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1
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Use of Guseinov's One-Center Expansion Formulae and Löwdin α Radial Function in Calculation of Two-Center Overlap Integrals over Slater Type Orbitals with Noninteger Principal Quantum Numbers

100%
Mamedov B., Çopuroğlu E.
Acta Physica Polonica A
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2011
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vol. 119
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issue 3
332-335
EN
An efficient calculation algorithm is presented for two-center overlap integrals over noninteger n* Slater type orbitals in molecular coordinate system based on the use of Guseinov's one-center expansion formulae and Löwdin α radial function. These integrals are expressed in terms of overlap integrals of integer n Slater type orbitals. The analytical formulae offer the advantage of direct and efficient calculation of the two-center overlap integrals over noninteger n* Slater type orbitals without the use of numerical methods. Several numerical results obtained are presented to demonstrate the improvements in convergence rates.
2
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Calculations of Energy Levels Using the Weakest Bound Electron Potential Model Theory

100%
Zhang T., Zheng N.
Acta Physica Polonica A
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2009
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vol. 115
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issue 3
629-635
EN
In this paper, we introduce a new method for calculation of energy levels in detail and give our results for several iso-spectrum-level series as examples: [He] 2s2p ^{1}P_{1}, [He] 2s2p ^{3}P_{0}, [He] 2s2p ^{3}P_{2}, and [He] 2s3s ^{3}S_{1} series of Be-like sequence; [Ne] 3s^{2}3d ^{2}D_{3/2} series and [Ne] 3s^{2}3d ^{2}D_{5/2} series of Al-like sequences; [Ne] 4p ^{2}P_{1/2} series, [Ne] 5d ^{2}D_{5/2} series, and [Ne] 6f ^{2}F_{7/2} series of Na-like sequences. In the method I(Z)=T_lim (Z)-T(Z,n), where I(Z), T_lim(Z), and T(Z,n) denote ionization potential, series limit, and energy level of a given member, respectively. The expression of non-relativistic part of I(Z) is derived from weakest bound election potential model theory and relativistic effects of I(Z) are included by using a six-order polynomial in Z. Our results are compared with the experimental data and with those obtained by other theoretical method.
3
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Theoretical Study of Energy Levels and Transition Probabilities of Boron Atom

100%
Tian-yi Z., Neng-wu Z.
Acta Physica Polonica A
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2009
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vol. 116
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issue 2
141-153
EN
Though the electrons configuration for boron atom is simple and boron atom has long been of interest for many researchers, the theoretical studies for properties of BI are not systematic, there are only few results reported on energy levels of high excited states of boron, and transition measurements are generally restricted to transitions involving ground states and low excited states without considering fine structure effects, provided only multiplet results, values for transitions between high excited states are seldom performed. In this article, by using the scheme of the weakest bound electron potential model theory calculations for energy levels of five series are performed and with the same method we give the transition probabilities between excited states with considering fine structure effects. The comprehensive set of calculations attempted in this paper could be of some value to workers in the field because of the lack of published calculations for the BI systems. The perturbations coming from foreign perturbers are taken into account in studying the energy levels. Good agreement between our results and the accepted values taken from NIST has been obtained. We also reported some values of energy levels and transition probabilities not existing on the NIST data bases.
4
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Excitation Energy Transport between the Ionic Forms of Rhodamine B in Viscous Solutions

100%
Bojarski P., Kułak L.
Acta Physica Polonica A
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1998
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vol. 94
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issue 5-6
725-734
EN
Excitation energy transport between zwitterion and cationic form of rhodamine B in glycerol-ethanol mixture is studied. Concentration course of the quantum yield exhibits a rapid drop at intermediate concentrations, where no dimers are formed contrary to the results of measurements carried out for solutions with a trace amount of acid or base in which single ionic forms are adopted. To describe properly such concentration behavior of the quantum yield forward and reverse, nonradiative excitation energy transport between the forms is considered. This task is performed by comparing experimental data with Monte-Carlo simulations.
5
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Two-Component Relativistic Hamiltonians and the Douglas-Kroll Approximation

100%
Barysz M.
Acta Physica Polonica A
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2002
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vol. 101
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issue 6
815-823
EN
The iterative solutions of the previously derived operator equation which defines an open-ended formalism for the reduction of the 4-component Dirac Hamiltonian to 2-component "electronic" operators of arbitrarily high accuracy, are discussed. It is shown that by departing from the approach based solely on the operator algebra one can define the initial iterative solution which leads to the 2-component Douglas-Kroll Hamiltonian. The present derivation reveals the origin of the success of methods based on the Douglas-Kroll Hamiltonian. It also shows that among relatively simple 2-component Hamiltonians, which are exact through the fourth power of the fine structure constant, the Douglas-Kroll operator is the most complete one. Also a computationally convenient and highly compact formula for matrix elements of the Douglas-Kroll Hamiltonian is obtained as a by-product of this investigation.
6
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Analytical Representation of Total Cross-Sections for Electron Atom Scattering: Application to Atomic Helium

100%
Mansouri A., Houamer S., Moulay M.
Acta Physica Polonica A
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2003
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vol. 104
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issue 1
25-34
EN
Based on the series expansion formalism, an analytical approach is proposed to evaluate the total cross-sections induced by electron impact excitation. As an illustration, an analytical expression of the total cross-section of the double excitation of helium atom by electron impact is obtained for the 2p^2 ^3P and 2p3p ^1P transitions within the framework of the distorted wave Born approximation. The available experimental data are well reproduced by the obtained expression of the total cross-section which is function of the only parameter of the incident electron energy. Comparisons are also made with numerical calculations.
7
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2D B_xC_{1-x} Layers as Predicted by the Cluster-Expansion Approach

100%
Gonzalez Szwacki N.
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vol. 126
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issue 5
1215-1217
EN
In this work, the cluster-expansion method combined with extensive first-principles calculations is used for predicting the most stable 2D B_xC_{1-x} (x ≤0.5) layers. For concentrations of B up to ≈ 38%, the honeycomb structure of the boron-carbon compound is preserved, whereas for larger concentrations, the boron atoms tend to form 2D clusters and/or ribbons that are fragments of a triangular boron sheet. Our studies indicate that the incorporation of boron into graphene is energetically unfavorable even for low concentrations of B, however, the graphene-like structure of the B_xC_{1-x} layer may be stabilized by a metallic substrate.
8
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A Comparison of Different Approximate Two-Component Relativistic Theories of Many-Electron Systems: A Case Study of the Ionization Energies of Two-Electron Ions

100%
Barysz M., Flocke N., Karwowski J.
Acta Physica Polonica A
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2001
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vol. 99
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issue 6
631-641
EN
The corrections to the ionization energies of two-electron ions due to relativistic effects are studied by different two-component relativistic methods. In particular, the results obtained by the standard Pauli-Cowan-Griffin method and by two variants of the Douglas-Kroll-Hess method (the one based on the free-particle transformation and the one in which the transformation accounts for the nuclear potential) are compared with those calculated using the four-component Dirac-Fock method. Limits of applicability of each of these methods have been indicated. Results acceptable in the whole range of the nuclear charge (relativistic corrections accurate up to 4% for Z≤85) are given only by the Douglas-Kroll-Hess method which goes beyond the free-particle transformation. Each of the other two approaches either underestimates or overestimates the corrections due to relativistic effects.
9
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On the Accuracy of the Discretization Techniques in Approximate Relativistic Methods

100%
Woźniak D., Sadlej A. J.
Acta Physica Polonica A
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2000
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vol. 98
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issue 6
673-690
EN
Several non-singular 2-component methods for relativistic calculations of the electronic structure of atoms and molecules lead to cumbersome operators which are partly defined in the coordinate representation and partly in the momentum representation. The replacement of the Fourier transform technique by the approximate resolution of identity in the basis set of approximate eigenvectors of the p^{2} operator is investigated in terms of the possible inaccuracies involved in this method. The dependence of the accuracy of the evaluated matrix elements on the composition of the subspace of these eigenvectors is studied. Although the method by itself appears to be quite demanding with respect to the faithfulness of the representation of the p^{2} operator, its performance in the context of the standard Gaussian basis sets is found to be encouragingly accurate. This feature is interpreted in terms of approximately even-tempered structure of the majority of Gaussian basis sets used in atomic and molecular calculations.
10
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Relativistic Paschen-Back Effect for the Two-Dimensional H-Like Atoms

80%
Poszwa A., Rutkowski A.
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issue 3
439-444
EN
The classification of states based on good quantum numbers for the two-dimensional Coulomb problem is proposed. The first order magnetic energy corrections are calculated using exact field-free analytic solutions of the Dirac equation as a zero-order approximation.
11
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Ground States of Helium Atom and Hydrogen Negative Ion in the Presence of Magnetic Field Using Variational Monte Carlo Technique

80%
Doma S., Shaker M., Farag A., El-Gammal F.
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vol. 126
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issue 3
700-705
EN
Using variational Monte Carlo method, we calculated the 1^1 0^{+} state energies, the derivatives of the total energy and the ionisation energies of the helium atom, and hydrogen negative ion in the presence of magnetic field regime between 0 a.u. and 10 a.u. Our calculations are based on using two types of compact and accurate trial wave functions used before to calculate energies in the absence of magnetic field. Our results are in good agreement with the most recent previous accurate values and also with the exact values.
12
Content available remote

Collisional Ionization in Lithium Vapor Excited by Nanosecond Laser Pulses

80%
Mahmoud M., El Tabal A., Nady M.
Acta Physica Polonica A
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2012
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vol. 122
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issue 1
71-77
EN
We report a theoretical study of the collisional ionization processes which occur under 2s → 2p excitation of lithium vapor excited with a nanosecond pulsed laser. The time evolution of the electron energy distribution function and the atomic ion density (Li^{+}) as well as the molecular ion density (Li^{+}_2) at different lithium vapor densities was investigated. The results show a nonlinear behavior of the energy spectra of the electrons created during the interaction of the laser with the lithium vapor. The nonlinear behavior results from superelastic collisions between the free electrons produced by collisional ionization and photoionization with Li(2p). The results also show that a competition exists between the collisional ionization and photoionization processes in producing the atomic ion and the molecular ions.
13
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Investigation of Relations between Atomic Number and Composition Weight Ratio in PZT and SMA and Prediction of Mechanical Behavior

80%
Monfared V., Khalili M.
Acta Physica Polonica A
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2011
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vol. 120
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issue 3
424-428
EN
In this paper there is presented the mechanical behavior of the one lead-zirconate-titanate by its atomic number and its certain mechanical behavior is simulated by the mathematical modeling and ABAQUS software for smart materials, as well as prediction of mechanical behaviors. Also in this smart material (Pb-Zr-Ti) the grain size according to molar ratio is studied. This mechanical behavior is modeled by the exponential and polynomial formula from one to ten degree. Next there are defined the new relations for mechanical behavior and composition weight ratio, between composed elements for triplex lead-zirconate-titanate and dual smart materials. Triplex lead-zirconate-titanate has been selected as main and important material for the development of smart structures. In addition, the relation between atomic number and weight ratio in one smart material (Ni-Ti) is investigated briefly. In this work, change of resistance and voltage, pressure, grain size, molar ratio, residual stress, content of zirconate and the other mechanical properties are studied.
14
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Effect of Linear Absorption on Efficiency of SHG in Layered Structure

80%
Soltanmohammadi J., Jamshidi-Ghaleh K., Masalehdan H.
Acta Physica Polonica A
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2013
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vol. 123
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issue 2
401-403
EN
The effect of linear absorptions on conversion efficiency of the fundamental radiation to the second harmonic wave in a layered structure is investigated under intensity constant approximation. Behaviour of the conversion efficiency after each layer, up to third layer, is graphically illustrated.
15
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Atomic Properties of the Two-Electron System using Variational Monte Carlo Technique

80%
Doma S., El-Gammal F.
Acta Physica Polonica A
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2012
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vol. 122
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issue 1
42-48
EN
Using variational Monte Carlo method we calculated the lowest order relativistic corrections for the ground state energies of the helium-like atoms, up to Z = 10, and also for some excited state energies of the helium atom. These relativistic corrections include: mass-velocity effect, orbit-orbit interaction, spin magnetic and dipole moments of the two electrons and the Darwin effect. Moreover, correction due to the nucleus motion has been also calculated. Our results were obtained by using two new types of compact and accurate trial wave functions for the helium ions. For excited states we used simple trial wave functions of good quality and accurate results. The obtained results are in good agreement with the most recent previous accurate values and also with the exact values.
16
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Analytic Approximations for Thomas-Fermi Equation

70%
El-Nahhas A.
Acta Physica Polonica A
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2008
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vol. 114
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issue 4
913-918
EN
In this paper, we give an analytic approximation to the solution of the Thomas-Fermi equation using the homotopy analysis method and with the use of a polynomial exponential basis.
17
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An Explicit Analytic Solution to the Thomas-Fermi Equation by the Improved Differential Transform Method

70%
Fatoorehchi H., Abolghasemi H.
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vol. 125
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issue 5
1083-1087
EN
In this paper, a newly proposed analytical scheme by the authors namely the improved differential transform method is employed to provide an explicit series solution to the Thomas-Fermi equation. The solution procedure is very straightforward, requiring merely elementary operations together with differentiation, and ends up in a recursive formula involving the Adomian polynomials to afford the unknown coefficients. Unlike many other methods, our approach is free of integration and hence can be of computational interest. In addition, a very good agreement between the proposed solution and the results from several well-known works in the literature is demonstrated.
18
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Exact Exchange Scheme in the Parallel r-Space Implementation of the Kohn-Sham Realization of the Density Functional Theory

70%
Marchwiany M., Birowska M., Majewski J.
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EN
In this communication, we present the r-space implementation of the Kohn-Sham realization of the density functional theory with the exact exchange functional within the computational algorithm for computers of parallel architecture. In comparison to the standard approach employing the local density functional, the scheme with exact exchange functional requires roughly ten times larger computational burden. The developed parallelization procedure accelerates the computations by a factor of four and six for the exact exchange and the local density functional schemes, respectively. It brings us closer to the treatment of dispersive van der Waals interactions on the fully ab initio level in the large class of systems.
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