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.

Jan 1, 201910 citations

Ultracold Atom-Atom Scattering with R-Matrix Methods

Tom Rivlin

Novel experimental methods have allowed for the routine production of ultracold (sub-Kelvin) atoms and small molecules. This has facilitated the study of chemical reactions involving only a small number of partial waves, allowing for unprecedented control over ultracold chemical reactions. This thesis describes work towards a new set of theories, based on Wigner's R-matrix methodology, which are adapted for so-called heavy particle scattering, and in particular atom-atom scattering. From these new theories a new set of methods are constructed to accurately simulate scattering observables such as scattering lengths, cross-sections, and resonances for atom-atom scattering events at ultracold temperatures by producing high resolution plots of these observables. The methods utilise software built for high-accuracy diatomic spectra, such as Duo, to provide molecular eigenenergies and wavefunctions of the bound system at short internuclear distances (in a region known as the inner region), only requiring as input a matrix of diatomic internuclear potential energy curves and couplings. These methods then act as 'harnesses', allowing this information to be used to perform an R-matrix propagation at long internuclear distances (in a region known as the outer region) using R-matrix propagation codes such as PFARM. The result of this propagation is then used to produce the aforementioned scattering observables. In this work these new R-matrix methods are applied to the case of a particle scattering off a Morse potential, to elastic argon-argon collisions, and to the intramultiplet mixing of oxygen when impacted by helium. This work also serves as a basis for the future simulation of more complex scattering events, such as atom-diatom collisions and higher polyatomic collisions.Novel experimental methods have allowed for the routine production of ultracold (sub-Kelvin) atoms and small molecules. This has facilitated the study of chemical reactions involving only a small number of partial waves, allowing for unprecedented control over ultracold chemical reactions. This thesis describes work towards a new set of theories, based on Wigner's R-matrix methodology, which are adapted for so-called heavy particle scattering, and in particular atom-atom scattering. From these new theories a new set of methods are constructed to accurately simulate scattering observables such as scattering lengths, cross-sections, and resonances for atom-atom scattering events at ultracold temperatures by producing high resolution plots of these observables. The methods utilise software built for high-accuracy diatomic spectra, such as Duo, to provide molecular eigenenergies and wavefunctions of the bound system at short internuclear distances (in a region known as the inner region), only requiring as input a matrix of diatomic internuclear potential energy curves and couplings. These methods then act as 'harnesses', allowing this information to be used to perform an R-matrix propagation at long internuclear distances (in a region known as the outer region) using R-matrix propagation codes such as PFARM. The result of this propagation is then used to produce the aforementioned scattering observables. In this work these new R-matrix methods are applied to the case of a particle scattering off a Morse potential, to elastic argon-argon collisions, and to the intramultiplet mixing of oxygen when impacted by helium. This work also serves as a basis for the future simulation of more complex scattering events, such as atom-diatom collisions and higher polyatomic collisions.

Dec 28, 20190 citations

Low-temperature scattering with the R-matrix method: from nuclear scattering to atom-atom scattering and beyond

Tom Rivlin, L. K. McKemmish, K. Eryn Spinlove +1 more

The R-matrix method is a fully-quantum time-independent scattering method, used to simulate nuclear, electron-atom, electron-ion, electron-molecule scattering and more. Here, a novel R-matrix method, RmatReact, is presented as applied to ultracold (sub-Kelvin) atom-atom scattering. This is in response to experimental methods which in recent decades have facilitated the routine use of ultracold atoms and small molecules in experiments. This project lays the groundwork for future codes to eventually simulate polyatom-polyatom reactive collisions. Results are presented in this paper for numerical comparisons to other established methods, and for resonances in the elastic scattering of ultracold argon atoms.The R-matrix method is a fully-quantum time-independent scattering method, used to simulate nuclear, electron-atom, electron-ion, electron-molecule scattering and more. Here, a novel R-matrix method, RmatReact, is presented as applied to ultracold (sub-Kelvin) atom-atom scattering. This is in response to experimental methods which in recent decades have facilitated the routine use of ultracold atoms and small molecules in experiments. This project lays the groundwork for future codes to eventually simulate polyatom-polyatom reactive collisions. Results are presented in this paper for numerical comparisons to other established methods, and for resonances in the elastic scattering of ultracold argon atoms.

arXiv:1911.00027Oct 31, 20190 citations

Low-temperature chemistry using the R-matrix method

Jonathan Tennyson, L. K. McKemmish, Tom Rivlin

Techniques for producing cold and ultracold molecules are enabling the study of chemical reactions and scattering at the quantum scattering limit, with only a few partial waves contributing to the incident channel, leading to the observation and even full control of state-to-state collisions in this regime. A new R-matrix formalism is presented for tackling problems involving low- and ultra-low energy collisions. This general formalism is particularly appropriate for slow collisions occurring on potential energy surfaces with deep wells. The many resonance states make such systems hard to treat theoretically but offer the best prospects for novel physics: resonances are already being widely used to control diatomic systems and should provide the route to steering ultracold reactions. Our R-matrix-based formalism builds on the progress made in variational calculations of molecular spectra by using these methods to provide wavefunctions for the whole system at short internuclear distances, (a regime known as the inner region). These wavefunctions are used to construct collision energy-dependent R-matrices which can then be propagated to give cross sections at each collision energy. The method is formulated for ultracold collision systems with differing numbers of atoms.Techniques for producing cold and ultracold molecules are enabling the study of chemical reactions and scattering at the quantum scattering limit, with only a few partial waves contributing to the incident channel, leading to the observation and even full control of state-to-state collisions in this regime. A new R-matrix formalism is presented for tackling problems involving low- and ultra-low energy collisions. This general formalism is particularly appropriate for slow collisions occurring on potential energy surfaces with deep wells. The many resonance states make such systems hard to treat theoretically but offer the best prospects for novel physics: resonances are already being widely used to control diatomic systems and should provide the route to steering ultracold reactions. Our R-matrix-based formalism builds on the progress made in variational calculations of molecular spectra by using these methods to provide wavefunctions for the whole system at short internuclear distances, (a regime known as the inner region). These wavefunctions are used to construct collision energy-dependent R-matrices which can then be propagated to give cross sections at each collision energy. The method is formulated for ultracold collision systems with differing numbers of atoms.

arXiv:1609.06059Faraday DiscussionsJan 1, 201615 citations

Elastic Scattering of Sodium Atoms at Ultracold Temperatures

Jicai Zhang, Jinfeng Sun, Jiemin Wang

The calculations of the elastic scattering properties for collisions between two 23Na atoms at ultra-cold temperatures are reported and compared with experimental and theoretical results in the detail. We present a parametric model potential for the triplet molecular state of the 23Na molecule, and calculate the scattering length ɑ(subscript t) and the effective range r(subscript e) by using the semiclassical and Numerov methods, respectively. The shape resonances occur in the collisions at low energies, and resonance positions and widths are computed by Briet-Wigner formula. In addition, we also present other results that include differential cross sections at zero energy limit.The calculations of the elastic scattering properties for collisions between two 23Na atoms at ultra-cold temperatures are reported and compared with experimental and theoretical results in the detail. We present a parametric model potential for the triplet molecular state of the 23Na molecule, and calculate the scattering length ɑ(subscript t) and the effective range r(subscript e) by using the semiclassical and Numerov methods, respectively. The shape resonances occur in the collisions at low energies, and resonance positions and widths are computed by Briet-Wigner formula. In addition, we also present other results that include differential cross sections at zero energy limit.

Journal of Atomic and Molecular PhysicsFeb 20, 20070 citations

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

Yongjun Cheng, Shi Liu, Song Bin Zhang +1 more

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.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.

Physical Review AJul 30, 20207 citations

2%

larger in magnitude than the most recent experimental estimate. In addition, the role of electron correlation effect are also investigated in these properties.