Non-spherical Potential Research Articles

Stark resonance parameters for the 3a1 orbital of the water molecule

The Stark resonance parameters for the 3a1 molecular orbital of H2O are computed by solving a system of partial differential equations in spherical polar coordinates. The starting point of the calculation is the non-spherical quantum potential derived for this orbital from a single-center expanded Hartree–Fock orbital. The resonance positions and widths are obtained after applying an exterior complex scaling technique to describe the ionization regime for external fields applied along the two distinct directions associated with the symmetry axis. Comparison is made with previous results for the 1b1 and 1b2 orbitals obtained from a spherical potential approximation.

Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

The Green function plays an essential role in the Korringa–Kohn–Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn–Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). The pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. By using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.

Probing electronic structure of stoichiometric and defectiveSnO2

The electronic structure of stoichiometric tin dioxide ($\mathrm{Sn}{\mathrm{O}}_{2}$) is studied by probing its unoccupied states using the fine structure in the electron energy-loss spectra (EELS) at the oxygen-$K$ (O-$K$) edge. The spectral measurements were performed both at room and at high temperatures (773 K) and compared to ab initio calculations carried out using the real-space multiple-scattering and linearized augmented-plane-wave methods. Important many-body effects are included via quasiparticle corrections calculated within the many-pole $GW$ self-energy approximation. An additional energy-dependent damping is calculated to account for vibrational effects. Results from this paper demonstrated that quantitative agreement between theoretical and experimental spectra can be obtained when nonspherical potentials and quasiparticle self-energy effects are considered and vibrational broadening is included. Modifications of the electronic structure by single oxygen vacancies, both in the bulk and at the (110) surface, also are predicted. Our predictions support the use of O-$K$ EELS as a probe of the defect structures in $\mathrm{Sn}{\mathrm{O}}_{2}$ surfaces and nanoparticles.

Determining the specific surface area of Metal Organic Frameworks based on a computational approach

A novel simulation approach is proposed for the representation and calculation of the specific surface area of crystalline nanoporous materials (e.g. MOFs). In brief, the simulation box that contains the framework atoms is discretized with voxels, which are filtered based on an atomistic forcefield according to specific criteria (i.e. whether a voxel can be occupied by a gas molecule or not). This produces a “phase” function that represents the spatial distribution of matter in the biphasic (solid–void) medium. The specific surface area is then derived by the correlation function of the phase function, a method well established for the calculation of the specific surface area of mesoporous media. The proposed methodology has the advantage of allowing the implementation of any atomic interaction potential and/or filter of choice. Thus, no assumption on the shape of the pores or even the framework atoms is in principle required (for instance non-spherical potentials including electrostatic interactions can be used). Furthermore, since the solid–void interface has been determined, an attempt to simulate the monolayer coverage process was carried out and pertinent surface areas where also calculated by simply counting the number of molecules that form the monolayer.The results were validated against full GCMC adsorption isotherm simulations and were further compared with experimental data indicating the suitability and effectiveness of the proposed non-stochastic computational approach for the reliable, fast and accurate determination of the surface area of nanoporous solids.

The orbital PDF: general inference of the gravitational potential from steady-state tracers

We develop two general methods to infer the gravitational potential of a system using steady-state tracers, i.e. tracers with a time-independent phase-space distribution. Combined with the phase-space continuity equation, the time independence implies a universal orbital probability density function (oPDF) dP(λ|orbit) ∝ dt, where λ is the coordinate of the particle along the orbit. The oPDF is equivalent to Jeans theorem, and is the key physical ingredient behind most dynamical modelling of steady-state tracers. In the case of a spherical potential, we develop a likelihood estimator that fits analytical potentials to the system and a non-parametric method (‘phase-mark’) that reconstructs the potential profile, both assuming only the oPDF. The methods involve no extra assumptions about the tracer distribution function and can be applied to tracers with any arbitrary distribution of orbits, with possible extension to non-spherical potentials. The methods are tested on Monte Carlo samples of steady-state tracers in dark matter haloes to show that they are unbiased as well as efficient. A fully documented c/python code implementing our method is freely available at a GitHub repository linked from http://icc.dur.ac.uk/data/#oPDF.

Autler-Townes Effects in Attosecond Circular Polarization Molecular Photoionization

We present molecular photoionization simulations by intense (I ~ 1016 W/cm2) few cycle circularly polarized attosecond extreme ultraviolet laser pulses for aligned H2+ from numerical solutions of the corresponding time-dependent Schrodinger equation. With appropriate laser pulse parameters, circular attosecond coherent electron wave packets (CEWPs) are created in excited Rydberg states. Such CEWPs are spatially localized during ionization processes, thus resulting in sufficient population oscillations between the resonant excited Rydberg states and the initial ground state. Consequently Autler-Townes splitting in circular polarization energy spectra is predicted, which is shown to be critically sensitive to the pulse intensity, duration, and polarization. The resulting photoelectron angular distributions are rotated with respect to the molecular axis due to the nonspherical Coulomb potential of the molecule, resulting in different ionization rates at different laser polarization-molecular angles.

TRACING THE ORPHAN STREAM TO 55 kpc WITH RR LYRAE STARS

We report positions, velocities and metallicities of 50 ab-type RR Lyrae (RRab) stars observed in the vicinity of the Orphan stellar stream. Using about 30 RRab stars classified as being likely members of the Orphan stream, we study the metallicity and the spatial extent of the stream. We find that RRab stars in the Orphan stream have a wide range of metallicities, from -1.5 dex to -2.7 dex. The average metallicity of the stream is -2.1 dex, identical to the value obtained by Newberg et al. (2010) using blue horizontal branch stars. We find that the most distant parts of the stream (40-50 kpc from the Sun) are about 0.3 dex more metal-poor than the closer parts (within ~30 kpc), suggesting a possible metallicity gradient along the stream's length. We have extended the previous studies and have mapped the stream up to 55 kpc from the Sun. Even after a careful search, we did not identify any more distant RRab stars that could plausibly be members of the Orphan stream. If confirmed with other tracers, this result would indicate a detection of the end of the leading arm of the stream. We have compared the distances of Orphan stream RRab stars with the best-fit orbits obtained by Newberg et al. (2010). We find that model 6 of Newberg et al. (2010) cannot explain the distances of the most remote Orphan stream RRab stars, and conclude that the best fit to distances of Orphan stream RRab stars and to the local circular velocity is provided by potentials where the total mass of the Galaxy within 60 kpc is M_{60}~2.7x10^{11} Msun, or about 60% of the mass found by previous studies. More extensive modelling that would consider non-spherical potentials and the possibility of misalignment between the stream and the orbit, is highly encouraged.

Ballistic Transfers Across the Resonance Around Vesta Following Invariant Manifolds

Motivated by the challenging crossing of the resonance planned for the Dawn mission a general transfer design strategy is developed using the manifold structure of near-synchronous, unstable periodic orbits. Two families of transfers across the resonance at the asteroid Vesta demonstrate the approach. A family of low-inclination low-energy transfers follows the stable and unstable manifolds of the libration orbits near Vesta’s equilibrium points (in a surface-fixed rotating frame). A high-inclination family of transfers arises similarly from the manifold structure of near-polar near-circular orbits. Ballistic resonance crossing transfers near Vesta are presented and characterized. This transfer design methodology applies well to any solar system body where the dynamics are dominated by gravitational acceleration from a nonspherical central-body potential.

Analytical Solution of Coupled Perturbation of Tesseral Harmonic Terms of Mars's Non-Spherical Gravitational Potential

The non-spherical gravitational potential of the planet Mars is sig- nificantly different from that of the Earth. The magnitudes of Mars’ tesseral harmonic coefficients are basically ten times larger than the corresponding val- ues of the Earth. Especially, the magnitude of its second degree and order tesseral harmonic coefficient J2,2 is nearly 40 times that of the Earth, and approaches to the one tenth of its second zonal harmonic coefficient J2. For a low-orbit Mars probe, if the required accuracy of orbit prediction of 1-day arc length is within 500 m (equivalent to the order of magnitude of 10−4 standard unit), then the coupled terms of J2 with the tesseral harmonics, and even those of the tesseral harmonics themselves, which are negligible for the Earth satellites, should be considered when the analytical perturbation solution of its orbit is built. In this paper, the analytical solutions of the coupled terms are presented. The anal- ysis and numerical verification indicate that the effect of the above-mentioned coupled perturbation on the orbit may exceed 10−4 in the along-track direc- tion. The conclusion is that the solutions of Earth satellites cannot be simply used without any modification when dealing with the analytical perturbation solutions of Mars-orbiting satellites, and that the effect of the coupled terms of Mars's non-spherical gravitational potential discussed in this paper should be taken into consideration.

DETECTING TRIAXIALITY IN THE GALACTIC DARK MATTER HALO THROUGH STELLAR KINEMATICS

Assuming the dark matter halo of the Milky Way as a non-spherical potential (i.e. triaxial, prolate, oblate), we show how the assembling process of the Milky Way halo, may have left long lasting stellar halo kinematic fossils only due to the shape of the dark matter halo. In contrast with tidal streams, associated with recent satellite accretion events, these stellar kinematic groups will typically show inhomogeneous chemical and stellar population properties. However, they may be dominated by a single accretion event for certain mass assembling histories. If the detection of these peculiar kinematic stellar groups is confirmed, they would be the smoking gun for the predicted triaxiality of dark halos in cosmological galaxy formation scenarios.

Origin of the Larger Values of Total Cross Section for Helium Scattering from Isolated Atomic Steps

The effect of surface relaxation and the electronic re-arrangement in the vicinity of a step on the total step cross section for helium scattering is investigated. A realistic helium interaction potential at a Cu(001) step is modeled by summing non-spherical pair potentials which allows for the possibility of varying the smoothing across the surface due to the itinerant aspects of the surface electronic structure. Numerical calculations reveal a significant increase in the magnitude of the total step cross section with large charge re-arrangement in the vicinity of the step. Also, the relaxation of surface layers has no effect whatsoever. The present study clearly shows that the origin of the experimentally observed large step cross section is the hard wall scattering from charge re-arrangement in the proximity of the step. Further, the charge re-arrangements probed by thermal helium atoms must be greater than predicted by pairwise models.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11532 Dhaka Univ. J. Sci. 60(2): 271-275, 2012 (July)

Linear and nonlinear intersubband optical absorption coefficients and refractive index changes with the ring-shaped non-spherical oscillator potential

Linear and nonlinear intersubband optical absorption coefficients and refractive index changes with the ring-shaped non-spherical oscillator potential (RNOP) are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron in the RNOP are obtained by using the effective mass approximation. It is found that the optical absorption coefficients and refractive index changes are strongly affected not only by the dimensionless parameters γ and β, but also by the confinement frequency ω0.

Non-central potentials, exact solutions and Laplace transform approach

Exact bound state solutions and the corresponding wave functions of the Schrödinger equation for some non-central potentials including Makarov potential, modified-Kratzer plus a ring-shaped potential, double ring-shaped Kratzer potential, modified non-central potential and ring-shaped non-spherical oscillator potential are obtained by using the Laplace transform approach. The energy spectrums of the Hartmann potential, modified-Kratzer potential and ring-shaped oscillator potential are also briefly studied as special cases. It is seen that our analytical results for all these potentials are consistent with those obtained by other works. We also give some numerical results obtained for the modified non-central potential for different values of the related quantum numbers.

Multiphoton ionization of H2+in xuv laser pulses

We consider the ionization of the hydrogen molecular ion after one-, two-, and three-photon absorption over a large range of photon energies between 9 and 40 eV in the fixed-nuclei approximation. The temporal development of the system is obtained in a fully ab initio time-dependent grid-based approach in prolate spheroidal coordinates. The alignment dependence of the one-photon ionization amplitude is highlighted in the framework of time-dependent perturbation theory. For one-photon ionization as a function of the nuclear separation, the calculations reveal a significant minimum in the ionization probability. The suppressed ionization is attributed to a Cooper-type minimum, which is similar, but not identical, to the cancellation effect observed in photoionization cross sections of some noble-gas atoms. The effect of the nonspherical two-center Coulomb potential is analyzed. For two- and three-photon ionization, the angle-integrated cross sections clearly map out intermediate-state resonances, and the predictions of the current computations agree very well with those from time-independent calculations. The dominant emission modes for two-photon ionization are found to be very similar in both resonance and off-resonance regions.

Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems

We present a model of near-Earth asteroid (NEA) rotational fission and ensuing dynamics that describes the creation of synchronous binaries and all other observed NEA systems including: doubly synchronous binaries, high- e binaries, ternary systems, and contact binaries. Our model only presupposes the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect, “rubble pile” asteroid geophysics, and gravitational interactions. The YORP effect torques a “rubble pile” asteroid until the asteroid reaches its fission spin limit and the components enter orbit about each other (Scheeres, D.J. [2007]. Icarus 189, 370–385). Non-spherical gravitational potentials couple the spin states to the orbit state and chaotically drive the system towards the observed asteroid classes along two evolutionary tracks primarily distinguished by mass ratio. Related to this is a new binary process termed secondary fission – the secondary asteroid of the binary system is rotationally accelerated via gravitational torques until it fissions, thus creating a chaotic ternary system. The initially chaotic binary can be stabilized to create a synchronous binary by components of the fissioned secondary asteroid impacting the primary asteroid, solar gravitational perturbations, and mutual body tides. These results emphasize the importance of the initial component size distribution and configuration within the parent asteroid. NEAs may go through multiple binary cycles and many YORP-induced rotational fissions during their approximately 10 Myr lifetime in the inner Solar System. Rotational fission and the ensuing dynamics are responsible for all NEA systems including the most commonly observed synchronous binaries.

Solving Dirac Equation with New Ring-Shaped Non-Spherical Harmonic Oscillator Potential

A new ring-shaped non-harmonic oscillator potential is proposed. The precise hound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 (2005) 94. The positive energy states of system are discussed and the conclusions are made properly.

Pseudospin symmetry for a new ring-shaped non-spherical harmonic oscillator potential

A new ring-shaped non-spherical harmonic oscillator potential is proposed, which consists of a generalized non-harmonic oscillator potential plus an angle-dependent potential, The pseudospin symmetry for a spin- particle moving in this potential is investigated by solving the Dirac equation with an equal mixture of scalar and vector potentials with opposite signs. The normalized spinor wave function and energy equation are obtained, and the algebraic property of the energy equation and some particular cases are also discussed.

Basic questions related to electron-induced sputtering in the TEM

Although the theory of high-angle elastic scattering of fast electrons is well developed, accurate calculation of the incident-energy threshold and cross section for surface-atom sputtering is hampered by uncertainties in the value of the surface-displacement energy E d and its angular dependence. We show that reasonable agreement with experiment is achieved by assuming a non-spherical escape potential with E d=(5/3) E sub, where E sub is the sublimation energy. Since field-emission sources and aberration-corrected TEM lenses have become more widespread, sputtering has begun to impose a practical limit to the spatial resolution of microanalysis for some specimens. Sputtering can be delayed by coating the specimen with a thin layer of carbon, or prevented by reducing the incident energy; 60 keV should be sufficiently low for most materials.

Self-consistent aspects of x-ray absorption calculations

We implemented a self-consistent, real-space x-ray absorption calculation within theFDMNES code. We performed the self-consistency within several schemes and identifiedwhich one is the most appropriate. We show a method that allows a rigorous setting of theFermi level and thus an estimation of the energy cutoff for the identification andelimination of the occupied states. We investigated what are the structures where onecan afford performing the self-consistent calculation at a lesser cluster radiusthan the absorption one. We exemplify the effects of the self-consistency at theK-edge and for several reference cases, including the copper Cu and the rutileTiO2. We verified the robustness of our procedure on the transitional 3d and 4d elements.Although amelioration can be noticed, the self-consistency performed at the K-edge doesnot bring a major improvement of the calculated spectra. Taking into consideration anon-self-consistent, non-spherical potential gives better results than a self-consistentmuffin-tin approximation calculation.

Pseudospin Symmetry for a Ring-Shaped Non-spherical Harmonic Oscillator Potential

The pseudospin symmetry for a ring-shaped non-spherical harmonic oscillator potential is investigated by solving the Dirac equation with equal mixture of scalar and vector potentials with opposite signs. The normalized spinor wave function and energy equation are obtained, the algebraic property of the energy equation and some particular cases are also discussed.