positive or large and negative. Scattering observables, specifically the scattering length, effective range, and partial and total cross-sections, are computed at low collision energies and compared to previous results. In general, good agreement is obtained, although our full scattering treatment yields resonances which are slightly lower in energy and narrower than previous determinations using the same potential energy curve.
Elastic cross-sections for electron scattering on neon from 0 energy up to 16 eV are analyzed by an analytical approach to the modified effective range theory (MERT). It is shown that energy and angular variations of elastic differential, integral and momentum transfer cross-sections can be accurately parameterized by six MERT coefficients up to the energy threshold for the first Feshbach resonance. MERT parameters are determined empirically by numerical comparison with large collection of available experimental data of elastic total (integral) cross-sections. The present analysis is validated against numerous electron beams and swarm experiments. The comparison of derived MERT parameters with those found for other noble gases, helium, argon and krypton, is done. The derived scattering length (for the s-partial wave) in neon, 0.227 a 0, agrees well with recent theories; it is small but, differently from Ar and Kr, still positive. Analogue parameters for the p-wave and the d-wave are negative and positive respectively for all the four gases compared.
Based on the relativistic Dirac R-matrix method, we calculate angle-dependent and momentum-transfer cross sections for electron scattering by Rb, Cs, and Fr atoms at impact energies below 3 eV. Our results for momentum transfer for ${e}^{\ensuremath{-}}+\mathrm{Rb}$ and Cs collisions are compared with available data from swarm experiments. We find clear evidence for a ${\mathrm{Cs}}^{\ensuremath{-}}{(}^{3}{F}^{o})$ shape resonance at 1.528 eV, in excellent agreement with angle-dependent electron-scattering measurements. We analyze and compare the 3Fo{}^{3}{F}^{o}3Fo shape resonance in ${e}^{\ensuremath{-}}+\mathrm{Rb},$ Cs, and Fr elastic collisions.
The results of a joint experimental and theoretical study concerning elastic electron scattering by laser-excited 138 Ba( ... 6s6p 1 P 1 ) atoms are described. These studies demonstrate several important aspects of elastic electron collisions with coherently excited atoms, and are the first such studies. From the measurements, collision and coherence parameters, as well as cross sections associated with an atomic ensemble prepared with an arbitrary in-plane laser geometry and linear polarization (with respect to the collision frame), or equivalently with any magnetic sublevel superposition, have been obtained at 20 eV impact energy and at 10°, 15° and 20° scattering angles. The convergent close-coupling (CCC) method was used within the non-relativistic LS -coupling framework to calculate the magnetic sublevel scattering amplitudes. From these amplitudes all the parameters and cross sections at 20 eV impact energy were extracted in the full angular range in 1° steps. The experimental and theoretical results were found to be in good agreement, indicating that the CCC method can be reliably applied to elastic scattering by 138 Ba( ... 6s6p 1 P 1 ) atoms, and possibly to other heavy elements when spin-orbit coupling effects are negligible. Small but significant asymmetry was observed in the cross sections for scattering to the left and to the right. It was also found that elastic electron scattering by the initially isotropic atomic ensemble resulted in the creation of significant alignment. As a byproduct of the present studies, elastic scattering cross sections for metastable 138 Ba atoms were also obtained.