Angular Momentum Expansion Research Articles

Third post-Newtonian gravitational radiation from two-body scattering. II. Hereditary energy radiation

We compute the hereditary part of the third post-Newtonian accurate gravitational energy radiation from hyperbolic scatterings (and parabolic scatterings) of non-spinning compact objects. We employ large angular momentum ($j$) expansion, and compute it to the relative $1/j^{11}$ order (so the first 12 terms). For parabolic scattering case, the exact solution is computed. At the end, the completely collected expression of the energy radiation upto the third post-Newtonian and from $1/j^{3}$ to $1/j^{15}$ order, is presented including the instantaneous contribution.

Scalarization of Chern-Simons-Kerr black hole solutions and wormholes

Chern-Simons gravity rotating Kerr-type black hole solutions are revisited from the point of view of their scalarization, namely examining the back reaction of pseudoscalar axion fields on the rotating geometry. To lowest order in an angular momentum expansion, and a long range approximation for both the axion field configuration and its back reaction onto the metric, such solutions had been discussed for the first time in the context of string theory. In this work, we extend the analysis to give analytic expressions for slowly rotating black holes outside the horizon, which formally include an all order expansion in inverse powers of the radial distance from the centre of the black hole, which allows to approach arbitrarily close the horizon. We also discuss in some detail the way Chern-Simons gravity violates the energy conditions, which leads to secondary axionic hair of the rotating black hole solutions. This discussion is extended to studies of wormhole solutions, which we construct in this article via the thin-shell procedure and we demonstrate that the presence of the axion field enforces the two black hole solutions to be counter-rotating and for slow rotation, there is no backreaction of the Cotton tensor on the thin-shell of the wormhole.

Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-Eccentricity Expansion.

We compute the conservative dynamics of nonspinning binaries at fourth post-Minkowskian order in the large-eccentricity limit, including both potential and radiation-reaction tail effects. This is achieved by obtaining the scattering angle in the worldline effective field theory approach and deriving the bound radial action via analytic continuation. The associated integrals are bootstrapped to all orders in velocities through differential equations, with boundary conditions in the potential and radiation regions. The large angular momentum expansion captures all the local-in-time effects as well as the trademark logarithmic corrections for generic bound orbits. Agreement is found in the overlap with the state of the art in post-Newtonian theory.

Scattering effects from neighboring atoms in core-level WSe2 photoemission

Methods of attosecond science originally developed to investigate systems in the gas phase are currently being adapted to obtain temporal information on the electron dynamics that takes place in condensed-matter systems. In particular, streaking measurements have recently been performed to determine photoemission time delays from the ${\mathrm{WSe}}_{2}$ dichalcogenide. In this work we present a fully atomistic description of the photoemission process in ${\mathrm{WSe}}_{2}$ and provide angularly resolved photoemission cross sections and time delays from the W $4f$, Se $3d$ and Se $4s$ core states of the system. Since these states are spatially localized, we propose a cluster approach in which we build up from smaller to larger clusters, so that we can assess the importance of scattering effects by each new layer of neighboring atoms. We use a static-exchange density functional theory method with $B$-spline functions, where a one-center angular-momentum expansion is supplemented by off-center expansions with fewer partial waves. This enhances convergence in comparison with a one-center expansion, which would require very high angular momenta to characterize the localized fast oscillations near each off-center atomic core. We find that the photoemission delays and fully differential cross sections are strongly affected by scattering events that take place off the neighboring atoms, implying the need to consider their effects for quantitative descriptions of the photoemission process.

A Sommerfeld toolbox for colored dark sectors

We present analytical formulas for the Sommerfeld corrections to the annihilation of massive colored particles into quarks and gluons through the strong interaction. These corrections are essential to accurately compute the dark matter relic density for coannihilation with colored partners. Our formulas allow us to compute the Sommerfeld effect, not only for the lowest term in the angular momentum expansion of the amplitude, but for all orders in the partial wave expansion. In particular, we carefully account for the effects of the spin of the annihilating particle on the symmetry of the two-particle wave function. This work focuses on strongly interacting particles of arbitrary spin in the triplet, sextet and octet color representations. For typical velocities during freeze-out, we find that including Sommerfeld corrections on the next-to-leading order partial wave leads to modifications of up to 10 to 20 percent on the total annihilation cross section. Complementary to QCD, we generalize our results to particles charged under an arbitrary unbroken SU(N) gauge group, as encountered in dark glueball models. In connection with this paper a Mathematica notebook is provided to compute the Sommerfeld corrections for colored particles up to arbitrary order in the angular momentum expansion.

Algorithm for Reconstruction of 3D Images of Nanorice Particles from Diffraction Patterns of Two Particles in Independent Random Orientations with an X-ray Laser

The method of angular correlations recovers quantities from diffraction patterns of randomly oriented particles, as expected to be measured with an X-ray free electron laser (XFEL), proportional to quadratic functions of the spherical harmonic expansion coefficients of the diffraction volume of a single particle. We have previously shown that it is possible to reconstruct a randomly oriented icosahedral or helical virus from the average over all measured diffraction patterns of such correlations. We point out in this paper that a structure of even simpler particles of 50 Å or so in diameter and consisting of heavier atomic elements (to enhance scattering) that has been used as a test case for reconstructions from XFEL diffraction patterns can also be solved by this technique. Even though there has been earlier work on similar objects (prolate spheroids), one advantage of the present technique is its potential to also work with diffraction patterns not only due to single particles as has been suggested on the basis on nonoverlapping delta functions of angular scattering. Accordingly, we calculated from the diffraction patterns the angular momentum expansions of the pair correlations and triple correlations for general particle images and reconstructed those images in the standard way. Although the images looked pretty much the same, it is not totally clear to us that the angular correlations are exactly the same as different numbers of particles due to the possibility of constructive or destructive interference between the scattered waves from different particles. It is of course known that, for a large number of particles contributing to a diffraction parttern, the correlations converge to that of a single particle. It could be that the lack of perfect agreement between the images reconstructed with one and two particles is due to uncancelling constructive and destructive conditions that are not found in the case of solution scattering.

The Korringa–Kohn–Rostoker method with projection potentials: exact result for the density

A well known problem in the Korringa–Kohn–Rostoker (KKR) multiple-scattering method concerns the error in density normalization arising from finite angular momentum expansions used in numerical treatments. It is shown that this problem can be solved if the potential around each atom is understood as a non-local projection potential in angular momentum space and that the density can be calculated exactly without infinite angular momentum sums if the projection acts on a finite subspace of spherical harmonics. This restriction implicates no loss of generality because an arbitrary potential can be approximated by increasing the subspace as closely as desired.

Spicing up continuum solvation models with SaLSA: the spherically averaged liquid susceptibility ansatz.

Continuum solvation models enable electronic structure calculations of systems in liquid environments, but because of the large number of empirical parameters, they are limited to the class of systems in their fit set (typically organic molecules). Here, we derive a solvation model with no empirical parameters for the dielectric response by taking the linear response limit of a classical density functional for molecular liquids. This model directly incorporates the nonlocal dielectric response of the liquid using an angular momentum expansion, and with a single fit parameter for dispersion contributions it predicts solvation energies of neutral molecules with a RMS error of 1.3 kcal/mol in water and 0.8 kcal/mol in chloroform and carbon tetrachloride. We show that this model is more accurate for strongly polar and charged systems than previous solvation models because of the parameter-free electric response, and demonstrate its suitability for ab initio solvation, including self-consistent solvation in quantum Monte Carlo calculations.

Harmonic generation by noble-gas atoms in the near-IR regime usingab initiotime-dependentR-matrix theory

We demonstrate the capability of ab-initio time-dependent R-matrix theory to obtain accurate harmonic generation spectra of noble-gas atoms at Near-IR wavelengths between 1200 and 1800 nm and peak intensities up to 1.8 X 10(14) W/cm(2) . To accommodate the excursion length of the ejected electron, we use an angular-momentum expansion up to Lmax = 279. The harmonic spectra show evidence of atomic structure through the presence of a Cooper minimum in harmonic generation for Kr, and of multielectron interaction through the giant resonance for Xe. The theoretical spectra agree well with those obtained experimentally.

Angular diffraction of an optical vortex induced by the Gouy phase

We investigate the diffraction of an optical vortex, when half of the beam is blocked by a knife edge. The Gouy phase is shown to influence the diffraction pattern strongly, in particular leading to the emergence of distorted and deformed diffraction fringes in the azimuthal direction. In analogy with single-slit diffraction, this phenomenon is analyzed in terms of angular diffraction within the azimuthal degree of freedom, by considering the uncertainty principle for the angular position and the angular momentum. Numerical simulations based on the fast-Fourier algorithm and the angular momentum expansion fit well with the experimental results.

Improving the charge density normalization in Korringa–Kohn–Rostoker Green-functioncalculations

The truncation of angular momentum expansions in the Korringa–Kohn–RostokerGreen-function method introduces a charge normalization error and disallowscalculation of the Fermi level and the charge density in a consistent manner. It isshown how this error can be compensated by Lloyd’s formula, in particular ifthis formula is applied to normalize the Green function everywhere along thecomplex energy contour used for the integration of the charge density. Theadvantages of the improved normalization over the conventional one are illustratedby density-functional calculations for CrAs, the dilute magnetic semiconductorGa1−xMnxN anda Si12Fe8 multilayer. It is shown that only the improved normalization leads to correctinteger values of the magnetic moments in the half-metallic state of CrAs andGa1−xMnxN and to a correct band alignment of Fe and Si states in the multilayer.

Full-potential multiple scattering for x-ray spectroscopies

We present a full-potential multiple scattering (FPMS) scheme for the interpretation of several x-ray spectroscopies that is a straightforward generalization of the more conventional muffin-tin version. Like this latter, it preserves the intuitive description of the physical process under consideration and overcomes some of the limitations of the existing FPMS codes. It hinges on a fast and efficient method for solving the single-cell scattering problem that avoids the convergence drawbacks of the angular momentum expansion of the cell shape function; it relies on an alternative derivation of the multiple scattering equations that allows us to work reliably with only one truncation parameter, i.e., the number of local basis functions in the expansion of the global scattering function determined by the classical relation ${l}_{\mathrm{max}}\ensuremath{\sim}kR$.

Bulk and surface properties of metals by full-charge-density screened Korringa-Kohn-Rostoker calculations

The full-charge-density screened Korringa-Kohn-Rostoker method is described and applied to calculate bulk and surface energies of transition metals. It is demonstrated that due to a truncated angular momentum expansion of the shape functions, the otherwise ultimate freedom of adding a constant to the potential in all space leads, in particular close to the cell boundaries, to potentials of fairly different shapes. Thus a dependence on this constant potential shift emerges for the calculated bulk total energies, equilibrium volumes, and bulk moduli, as well as for the surface energies and the work functions. A reasonable choice for the constant shift seems to set the bulk potential at the muffin-tin radius to zero. By making this choice the calculations give results that are in very good agreement to those calculated by other full-charge-density or full-potential methods.

Large spin limit of AdS5× S5 string theory and low energy expansion of ferromagnetic spin chains

By considering AdS 5× S 5 string states with large S 5 angular momenta one can provide non-trivial quantitative checks of the AdS/CFT duality. A string rotating in S 5 with two angular momenta J 1, J 2 is dual to an operator in N=4 SYM theory whose conformal dimension can be computed by diagonalizing a (generalization of) spin 1/2 Heisenberg chain Hamiltonian. It was recently argued and verified to lowest order in a large J= J 1+ J 2 expansion, that the Heisenberg chain can be described using a non-relativistic low energy effective 2d action for a unit vector field n i which exactly matches the corresponding large J limit of the classical AdS 5× S 5 string action. In this paper we show that this agreement extends to the next order and develop a systematic procedure for computing higher orders in such large angular momentum expansion. This involves several non-trivial steps. On the string side, we need to choose a special gauge with a non-diagonal world-sheet metric which insures that the angular momentum is uniformly distributed along the string, as indeed is the case on the spin chain side. We need also to implement an order by order redefinition of the field n i to get an action linear in the time derivative. On the spin chain side, it turns out to be crucial to include the effects of integrating out short wave-length modes. In this way we gain a better understanding of how (a subsector of) the string sigma model emerges from the dual gauge theory, allowing us to demonstrate the duality beyond comparing particular examples of states with large J.

Korringa-Kohn-Rostoker Green-function formalism for ballistic transport

We develop a method for the calculation of ballistic transport from first principles. The multiple scattering screened Korringa-Kohn-Rostoker (KKR) method is combined with a Green's function formulation of the Landauer approach for the ballistic transport. We obtain an efficient O(N) algorithm for the calculation of ballistic conductance through a scattering region connected to semi-infinite crystalline leads. In particular we generalize the results of Baranger and Stone in the case of Bloch wave boundary conditions and we discuss relevant properties of the S-matrix. We consider the implications on the application of the formalism in conjunction with a cellular multiple scattering description of the electronic structure, and demonstrate the convergence properties concerning the angular momentum expansions.

Ab initio calculation of forces and lattice relaxations in metallic alloys

Abstract We present first-principles calculations of forces and lattice relaxations in bcc Fe. In particular, relaxations around 3d, 4d and 5d transition metal impurities are calculated. The calculations are based on a full-potential Korringa-Kohn- Rostoker Green's function method for defects and employ the local spin density approximation for the exchange and correlation effects. The non- spherical parts of the potential and the charge density are treated correctly, while the forces are calculated by an ionic version of the Hellmann-Feynman theorem. Lattice statics methods are used to describe the longer ranged relaxations. The results are compared with lattice parameter measurements for the volume changes. Because of the correct treatment of the sharp shape of the Wigner-Seitz cell, the angular momentum expansion coefficients of the cell potential have discontinuities in the first derivative, which cause some complications when solving the radial equations. An effective method to get around these discontinuities is introduced.

Ab initio calculation of forces and lattice relaxations in metallic alloys

Abstract We present first-principles calculations of forces and lattice relaxations in bcc Fe. In particular, relaxations around 3d, 4d and 5d transition metal impurities are calculated. The calculations are based on a full-potential Korringa-Kohn- Rostoker Green's function method for defects and employ the local spin density approximation for the exchange and correlation effects. The non- spherical parts of the potential and the charge density are treated correctly, while the forces are calculated by an ionic version of the Hellmann-Feynman theorem. Lattice statics methods are used to describe the longer ranged relaxations. The results are compared with lattice parameter measurements for the volume changes. Because of the correct treatment of the sharp shape of the Wigner-Seitz cell, the angular momentum expansion coefficients of the cell potential have discontinuities in the first derivative, which cause some complications when solving the radial equations. An effective method to get around these discon...

Computation of photo-electron and Auger-electron diffraction II. Multiple scattering cluster calculation PAD2

In this paper, we describe the second (PAD2) of the suite of computer programs for the calculation of angle-resolved photo- or Auger-electron diffraction intensities, using a concentric-shell algorithm (CSA). The function of the present program is to evaluate the scattering matrix that relates the wavefunction of an electron immediately after its emission from an atomic core to the wavefield that may be detected outside a sample, using an angular-momentum expansion centered on the emitter atom. This program allows that matrix to be evaluated by any of the following schemes (in ascending order of accuracy, and computer requirements): single scattering (SS), outward multiple scattering (OS) and full multiple scattering (MS).

Comparison of Strengths of the Quadrupole Pairing Force in the Angular-Momentum Expansion of the Rotational Energy

Comparison of Strengths of the Quadrupole Pairing Force in the Angular-Momentum Expansion of the Rotational Energy

Approximations made in evaluating the residual electrical dc resistivity of disordered alloys.

The residual electrical dc resistivity of the transition-metal-alloy system Cu-Pt is evaluated by making use of the relativistic version of the Korringa-Kohn-Rostoker--coherent potential approximation and the one-electron Kubo-Greenwood formula for disordered systems. Starting from the results of a previous calculation the influence of truncation of the angular momentum expansion, the effects of self-consistency of the alloy potential, the importance of vertex corrections, and the difference between the nonrelativistic and the relativistic current operator are examined.