Coulomb interaction energy including overlap effects for the ground state of RbCs beyond 7 Å

1996 ◽  
Vol 74 (3-4) ◽  
pp. 155-158
Author(s):  
K. Hussein
Keyword(s):  
Interaction Energy ◽  
Coulomb Interaction ◽  
Configuration Space ◽  
Ground State ◽  
Present Method ◽  
Second Order ◽  
Experimental Results ◽  
Coulomb Energy ◽  
First Order ◽  
Dispersion Terms

We use a perturbative model based on a partition of the configuration space into four regions to calculate the Coulomb energy including charge-overlap effects (induction and dispersion terms) for the interaction between two atoms Rb(5s2S) and Cs(6s2S). Results for first-order electrostatic as well as second-order induction and dispersion energies will be presented in the range 13 < R < 25 a.u. The damping functions for the various dispersion terms varying as R−6, R−8, and R−10 in the range of large R have also been determined, and fitted analytical forms will be displayed for these terms. From comparison with accurate experimental results, the present method is seen to be valid for values of R beyond 7 Å (1 Å = 10−10 m).

The forces between polyatomic molecules I. Long-range forces

1961 ◽  
Vol 259 (1299) ◽  
pp. 433-441 ◽  
Keyword(s):  
Interaction Energy ◽  
Long Range ◽  
Electron Correlation ◽  
Polyatomic Molecules ◽  
Second Order ◽  
Multipole Moments ◽  
Double Integral ◽  
Order Interaction ◽  
First Order ◽  
Dispersion Terms

It is known that the electrostatic long-range forces between two molecules are 'locally additive' in the sense that the first-order interaction energy between molecules bearing charges or permanent multipole moments may be written as a double integral over pairs of points, one in each molecule. In this paper we examine the second-order interaction energy, which comprises polarization and dispersion terms, and find that the corresponding forces are locally additive or not according as the electron correlation within each molecule does or does not die away rapidly with distance.

A Percolation Equation for Modeling Experimental Results for Continuum Percolation Systems

2001 ◽  
Vol 699 ◽  
Author(s):  
D.S. McLachlan ◽  
C. Chiteme ◽  
W.D. Heiss ◽  
Junjie Wu
Keyword(s):  
Experimental Data ◽  
Ac Conductivity ◽  
Volume Fraction ◽  
Power Laws ◽  
Second Order ◽  
Experimental Results ◽  
Analytical Equation ◽  
Scaling Properties ◽  
First Order ◽  
Dc And Ac Conductivity

AbstractThe standard percolation equations or power laws, for dc and ac conductivity (dielectric constant) are based on scaling ansatz, and predict the behaviour of the first and second order terms, above and below the percolation or critical volume fraction (øc), and in the crossoverregion. Recent experimental results on ac conductivity are presented, which show that these equations, with the exception of real σm above øc and the first order terms in the crossover region, are only valid in the limit σi/σc = 0, where for an ideal dielectric σi=ωε0εr.A single analytical equation, which has the same parameters as the standard percolation equations, and which, for ac conductivity, reduces to the standard percolation power laws in the limit σi(ωε0εr)/σc = 0 for all but one case, is presented. The exception is the expression for real σm below øc, where the standard power law is always incorrect. The equation is then shown to quantitatively fit both first and second order dc and ac experimental data over the entire frequency and composition range. This phenomenological equation is also continuous, has the scaling properties required at a second order metal-insulator and fits scaled first order dc and ac experimental data. Unfortunately, the s and t exponents that are necessary to fit the data to the above analytical equation are usually not the simple dimensionally determined universal ones and depend on a number of factors.

THERMAL PROPERTIES AND GROUND STATE ENERGY SHIFT OF CHARGED ANYONS

1994 ◽  
Vol 09 (20) ◽  
pp. 3683-3705
Author(s):  
J.Y. KIM ◽  
Y.S. MYUNG ◽  
S.H. YI
Keyword(s):  
Coulomb Interaction ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Correlation Energy ◽  
Virial Coefficients ◽  
Energy Shift ◽  
Second Order ◽  
Quantization Scheme ◽  
Coulomb Interactions

We derive the second and third virial coefficients and the ground state energy shift for charged anyons within the Hartree-Fock approximation. A second quantization scheme at finite temperature is introduced for this calculation up to the second order and the vertex is composed of anyonic, point, constant as well as Coulomb interactions. The thermodynamic potential for the second order correlation diagram of Coulomb interaction leads to the logarithmic divergence (V ln V). Hence, we find the heat capacity and the correlation energy of anyons without Coulomb-Coulomb interaction. Finally, we discuss the magnetic-field-induced localization at low filling ν, including the Wigner crystal phase.

Perturbation treatment of the Hartree–Fock equations for the ground states of the boron-like ions

1969 ◽  
Vol 47 (7) ◽  
pp. 699-705 ◽  
Author(s):  
C. S. Sharma ◽  
R. G. Wilson
Keyword(s):  
Ground State ◽  
Atomic System ◽  
Ground States ◽  
Great Accuracy ◽  
Second Order ◽  
Expectation Values ◽  
Third Order ◽  
First Order ◽  
Hartree Fock ◽  
The Third

The first-order Hartree–Fock and unrestricted Hartree–Fock equations for the ground state of a five electron atomic system are solved exactly. The solutions are used to evaluate the corresponding second-order energies exactly and the third-order energies with great accuracy. The first-order terms in the expectation values of 1/r, r, r2, and δ(r) are also calculated.

scholarly journals Localized Conical Edge Modes of Higher Orders in Photonic Liquid Crystals

Crystals ◽  
2019 ◽  
Vol 9 (10) ◽  
pp. 542 ◽  
Author(s):  
Vladimir A. Belyakov ◽  
Sergei V. Semenov
Keyword(s):  
Liquid Crystals ◽  
Maxwell Equations ◽  
Analytic Solution ◽  
Second Order ◽  
Experimental Results ◽  
Analytical Theory ◽  
Exact Analytic Solution ◽  
Localized Modes ◽  
First Order ◽  
Order Diffraction

Most studies of the localized edge (EM) and defect (DM) modes in cholesteric liquid crystals (CLC) are related to the localized modes in a collinear geometry, i.e., for the case of light propagation along the spiral axis. It is due to the fact that all photonic effects in CLC are most pronounced just for a collinear geometry, and also partially due to the fact that a simple exact analytic solution of the Maxwell equations is known for a collinear geometry, whereas for a non-collinear geometry, there is no exact analytic solution of the Maxwell equations and a theoretical description of the experimental data becomes more complicated. It is why in papers related to the localized modes in CLC for a non-collinear geometry and observing phenomena similar to the case of a collinear geometry, their interpretation is not so clear. Recently, an analytical theory of the conical modes (CEM) related to a first order of light diffraction was developed in the framework of the two-wave dynamic diffraction theory approximation ensuring the results accuracy of order of δ, the CLC dielectric anisotropy. The corresponding experimental results are reasonably well described by this theory, however, some numerical problems related to the CEM polarization properties remain. In the present paper, an analytical theory of a second order diffraction CEM is presented with results that are qualitatively similar to the results for a first order diffraction order CEM and have the accuracy of order of δ2, i.e., practically exact. In particular, second order diffraction CEM polarization properties are related to the linear σ and π polarizations. The known experimental results on the CEM are discussed and optimal conditions for the second order diffraction CEM observations are formulated.

scholarly journals Signatures of Noncommutativity in Bar Detectors of Gravitational Waves

2019 ◽  
Vol 64 (11) ◽  
pp. 1029 ◽  
Author(s):  
S. Gangopadhyay ◽  
S. Bhattacharyya ◽  
A. Saha
Keyword(s):  
Gravitational Wave ◽  
Gravitational Waves ◽  
Excited States ◽  
Ground State ◽  
Order Term ◽  
Second Order ◽  
Length Scale ◽  
Length Variation ◽  
Wave Perturbation ◽  
First Order

The comparison between the noncommutative length scale √θ and the length variation δL = hL, detected in the GW detectors, indicates that there is a strong possibility to detect the noncommutative structure of space in the GW detector setup. Therefore, we explore how the response of a bar detector gets affected due to the presence of a noncommutative structure of space keeping terms up to the second order in a gravitational wave perturbation (h) in the Hamiltonian. Interestingly, the second-order term in h shows a transition between the ground state and one of the perturbed second excited states that was absent, when the calculation was restricted only to the first order in h.

Critical behaviors and phase diagrams of the mixed spin-1 and spin-7/2 Blume-Capel (BC) Ising model on the Bethe lattice (BL)

2015 ◽  
Vol 29 (28) ◽  
pp. 1550194 ◽  
Author(s):  
M. Karimou ◽  
R. Yessoufou ◽  
F. Hontinfinde
Keyword(s):  
Phase Transitions ◽  
Phase Diagrams ◽  
Ground State ◽  
Tricritical Point ◽  
Bethe Lattice ◽  
Second Order ◽  
Temperature Phase ◽  
First Order ◽  
Crystal Fields ◽  
Mixed Spin

Using the recursion equations technique, the influences of the single-ion anisotropies or crystal-fields interactions on the magnetic properties of the mixed spin-1 and spin-7/2 Blume-Capel (BC) Ising ferrimagnetic system are studied on the Bethe lattice (BL). The ground-state phase diagram is constructed, the thermal behaviors of the order-parameters and the free-energy are thoroughly investigated in order to characterize the nature of the phase transitions and to obtain the phase transition temperature. Then, the temperature phase diagrams are obtained in the case of equal crystal-field interactions on the ([Formula: see text] and [Formula: see text]) planes when q = 3, 4 and 6 and in the case of unequal crystal-fields interactions on the ([Formula: see text] and [Formula: see text]) and [Formula: see text] and [Formula: see text]) planes for selected values of [Formula: see text] and [Formula: see text] respectively when q = 3. The model shows first-order and second-order phase transitions, and where the lines are connected is the tricritical point. Besides the first-order and second-order phase transitions, the system also exhibits compensation temperatures depending on appropriate values of the crystal-fields interactions.

Study on Adsorption Property of Collagen Fiber Loaded Hyperbranched Polyamide-Amine Toward Cr (VI)

2012 ◽  
Vol 610-613 ◽  
pp. 514-517 ◽  
Author(s):  
Xue Chuan Wang ◽  
Fei Fei Zhang ◽  
Tao Tao Qiang
Keyword(s):  
Collagen Fiber ◽  
Adsorption Process ◽  
Adsorption Property ◽  
Second Order ◽  
Experimental Results ◽  
Order Model ◽  
First Order ◽  
Before And After ◽  
Pseudo Second Order ◽  
Hyperbranched Polyamide

Collagen fiber loaded hyperbranched polyamide-amine(CF-HBPN) was prepared by the crosslinking power of glutaraldehyde. The structure of CF-HBPN before and after adsorption was characterized and analyzed via scanning electron microscopy. The CF-HBPN was effective adsorbent for the removal of Cr(VI) from aqueous solutions. The adsorption isotherm and kinetic of the adsorption process were studied. The experimental results were fitted using the Langmuir, Freundlich and Temkin equations. The experimental results indicated that the Langmuir isotherm was better in describing the adsorption process. Two kinetic models, the pseudo-first order and pseudo-second order, were used to analyze the kinetic data. The pseudo-second order model was proven to be better in describing the adsorption behavior.

Experimental Results on the Combined 1st and 2nd Order Dynamics of a Small-Scale Taut-Leg Mooring Line

2005 ◽  
Author(s):  
Alexandre N. Simos ◽  
Andre´ L. C. Fujarra ◽  
Fa´bio G. Palazzo
Keyword(s):  
Second Order ◽  
Experimental Results ◽  
Mooring Line ◽  
Small Scale ◽  
Experimental Paradigm ◽  
Current Profile ◽  
Mooring Lines ◽  
Towing Tank ◽  
Calibration And Validation ◽  
First Order

A set of experimental results on the dynamics of taut-leg mooring-lines was generated by means of towing-tank tests. These results will be employed by Petrobras as an experimental paradigm for the calibration and validation of numerical codes based on finite-elements method (FEM). The setup allowed combining first and second order motions on the top of the line with different amplitudes and frequencies. The first order motions were emulated by means of circular harmonic motions while alternate horizontal translations represented the drift motions. It was also possible to emulate a uniform in-plane current profile along the suspended length of the model. The model was composed by three different segments. An intermediate rubber hawser connected the top and anchor chain segments and allowed considerable elongation of the line during the tests. Tension at the top of the model was measured by means of a load cell and the second-order motion was registered optically. This paper presents the procedure adopted for the tests and also some preliminary comparisons between experimental results and numerical simulations.

scholarly journals INFLUENCE OF PRESSURE ON SMECTIC A-NEMATIC PHASE TRANSITION

1999 ◽  
Vol 13 (09n10) ◽  
pp. 275-283 ◽  
Author(s):  
KISOR MUKHOPADHYAY ◽  
PRABIR K. MUKHERJEE
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Phenomenological Model ◽  
Order Parameter ◽  
Nematic Phase ◽  
Tricritical Point ◽  
Second Order ◽  
Experimental Results ◽  
First Order ◽  
Smectic A

We propose a Landau-de Gennes phenomenological model to describe the pressure induced smectic A-nematic phase transition. The influence of pressure on smectic A-nematic phase transitions are discussed for varying coupling between orientational and translational order parameter with pressure. Increasing the pressure, the first order nematic-smectic A transition becomes second order at a tricritical point which agrees fairly well with available experimental results.

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