Effective Single-particle Potential Research Articles

High-Energy Ejection of Molecules and Gas-Dust Outbursts in Coal Mines.

In the current work, using the framework of the formalism found in the Bogolyubov–Born–Green–Kirkwood–Yvon (BBGKY) equations for the distribution functions of particle groups, the effective single-particle potential near the surface of the liquid was analyzed. The thermodynamic conditions under which a sudden opening of the liquid surface leads to high-energy ejection of atoms and molecules were found. The energies of the emitted particles were observed to be able to significantly exceed their thermal energy. Criteria of the ejection stability of the liquid surface and the self-acceleration of ejection were formulated. The developed theory was used to explain the phenomenon of the self-acceleration of gas-dust outbursts in coal mines during the explosive opening of methane traps. The results also explained the mechanisms of generating significant amounts of methane and the formation of coal nanoparticles in gas-dust outbursts. The developed approach was also used to explain the phenomenon of the self-ignition of hydrogen when it enters the atmosphere.

Nonmonotonic confining potential and eigenvalue density transition for generalized random matrix model

We consider several limiting cases of the joint probability distribution for a random matrix ensemble with an additional interaction term controlled by an exponent γ (called the γ ensembles). The effective potential, which is essentially the single-particle confining potential for an equivalent ensemble with γ=1 (called the Muttalib-Borodin ensemble), is a crucial quantity defined in solution to the Riemann-Hilbert problem associated with the γ ensembles. It enables us to numerically compute the eigenvalue density of γ ensembles for all γ>0. We show that one important effect of the two-particle interaction parameter γ is to generate or enhance the nonmonotonicity in the effective single-particle potential. For suitable choices of the initial single-particle potentials, reducing γ can lead to a large nonmonotonicity in the effective potential, which in turn leads to significant changes in the density of eigenvalues. For a disordered conductor, this corresponds to a systematic decrease in the conductance with increasing disorder. This suggests that appropriate models of γ ensembles can be used as a possible framework to study the effects of disorder on the distribution of conductances.

Predictions of identification and production of new superheavy nuclei with Z=119 and 120

Effective single-particle potentials obtained from the established nonrelativistic nuclear energy density functional approach are incorporated into the microscopic-macroscopic method to calculate the ground-state shell corrections, mass excesses, and ${Q}_{\ensuremath{\alpha}}$ values for heaviest nuclei. The low-lying one-quasiparticle states are studied in the isotonic chains with neutron numbers $N=175$, 176, and 177. The isomeric states are discussed in the odd isotopes. The possible $\ensuremath{\alpha}$-decay chains of nuclei $^{295}119$ and $^{295,297}120$ are analyzed and compared with the available experimental data. The termination of the $\ensuremath{\alpha}$-decay chains by spontaneous fission is analyzed. The production cross sections are calculated for superheavy nuclei with $112\ensuremath{\le}Z\ensuremath{\le}120$ in the actinide-based complete fusion reactions with projectiles $^{48}\mathrm{Ca}, ^{48,50}\mathrm{Ti}, ^{54}\mathrm{Cr}, ^{58}\mathrm{Fe}$, and $^{64}\mathrm{Ni}$.

The effective single particle potential and the tadpole

The Energy Density Functional (EDF) theory is extremely successful within the effective force approach, noticeably the Skyrme or Gogny forces, in reproducing the nuclear binding energies and other nuclear properties along the whole mass table. The EDF is in this case represented formally as the Hartree-Fock (HF) mean field of an effective force, and the associated single particle states can be considered the eigenstates of the corresponding effective mean field. In general, the phenomenological single particle spectrum is not accurately reproduced. To overcome this difficulty one can improve the functional in order to incorporate in the mean field additional correlations in an effective way. In an alternative viable scheme one can introduce explicitly many-body correlations which affect the single particle motion at both dynamic and static levels. In particular, the particle-vibration coupling scheme modifies the positions of the individual single particle energies. In this case one also introduce the fragmentation of the single particle states, a feature that cannot be described at the mean field level. At the same time the so-introduced correlations modify the static single particle potential, and the single particle states that diagonalize the corresponding density matrix are not the orbitals of a mean field with occupation numbers 1 (occupied orbitals) and 0 (unoccupied orbitals) anymore. In this paper we show that both static and dynamic effects on the single particle motion can be introduced within a previously developed scheme, based on the conserving approximations, and that the static part can be identified with the so-called tadpole term introduced by Khodel in the self-consistent theory of finite Fermi systems. The treatment remains at the formal level, but we hope that several aspects of the particle-vibration coupling scheme will be clarified.

Incorporating self-consistent single-particle potentials into the microscopic-macroscopic method

Effective single-particle potentials obtained by self-consistent HFB calculations from the established non-relativistic and relativistic nuclear EDF approaches are incorporated into the microscopic-macroscopic method, a widely and successfully used approach for superheavy nuclei. We determine the Schrodinger-equivalent central and spin-orbit potentials incorporating effective mass effects. The method can be applied to non-relativistic and relativistic mean-fields. A parametrization in terms of the Wood-Saxon form is introduced to derive the proton and neutron potentials, appropriate for the microscopic-macroscopic method. As the first application, the extended microscopic-macroscopic approach is used to calculate the shell corrections in the heaviest nuclei. Constraints on parameters sets for central and spin-orbit potentials are derived for which the shell effects are amplified towards $ Z=120$ .

Excitonic giant-dipole potentials in cuprous oxide

In this work we predict the existence of a novel species of Wannier excitons when exposed to crossed electric and magnetic fields. In particular, we present a theory of giant-dipole excitons in $\textrm{Cu}_2\rm O$ in crossed fields. Within our theoretical approach we perform a pseudoseparation of the center-of-mass motion for the field-dressed excitonic species, thereby obtaining an effective single-particle Hamiltonian for the relative motion. For arbitrary gauge fields we exactly separate the gauge-dependent kinetic energy terms from the effective single-particle interaction potential. Depending on the applied field strengths and the specific field orientation, the potential for the relative motion of electron and hole exhibits an outer well at spatial separations up to several micrometers and depths up to $380\, \mu \rm eV$, leading to possible permanent excitonic electric dipole moments of around three million Debye.

Spectrum, radial wave functions, and hyperfine splittings of the Rydberg states in heavy alkali-metal atoms

We calculate the bound state spectrum of the highly excited valence electron in the heavy alkali atoms solving the radial Schr\"odinger eigenvalue problem numerically with an accurate spectral collocation algorithm that applies also for a large principal quantum number $n\gg1$. As an effective single-particle potential we favor the reputable potential of Marinescu \emph{et al}., {[}Phys. Rev.A \textbf{49}, 982(1994){]}. Recent quasiclassical calculations of the quantum defect of the valence electron agree for orbital angular momentum $l=0,1,2,...$ overall remarkably well with the results of the numerical calculations, but for the Rydberg states of rubidium and also cesium with $l=3$ this agreement is less fair. The reason for this anomaly is that the potential acquires for $l=3$ deep inside the ionic core a tiny second classical region, thus invalidating a standard WKB calculation with two widely spaced turning points. Comparing then our numerical solutions of the radial Schr\"odinger eigenvalue problem with the uniform analytic WKB approximation of Langer we observe everywhere a remarkable agreement, apart from a tiny region around the inner turning point. With help of an ansatz proposed by Fock we obtain for the \emph{s}-states a second uniform analytic approximation to the radial wave function complementary to the WKB approximation of Langer, which is exact for $r\to0^{+}$. The value of the radial \emph{s}-wave function at $r=0$ is analytically found, thus validating the Fermi-Segr\`e formula for the magnetic dipole interaction constant $A_{n,j,0}^{\left(\mathrm{HFS}\right)}$.

Symmetry-preserving mean field theory for electrostatics at interfaces.

We derive an instantaneous symmetry-preserving mean field equation relating the long-ranged component of the intermolecular interaction to an effective single particle potential. We verify the efficiency and accuracy of the symmetry-preserving mean field approach to treat complex nonuniform electrostatics and foresee its application to study self-assembly and disassembly processes at interfaces in many computer simulations.

Efficient calculation of the effective single-particle potential and its application in electron microscopy

We present an efficient method for obtaining the effective single-particle potential for electrons within density functional theory (DFT). In contrast to the independent atom model (IAM) often used to interpret microscopy experiments, our method includes the contributions from charge redistribution and exchange-correlation interactions in a realistic system. The method allows calculation of the effective potential through the widely used pseudopotential formalism instead of the costly all-electron calculations. A transferable and spin-independent core potential for each element is calculated once and for all. The nonlinear exchange-correlation interaction is treated explicitly. This scheme can be readily implemented in pseudopotential DFT codes. We demonstrate the usefulness of our method by calculating the scattering potential and simulating images of nitrogen point defects in graphene for transmission electron microscopy (TEM). The results are in good agreement with experiments.

Dirac particle in a spherical scalar potential well

In this paper we investigate a solution of the Dirac equation for a spin-$\frac{1}{2}$ particle in a scalar potential well with full spherical symmetry. The energy eigenvalues for the quark particle in ${s}_{1/2}$ states (with $\ensuremath{\kappa}=\ensuremath{-}1$) and ${p}_{1/2}$ states (with $\ensuremath{\kappa}=1$) are calculated. We also study the continuous Dirac wave function for a quark in such a potential, which is not necessarily infinite. Our results, at infinite limit, are in good agreement with the MIT bag model. We make some remarks about the sharpness value of the wave function on the wall. This model, for finite values of potential, also could serve as an effective model for the nucleus where $U(r)$ is the effective single particle potential.

Efficient Solutions of Self-Consistent Mean Field Equations for Dewetting and Electrostatics in Nonuniform Liquids

We use a new configuration-based version of linear response theory to efficiently solve self-consistent mean field equations relating an effective single particle potential to the induced density. The versatility and accuracy of the method is illustrated by applications to dewetting of a hard sphere solute in a Lennard-Jones fluid, the interplay between local hydrogen bond structure and electrostatics for water confined between two hydrophobic walls, and to ion pairing in ionic solutions. Simulation time has been reduced by more than an order of magnitude over previous methods.

Dependence of Response Functions and Orbital Functionals on Occupation Numbers.

Explicitly orbital-dependent approximations to the exchange-correlation energy functional of density functional theory typically not only depend on the single-particle Kohn-Sham orbitals but also on their occupation numbers in the ground-state Slater determinant. The variational calculation of the corresponding exchange-correlation potentials with the optimized effective potential (OEP) method therefore also requires a variation of the occupation numbers with respect to a variation in the effective single-particle potential, which is usually not taken into account. Here it is shown under which circumstances this procedure is justified.

Remarkable microstructure evolution in biogenic crystals upon mild annealing

24 European Crystallographic Meeting, ECM24, Marrakech, 2007 Page s77 Acta Cryst. (2007). A63, s77 average structure reveals the distribution of the ions as described by the probability density function, which can be obtained either by Fourier transformation of the Debye Waller factor (including anharmonic terms [1]) or by Fourier methods. The former is more appropriate for interstitial diffusion processes, i.e. when the migration of the ions proceeds directly to adjacent vacant sites. In this case a continuous density is found directly representing the diffusion pathway. Moreover, by applying Boltzmann statistics effective single particle potentials can be derived containing the potential barriers to migration which can be compared with otherwise measured activation energies. On the other hand, if interstitialcy (exchange) processes prevail, it is more meaningful to analyse difference Fourier maps and/or to introduce additional (metastable) positions. All this will be illustrated by various examples. For fluorite like ZrO2 doped with cations and anions (e.g. Sc and N [2]) one generally finds anion diffusion pathways directly through an edge of the surrounding cation tetrahedron along to a neighbouring site. Derived activation energies agree with those obtained from conductivity measurements showing that no additional energy is needed for the creation of defects. By comparing samples with and without N it is possible to derive separate activation energies for O and N. In perovskite like LaGaO3 doped with Mg and Sr the pathways are curved. These and the corresponding potentials are significantly altered when measured under electric fields [3] or microwave irradiation [4]. An example of interstitialcy diffusion is provided by mayenite (Ca12Al14O33) [5]. Its structure may be described as a calciumaluminate framework containing 32 of the 33 O atoms, while the remaining “free” oxygen statistically occupies 1/6 of larger cages in the structure. In spite of the presence of vacancies and rather large openings between adjacent cages no continuous density was found, therewith ruling out interstitial diffusion (probably because of too long jump distances). On the other hand, difference Fourier maps revealed various other weakly occupied positions which can be related to an exchange process with particular framework O. Moreover, each jump process is connected with a relaxation of Ca, i.e. there is considerable interaction with the framework. Interestingly, the mechanism is different when the “free” O is replaced by N, i.e. nitrogen shows the interstitial type of diffusion within the same framework.

Anion diffusion in Y- and N-doped ZrO2

Effective single particle potentials governing the motion of O2 and N3- anions have been determined by single crystal neutron diffraction at high temperatures for three samples of ZrO2 doped with different amounts of Y and N. Diffusion jumps take place directly to vacant nearest neighbour anion sites through the edges of the surrounding cation tetrahedra along (100)-directions. Activation enthalpies of migration for O (1.09 eV) and N (1.99 eV) are in good agreement with values obtained from tracer diffusion measurements (M. Kilo, C. Argirusis, G. Borchardt and R. A. Jackson, Phys. Chem. Chem. Phys., 2003, 5, 2219 and M. Kilo, M. A. Taylor, C. Argirusis, G. Borchardt, M. Lerch, O. Kaitasov and B. Lesage, Phys. Chem. Chem. Phys., 2004, 6, 3645). The diffusion process is facilitated by local short range order and anharmonic thermal vibrations. It is therefore advocated that the interactions with the phonons have to be taken into account in the description of the diffusion process.

In-plane optical features of the underdoped La 2CuO 4 based compounds: theoretical multiband analysis

The three-component ab-plane optical conductivity of the high- T c cuprates is derived using the gauge invariant response theory, and compared to the data previously obtained from the optical reflectivity measurements in the La 2CuO 4 based families. The valence electrons are described by the Emery three-band model with the antiferromagnetic correlations represented by an effective single-particle potential. In the 0< δ<0.3 doping range, it is shown that the total spectral weight of the three-band model is shared between the intra- and interband channels nearly in equal proportions. At optimum doping, the low-frequency conductivity has a (non-Drude) nearly single-component form, which transforms with decreasing doping into a two-component structure. The mid-infrared spectral weight is found to be extremely sensitive to the symmetry of the effective single-particle potential, as well as to the doping level. The gauge invariant form of the static and elastic Raman vertices is determined, allowing explicit verification of the effective mass theorem and the related conductivity sum rules.

Optimized effective potential method for polymers

The optimized effective potential (OEP) method allows for calculation of the local, effective single particle potential of density functional theory for explicitly orbital-dependent approximations to the exchange-correlation energy functional. In the present work the OEP method is used together with the approximation due to Krieger, Li, and Iafrate (KLI). We present the first application of this method to polymers. KLI calculations have been performed for the insulating polyethylene and the results have been compared to those from other orbital-dependent potentials. Various properties of the band structure are also calculated. The single-particle band gap strongly depends on the basis set with larger basis sets yielding narrow gaps. For certain physical quantities such as the total energy and the exchange energy, the various orbital-dependent Kohn–Sham exchange-only and Hartree–Fock results differ only slightly. For the highest occupied orbital energy the difference is more significant than expected. In order to get the right band gap in OEP the exchange contribution to the derivative discontinuity is calculated and added to the Kohn–Sham gap. The corrected gap obtained by the KLI approach is 12.8 eV compared with the Hartree–Fock and experimental values of 16.6 and 8.8 eV, respectively. We observe, however, the strong dependence of the derivative discontinuity on the basis set.

Quantum-mechanical description of ionization, capture, and excitation in proton collisions with atomic oxygen

The basis generator method is used to propagate effective single-particle equations for ion-atom collisions to provide a mean-field description for the proton-oxygen collision system. The pure capture and ionization as well as transfer ionization cross sections are calculated using two alternative prescriptions to extract the physical information from the propagated orbitals. The sensitivity of the resonant single capture cross section to the effective single-particle potential for atomic oxygen is tested. Cross sections are calculated for 1--2000 keV proton impact and good overall agreement is found with available experiments, while some of the results are at variance with a recent model calculation. The single-particle excitation amplitudes are combined in the LS coupling scheme to obtain excitation cross sections for particular atomic oxygen configurations. The latter are compared with recent measurements for proton and electron impact. Reasonable agreement is found for many one-electron excitations and some two-electron processes.

Force between charged particles with ion condensation

We have numerically calculated the interaction forces between two highly charged spherical particles embedded in a cloud of small ions with or without charge redistribution on the particle surfaces. Ion condensation near the charged particles leads to reduced electrostatic interaction between the particles, and we find that the effective two-particle interaction is significantly smaller than the values expected from considering only effective single-particle potentials.

Effective single-particle potentials for MnO in light of interatomic magnetic interactions: Existing theories and perspectives

It is shown that the fundamental gauge-symmetry constraints superimposed on the admissible form of the exchange-correlation energy functional lead to the generalized local force theorem for small nonuniform rotations of the spin magnetic moments near equilibrium. The theorem suggests that the magnetic interactions responsible for the low-energy spin-wave excitations near the ground state can be expressed in terms of the effective single-particle potential designed for the ground-state spin-magnetization density. The theorem allows us to obtain an empirical effective potential for MnO by fitting the experimental low-temperature spin-wave dispersion curve. The theorem is further applied to investigate abilities of several different first-principles techniques: local-(spin)-density approximation, LDA plus ``Hubbard $U$'' $(\mathrm{LDA}+U)$ and optimized effective potential (OEP). None of these approaches treats the magnetic interactions in MnO properly. Limitations of the one-electron band picture underlying the failure are elucidated in each case. As one of the perspective techniques to deal with the electronic structure of narrow-band materials, we propose to combine the $\mathrm{LDA}+U$ form of the single-particle equations with the variational principles of the OEP approach. Several possible approximations along this line are discussed.

Atomic resonances of hydrogen near aluminum surfaces:mAdiabatic evolution of the ground state

Complex adiabatic potential curves are an essential input to atomic surface scattering calculations employing the coupled-states method. We present calculations for the ground state of hydrogen near a jellium surface with the density of aluminum. Two complementary techniques have been implemented: the complex rotation method and the stabilization method. We employ large-scale matrix diagonalization and realistic effective single-particle potentials. The influence of the surface potential on the adiabatic evolution of the wave function and the resonance parameters as a function of the distance d from the surface have been investigated. Application to the ground state H(1s) yields significant differences for the position and width of the resonance compared to previously available data. The applicability of semiclassical theory for resonance parameters is tested and the role of over-barrier transitions is highlighted.