Many-body Theory Calculations Research Articles

Many-body theory calculations of positron binding to halogenated hydrocarbons

Positron binding energies in halogenated hydrocarbons are calculated using many-body theory. For chlorinated molecules, including planars for which the interaction is highly anisotropic, very good to excellent agreement with experiment and recent density-functional-theory-based model-potential calculations is found. Predictions for fluorinated and brominated molecules are presented. The comparative effect of fluorination, chlorination, and bromination is elucidated by identifying trends within molecular families including dihaloethylenes and halomethanes based on global molecular properties (dipole moment, polarizability, ionization energy). It is shown that relative to brominated and chlorinated molecules, fluorinated molecules generate a less attractive positron-molecule potential due to larger ionization energies and smaller density of molecular orbitals close to the highest occupied molecular orbital, resulting in very weak, or in most cases loss of, positron binding. Overall, however, it is shown that the global molecular properties are not universal predictors of binding energies, exemplified by consideration of CH3Cl vs -C2H2F2: Despite the latter having a larger dipole moment, lower ionization energy, and similar polarizability, its binding energy is significantly smaller (25 vs 3 meV, respectively), owing to the important contribution of multiple molecular orbitals to, and the anisotropy of, the positron-molecule correlation potential. Published by the American Physical Society 2024

Many-body theory calculations of positron binding to hydrogen cyanide

Positron bound state properties in hydrogen cyanide are studied via many-body theory calculations that account for strong positron-electron correlations including positron-induced polarization, screening of the electron–positron Coulomb interaction, virtual-positronium formation and positron–hole repulsion. Specifically, the Dyson equation is solved using a Gaussian basis, with the positron self-energy in the field of the molecule calculated using the Bethe–Salpeter equations for the two-particle and particle–hole propagators. The present results suggest near cancellation of screening corrections to the bare polarization, and the non-negligible role of the positron–hole interaction. There are no existing measurements to compare to for HCN. Previous configuration interaction (CI) and fixed-node diffusion Monte Carlo (FN-DMC) calculations give positron binding energies in the range 35–44 meV, most of which used a single even-tempered basis centred near the nitrogen atom. Using a similar single-centre positron basis we calculate a positron binding energy of 41 meV, in good agreement. However, we find that including additional basis centres gives an improved description of the positron wave function near the nuclei, and results in a converged binding energy in the range 63–73 meV (depending on geometry and approximation to the positron–molecule correlation potential used).Graphical

Many-body theory calculations of positronic-bonded molecular dianions.

The energetic stability of positron-dianion systems [A-;e+; A-] is studied via many-body theory, where A- includes H-, F-, Cl-, and the molecular anions (CN)- and (NCO)-. Specifically, the energy of the system as a function of ionic separation is determined by solving the Dyson equation for the positron in the field of the two anions using a positron-anion self-energy as constructed in Hofierka et al. [Nature 606, 688 (2022)] that accounts for correlations, including polarization, screening, and virtual-positronium formation. Calculations are performed for a positron interacting with H22-, F22-, and Cl22- and are found to be in good agreement with previous theory. In particular, we confirm the presence of two minima in the potential energy of the [H-;e+; H-] system with respect to ionic separation: a positronically bonded [H-;e+; H-] local minimum at ionic separations r ∼ 3.4 Å and a global minimum at smaller ionic separations r ≲ 1.6 Å that gives overall instability of the system with respect to dissociation into a H2 molecule and a positronium negative ion, Ps-. The first predictions are made for positronic bonding in dianions consisting of molecular anionic fragments, specifically for (CN)22- and (NCO)22-. In all cases, we find that the molecules formed by the creation of a positronic bond are stable relative to dissociation into A- and e+A- (positron bound to a single anion), with bond energies on the order of 1eV and bond lengths on the order of several ångstroms.

Many-body theory calculations of positron scattering and annihilation in noble-gas atoms via the solution of Bethe–Salpeter equations using the Gaussian-basis code EXCITON+

Scattering phase shifts and annihilation rates for low-energy positrons interacting with noble gas atoms are calculated ab initio using many-body theory implemented in the Gaussian-orbital code EXCITON+. Specifically, we construct the positron–atom correlation potential (self-energy) as the sum of three classes of infinite series describing the screened polarization, virtual positronium formation, and positron-hole repulsion found via the solution of Bethe–Salpeter equations for the two-particle propagators. The normalization of the continuum states is determined using the shifted pseudostates method [A. R. Swann and G. F. Gribakin, Phys. Rev. A 101, 022702 (2020)]. Comparison with the previous sophisticated B-spline many-body approach, which is restricted to atoms [J. Ludlow, D. G. Green, and G. F. Gribakin, Phys. Rev. A 90, 032712 (2014)], validates the EXCITON+ code, which can be used for multicentered targets including molecules, clusters, and condensed matter. Moreover, the relative effects of higher-order diagrams are quantified. It is found that the screening of the electron–positron Coulomb interaction represented by the infinite ring-diagram series (random-phase approximation) is compensated effectively by the additional electron-hole attraction corrections to it (the Bethe–Salpeter equation approximation) and that the use of the screened Coulomb interaction (screened at BSE level) in place of the bare Coulomb interaction in the virtual positronium and positron-hole ladder diagrams has negligible effect on both the phase shifts and Zeff. Our scattering length for Ne and Kr is in improved agreement with the convergent close-coupling result, and for Ar, the scattering length is in better agreement with the experiment compared with the previous B-spline many-body approach.

Hot and dense matter equation of state probability distributions for astrophysical simulations

We add an ensemble of nuclei to the equation of state for homogeneous nucleonic matter to generate a new set of models suitable for astrophysical simulations of core-collapse supernovae and neutron star mergers. We implement empirical constraints from (i) nuclear mass measurements, (ii) proton-proton scattering phase shifts, and (iii) neutron star observations. Our model is also guided by microscopic many-body theory calculations based on realistic nuclear forces, including the zero-temperature neutron matter equation of state from quantum Monte Carlo simulations and thermal contributions to the free energy from finite-temperature many-body perturbation theory. We ensure that the parameters of our model can be varied while preserving thermodynamic consistency and the connection to experimental or observational data, thus providing a probability distribution of the astrophysical hot and dense matter equation of state. We compare our results with those obtained from other available equations of state. While our probability distributions indeed represent a large number of possible equations of state, we cannot yet claim to have fully explored all of the uncertainties, especially with regard to the structure of nuclei in the hot and dense medium.

Dispersion relation of Landau elementary excitations and thermodynamic properties of superfluid He4

Superfluid ${}^{4}$He, a strongly correlated Bose-Einstein condensed many-body system, displays sharp phonon-roton quantized excitations. Here, the authors report a complete determination of the dispersion relation of these excitations, using the most advanced inelastic neutron scattering methods as well as detailed dynamic many-body theory calculations. From the measured dispersion, the authors obtain, analytically as well as numerically, accurate tables of the thermodynamic properties. These highly precise results provide indispensable reference for a large variety of fundamental experimental and theoretical studies.

BSHF: A program to solve the Hartree–Fock equations for arbitrary central potentials using a B-spline basis

BSHF solves the Hartree–Fock equations in a B-spline basis for atoms, negatively charged ions, and systems of N electrons in arbitrary central potentials. In the B-spline basis the Hartree–Fock integro-differential equations are reduced to a computationally simpler eigenvalue problem. As well as solving this for the ground-state electronic structure self-consistently, the program can calculate discrete and/or continuum excited states of an additional electron or positron in the field of the frozen-target N-electron ground state. It thus provides an effectively complete orthonormal basis that can be used for higher-order many-body theory calculations. Robust and efficient convergence in the self-consistent iterations is achieved by a number of strategies, including by gradually increasing the strength of the electron–electron interaction by scaling the electron charge from a reduced value to its true value. The functionality and operation of the program is described in a tutorial style example. Program summaryProgram Title: BSHFProgram Files doi:http://dx.doi.org/10.17632/fj3y6c58dy.1Code Ocean Capsule:https://doi.org/10.24433/CO.1226817.v2Licensing provisions: GPLv3Programming language: Fortran 90.External routines/libraries: LAPACK.Nature of problem: Self-consistent solution of electronic structure for atoms and electrons in arbitrary central potentials in the Hartree–Fock approximation.Solution method: A B-spline basis is employed that transforms the Hartree–Fock integro-differential equations to a computationally simpler eigenvalue problem. The eigenvalue problem is solved iteratively until self-consistency is achieved.Unusual or notable features:1. Robust and efficient convergence in the self-consistent iterations is achieved by gradually increasing the value of the electron charge from a reduced value to its true value, i.e., increasing the strength of the electron–electron interaction. In this way all orbitals are calculated simultaneously at every iteration of the self-consistency loop, i.e., without the need to successively fill the occupied shells from the core to valence (as most other Hartree–Fock codes require for convergence).2. In addition to atoms and negative ions, the program solves the Hartree–Fock equations for systems of N electrons confined in an arbitrary central potential specified by the user: thus the program can be used to e.g., calculate the structure of electrons confined in harmonic potentials, which are known to approximate the electron gas.3. In addition to calculating the ground state of the N-electron system, the program calculates the discrete and/or continuum excited states for an additional electron or positron in the field of the ‘frozen’ N-electron target. It thus provides an orthonormal basis that can be used as input for many-body theory calculations.Restrictions: The program solves non-relativistic Hartree–Fock equations for spherically symmetric systems only (in modelling systems other than atoms, e.g., harmonically confined electron gas or jellium-type models of clusters, relativistic effects can often be negligible and a non-relativistic treatment is perfectly suitable). For open-shell atoms the central-field approximation is used, i.e., the potential is angularly averaged.

Orbital-differentiated coherence-incoherence crossover identified by photoemission spectroscopy in LiFeAs

In the iron-based superconductors (FeSCs), orbital differentiation is an important phenomenon, whereby correlations stronger on the dxy orbital than on the dxz/yz orbital yield quasi-particles with dxy} orbital character having larger mass renormalization and abnormal temperature evolution. However, the physical origin of this orbital differentiation is debated between the Hund's coupling induced unbinding of spin and orbital degrees of freedom and the Hubbard interaction instigated orbital selective Mott transition. Here we use angle-resolved photoemission spectroscopy to identify an orbital-dependent correlation-induced quasi-particle (QP) anomaly in LiFeAs. The excellent agreement between our photoemission measurements and first-principles many-body theory calculations shows that the orbital-differentiated QP lifetime anomalies in LiFeAs are controlled by the Hund's coupling.

Dynamics in dense hard-sphere colloidal suspensions

The dynamic behavior of a hard-sphere colloidal suspension was studied by x-ray photon correlation spectroscopy and small-angle x-ray scattering over a wide range of particle volume fractions. The short-time mobility of the particles was found to be smaller than that of free particles even at relatively low concentrations, showing the importance of indirect hydrodynamic interactions. Hydrodynamic functions were derived from the data, and for moderate particle volume fractions (Φ≤ 0.40) there is good agreement with earlier many-body theory calculations by Beenakker and Mazur [Physica A 120, 349 (1984)]. Important discrepancies appear at higher concentrations, above Φ≈ 0.40, where the hydrodynamic effects are overestimated by the Beenakker-Mazur theory, but predicted accurately by an accelerated Stokesian dynamics algorithm developed by Banchio and Brady [J. Chem. Phys. 118, 10323 (2003)]. For the relaxation rates, good agreement was also found between the experimental data and a scaling form predicted by the mode coupling theory. In the high concentration range, with the fluid suspensions approaching the glass transition, the long-time diffusion coefficient was compared with the short-time collective diffusion coefficient to verify a scaling relation previously proposed by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)]. We discuss our results in view of previous experimental attempts to validate this scaling law [L. Lurio et al., Phys. Rev. Lett. 84, 785 (2000)].

High-precision x-ray spectroscopy in few-electron ions

The experimental and spectrum analysis procedures that led to about 15 new, high-precision, relative x-ray line energy measurements are presented. The measured lines may be used as x-ray reference lines in the 2.4–3.1 keV range. Applications also include tests of the atomic theory, and in particular of quantum electrodynamics and of relativistic many-body theory calculations. The lines originate from 2- to 4-electron ions of sulfur (Z=16), chlorine (Z=17) and argon (Z=18). The precision reached for their energy ranges from a few parts per million (ppm) to about 50 ppm. This places the new measurements among the most precise performed in mid-Z highly charged ions (Z is the nuclear charge number). The elements of the experimental setup are described: the ion source (an electron cyclotron resonance ion trap), the spectrometer (a single, spherically bent crystal spectrometer), as well as the spectrum acquisition camera (low-noise, high-efficiency CCD). The spectrum analysis procedure, which is based on a full simulation of the spectrometer response function, is also presented.

Reevaluating electron-phonon coupling strengths: Indium as a test case forab initioand many-body theory methods

Using indium as a test case, we investigate the accuracy of the electron-phonon coupling calculated with state-of-the-art ab initio and many-body theory methods. The ab initio calculations -- where electrons are treated in the local-density approximation, and phonons and the electron-phonon interaction are treated within linear response -- predict an electron-phonon spectral function alpha^2 F(omega) which translates into a relative tunneling conductance that agrees with experiment to within one part in 1000. The many-body theory calculations -- where alpha^2 F(omega) is extracted from tunneling data by means of the McMillan-Rowell tunneling inversion method -- provide spectral functions that depend strongly on details of the inversion process. For the the most important moment of alpha^2 F(omega), the mass-renormalization parameter lambda, we report 0.9 +/- 0.1, in contrast to the value 0.805 quoted for nearly three decades in the literature. The ab initio calculations also provide the transport electron-phonon spectral function alpha_{tr}^2 F(omega), from which we calculate the resistivity as a function of temperature in good agreement with experiment.

Polarization fractions for the 21P, 31P and 31D states of helium

The polarization fractions for the 21P, 31P and 31D states of helium, determined from a 10-channel semiclassical eikonal calculation, are compared with a recent first-order many-body theory calculation of Csanak et al. (1989), and with experiment. A number of interesting points on the importance of channel coupling effects on the polarization fractions for the 21P, 31P and 31D states of He are addressed.