Schwinger Variational Principle Research Articles

Theoretical study of time-resolved photoelectron circular dichroism in the photodissociation of a chiral molecule.

Photoelectron circular dichroism (PECD), the forward-backward asymmetry of the photoelectron angular distribution when ionizing randomly oriented chiral molecules with circularly polarized light, is an established method to investigate chiral properties of molecules in their electronic ground state. Here, we develop a computational strategy for predicting time-resolved PECD (TRPECD) of chemical reactions and demonstrate the method on the photodissociation of 1-iodo-2-methylbutane. Our approach combines multi-configurational quantum-chemical calculations of the relevant potential-energy surfaces of the neutral and singly ionized molecule with ab initio molecular-dynamics (AIMD) calculations. The PECD parameters along the AIMD trajectories are calculated with the aid of electron-molecule scattering calculations based on the Schwinger variational principle implemented in ePolyScat. Our calculations have been performed for two probe wavelengths (133 and 160 nm) accessible through low-order harmonic generation in gases. Our results show that the TRPECD is a highly sensitive probe of photochemical reaction dynamics. Most interestingly, the TRPECD is found to change sign multiple times along the photodissociation coordinate, in agreement with recent experiments on CHBrFI [Svoboda et al., "Femtosecond photoelectron circular dichroism of chemical reactions," Sci. Adv. 8, eabq2811 (2022)]. The computational protocol introduced in the present work is general and readily applicable to other chiral photochemical processes.

Rearrangement Collisions in the Schwinger Variational Principle: A Long-Standing Problem in Positron Scattering Physics.

In this letter, we propose a functional on the basis of the Schwinger variational principle that accounts for the particle rearrangement by solving a projected Lippmann-Schwinger equation system. The method is tested in the static-coupled approximation for positron-H, where excellent agreements with benchmark results are found for the elastic, positronium (Ps) formation and annihilation cross sections. The effect of virtual Ps formation is evidenced through the analysis of the annihilation map. A significant increase in the electron-positron density in the vicinity of the atom is obtained.

The basis set, scattering wavefunction and Schwinger variational principle: an application for low energy positron-atom scattering

The quality of the positron wavefunction produced by applying the Schwinger variational principle (SVP) is scrutinized. An optical potential formalism is applied considering a semiempirical polarization potential. The positron wavefunction is expanded into a basis set formed by hydrogen-like atom eigenfunctions. Two different forms for the ansatz are tested out. The model is applied to positron scattering and annihilation by hydrogen, and by argon atoms as examples. The results are compared to the ones obtained through the direct integration of the Schrödinger equation. We found that the positron wavefunction generated by the SVP is of good quality only if the basis functions are mainly located inside the potential range. We also found that to provide the best scattering amplitude possible, the SVP may produce intentional deviations all along the positron wavefunction to compensate for local basis set deficiencies. We proposed a criterion based on the Lippmann–Schwinger equation to evaluate the accuracy of the positron wavefunction.

A pedagogical introduction to the Schwinger variational principle: an application to low energy positron-atom scattering

We present a pedagogical introduction to the Schwinger variational principle. As a model problem, we consider the low energy positron-atom scattering in the static approximation. The mathematical aspects and physical assumptions of the method, with attention to the construction and selection of trial scattering basis sets, are discussed in detail. Emphasis is given in the numerical implementation, usually neglected in scattering textbooks where the Schwinger variational principle is presented. Issues of convergence, phase shifts, scattering lengths and elastic cross sections are presented for positron-hydrogen and positron-krypton scattering.

Scattering of charged particles in quantum plasmas: Zero energy resonances

The scattering of charged particles in quantum plasmas (QPs) has been investigated by employing a fully quantum mechanical treatment within the framework of the Schwinger variational principle in the momentum space. The effective potential in QP has been described by a modified Debye-Huckel potential. Scattering phase shifts for various plasma screening strengths have been obtained accurately by a convergent scheme of the Schwinger variational method. The accuracy of the results has been corroborated by solving the corresponding Schrodinger equation with accurate numerical techniques. The nature of scattering for a wide range of plasma screening has been studied. The role of quantum mechanical effects in plasma is examined by comparing the results in QP with the corresponding results in classical weakly coupled plasma for which effective potential has been described by Debye-Huckel potential. Special emphasis has been made to study the dynamics at low energies. In particular, a detailed investigation has been made on the zero-energy resonance phenomenon.

Variational study of atomic hydrogen excitation by proton impact at intermediate velocities: target continuum states contribution

The Schwinger variational principle is used to evaluate the cross section for the excitation and Balmer-α emission of the hydrogen atom. The target is projected by proton impact at energies between 2 and 200 keV. To describe the strong coupling between the excitation and capture channels at intermediate impact energies, the Coulomb wave function, that is, exact continuum states of the hydrogen atom, have been added in the expansion of the scattering wave function. From comparison with the available experimental data and other theoretical findings we remark that taking into account the continuum states of the target is a good choice to describe the capture states at medium and low velocities, thus making the variational approach given in this work an easy way to successfully study the excitation of atoms by ion impacts at intermediate velocities.

Schwinger-variational-principle theory of collisions in the presence of multiple potentials

A theoretical method for treating collisions in the presence of multiple potentials is developed by employing the Schwinger variational principle. The current treatment agrees with the local (regularized) frame transformation theory and extends its capabilities. Specifically, the Schwinger variational approach gives results without the divergences that need to be regularized in other methods. Furthermore, it provides a framework to identify the origin of these singularities and possibly improve the local frame transformation. We have used the method to obtain the scattering parameters for different confining potentials symmetric in $x,y$. The method is also used to treat photodetachment processes in the presence of various confining potentials, thereby highlighting effects of the infinitely many closed channels. Two general features predicted are the vanishing of the total photoabsorption probability at {\it every} channel threshold and the occurrence of resonances below the channel thresholds for negative scattering lengths. In addition, the case of negative ion photodetachment in the presence of uniform magnetic fields is also considered where unique features emerge at large scattering lengths.

Alkali-atom photoionization and negative-ion photodetachement processes in the presence of external fields

SynopsisProcesses of alkali-atom photoionization and negative ion photodetachement in the presence of external fields are investigated. The corresponding photoabsorption spectra are interpreted by employing the theoretical framework of Schwinger variational principle and the local frame transformation theory.

Recent advances in the application of the Schwinger multichannel method with pseudopotentials to electron-molecule collisions

The Schwinger multichannel method [K. Takatsuka and V. McKoy, Phys. Rev. A 30, 1734 (1984)], which is based on the Schwinger variational principle for the scattering amplitude [J. Schwinger, Phys. Rev. 72, 742 (1947)], was designed to account for exchange, polarization and electronically multichannel coupling effects in the low-energy region of electron scattering from molecules with arbitrary geometry. The applications of the method became more ambitious with the availability of computer power combined with parallel processing, use of norm-conserving pseudopotentials and improvement of the description of target excited states (minimal orbital basis for single configuration interaction). The most recent applications involving 33 and 45 electronically open channels for phenol and ethylene molecules, represent good examples of the present status of the method. In this colloquium, we review the strategy and point out new directions to apply the method in its full extension.

Schwinger Variational Approach for the Evaluation of Balmer-α Emission Cross Sections in Proton-Hydrogen Atom Collision at Intermediate Impact Energies

A variational impact parameter approach based on the Schwinger variational principle used to evaluate the Balmer-α excitation cross sections of hydrogen targets impacted by protons for incident energies ranging from 10 to 200 keV is here reported. The obtained total cross sections are compared to the available data, and the huge discrepancies between the existing theoretical predictions and the experimental measurements are pointed out.

Schwinger’s variational principle in Einstein-Cartan gravity

By applying Schwinger's variational principle to the Einstein-Cartan action for the gravitational field, we derive quantum commutation relations between the metric and torsion tensors.

Excitation Cross Section within Schwinger Variational Principal and Pseudo State Method in a Set of Slater Type Functions

We use Schwinger variational principle to evaluate excitation cross section of atomic hydrogen by proton impact at energy range between 2keV and 200keV. Contribution of the continuum near ionization threshold was introduced in a model using L2 method developed in a pseudo-space spanned by a set of Slater type functions. Our results were compared with those of Bouamoud (1988-1989) using 1s, 2s and 2p state of hydrogen atom.

Bending-induced diminution of shape resonances in the core-level absorption region of hot CO2 and N2O

We have measured the initial vibrational-state-specific, symmetry-resolved ion-yield spectra of CO2 and N2O in the shape resonance regions above the K-shell ionization thresholds. For both molecules, significant diminution of the shape resonances by bending excitation in the initial electronic ground state is observed. The measured ion-yield spectra are well reproduced by calculations employing the Schwinger variational principle. The observed changes in the spectra are seen to be due to a shift of the resonances to lower energy and an initial increase in width with bending.

A study of pseudoresonances in the application of the schwinger variational principle to electron scattering from atomic hydrogen

The Schwinger variational principle is applied to s-wave electron-hydrogen atom scattering. Computationally, consistent with a recent paper by Apagyi et al. (1988), there are pseudoresonances at the static exchange level of approximation, but not at the static level. The T-matrix as well as the K-matrix version of the Schwinger principle is used with a real Slater basis, and the same results are obtained in both. The origin of the pseudoresonances from singularities in the separable potential that is effectively employed in the Lippman-Schwinger equation from which the Schwinger variational principle can be derived. The determination of the pseudoresonance parameters from the separable potential is computationally inexpensive and may be used to predict the pseudoresonance parameters for the scattering calculations so as to avoid them.

Exponential correlated basis in Schwinger variational principle for positronium formation in hydrogen

An exponential correlated basis set is tested within the framework of multi-channel Schwinger variational principle in the momentum space. It is found that inclusion of only the positron-electron correlation in the basis set is enough to obtain accurate results for all significant partial waves for ground state positronium formation in positron-hydrogen collisions at low and intermediate energies (6.856–75 eV). Results are in conformity with other accurate variational and non-variational calculations as well as observed data available in the literature.

Massless DKP field in a Lyra manifold

Massless scalar and vector fields are coupled to the Lyra geometry by means of the Duffin–Kemmer–Petiau (DKP) theory. Using the Schwinger variational principle, the equations of motion, conservation laws and gauge symmetry are implemented. We find that the scalar field couples to the anholonomic part of the torsion tensor, and the gauge symmetry of the electromagnetic field does not break by the coupling with torsion.

Spinorial Field and Lyra Geometry

The Dirac field is studied in a Lyra space-time background by means of the classical Schwinger Variational Principle. We obtain the equations of motion, establish the conservation laws, and get a scale relation relating the energy-momentum and spin tensors. Such scale relation is an intrinsic property for matter fields in Lyra background.

Elastic electron scattering by fullerene,C60

We report cross sections for elastic scattering of low-energy electrons by fullerene, C60, calculated within the static-exchange approximation. The calculations are carried out via the Schwinger multichannel (SMC) method, equivalent in this case to the standard Schwinger variational principle. Combining the high parallel efficiency of the SMC method with a quadrature specially adapted to the high symmetry of C60 facilitates the most demanding step of the calculation and so permits the use of a large basis set. We analyze the structure of the cross section with reference to a simple spherical-shell model, and we compare our results to prior measurements and calculations.

Electromagnetic field in Lyra manifold: a first order approach

We discuss the coupling of the electromagnetic field with a curved and torsioned Lyra manifold using the Duffin-Kemmer-Petiau theory. We will show how to obtain the equations of motion and energy-momentum and spin density tensors by means of the Schwinger Variational Principle.

Correlated dipole-polarized basis in Schwinger’s principle for elastic positron-hydrogen collisions

Definitive results for elastic positron-hydrogen collisions are obtained using the Schwinger variational principle in the momentum space at low and intermediate energies corresponding to momenta in the range ${k}_{i}=0\text{--}3.5\phantom{\rule{0.3em}{0ex}}\text{atomic units}$. The discrete basis set used in the calculation makes allowance for long-range dipole polarization, atomic distortion, and infinite-order short-range positron-electron correlation. Results for the scattering parameters, such as the scattering length, phase shifts for all significant partial waves, and total cross section, are in conformity with other accurate variational and nonvariational calculations available in the literature.