scholarly journals Polarizabilities and Rydberg States in the Presence of a Debye Potential

Atoms ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 86
Author(s):  
Anand Bhatia ◽  
Richard Drachman
Keyword(s):  
Effective Potential ◽  
Rydberg States ◽  
Electron Correlations ◽  
Outer Electron ◽  
Nonlinear Parameters ◽  
Debye Potential ◽  
Screening Parameter ◽  
Higher Order Terms ◽  
Variational Calculations ◽  
Good Agreement

Polarizabilities and hyperpolarizabilities, α1, β1, γ1, α2, β2, γ2, α3, β3, γ3, δ and ε of hydrogenic systems have been calculated in the presence of a Debye–Huckel potential, using pseudostates for the S, P, D and F states. All of these converge very quickly as the number of terms in the pseudostates is increased and are essentially independent of the nonlinear parameters. All the results are in good agreement with the results obtained for hydrogenic systems obtained by Drachman. The effective potential seen by the outer electron is −α1/x4 + (6β1 − α2)/x6 + higher-order terms, where x is the distance from the outer electron to the nucleus. The exchange and electron–electron correlations are unimportant because the outer electron is far away from the nucleus. This implies that the conventional variational calculations are not necessary. The results agree well with the results of Drachman for the screening parameter equal to zero in the Debye–Huckel potential. We can calculate the energies of Rydberg states by using the polarizabilities and hyperpolarizabilities in the presence of Debye potential seen by the outer electron when the atoms are embedded in a plasma. Most calculations are carried out in the absence of the Debye–Huckel potential. However, it is not possible to carry out experiments when there is a complete absence of plasma at a particular electron temperature and density. The present calculations of polarizabilities and hyperpolarizabilities will provide accurate results for Rydberg states when the measurements for such states are carried out.

Validity of the Finite Fracture Mechanics Based Asymptotic Analysis for Predictions of Crack Deflection in Thin Layers of Ceramic Laminates

2014 ◽  
Vol 627 ◽  
pp. 237-240 ◽  
Author(s):  
Oldřich Ševeček ◽  
Dominique Leguillon ◽  
Tomáš Profant ◽  
Michal Kotoul
Keyword(s):  
Potential Energy ◽  
Asymptotic Solution ◽  
Asymptotic Analysis ◽  
Crack Extension ◽  
Crack Deflection ◽  
Thin Layers ◽  
Reference Solution ◽  
Finite Fracture Mechanics ◽  
Higher Order Terms ◽  
Good Agreement

The work studies and compares different approaches suitable for predictions of the crack deflection (bifurcation) in ceramic laminates containing thin layers under high residual stresses and discuss a suitability and limits of using of the asymptotic analysis for such problems. The thickness of the thin compressive layers where the crack deflection occurs is only one order higher than the crack extension lengths considered within the solution. A purely FEM based calculation of the energy and stress conditions, necessary for the crack propagation, serves as the reference solution to the problem. The asymptotic analysis is used after for calculations of the same quantities (especially of energy release rate – ERR). This concept enables semi-analytical calculations of ERR or changes in potential energy induced by the crack extensions of different lengths and directions. Such approach can save a large amount of simulations and time compared with the pure FEM based calculations. It was found that the asymptotic analysis provides a good agreement for investigations of the crack increments enough far from the adjacent interfaces but for longer extensions (of length above 1/5-1/10 of the distance from the interface) starts more significantly to deviate from the correct solution. Involvement of the higher order terms in the asymptotic solution or other improvement of the model is thus advisable.

scholarly journals Variational Solution of the Gross–Neveu Model: Finite N and Renormalization

1997 ◽  
Vol 12 (19) ◽  
pp. 3307-3334 ◽  
Author(s):  
C. Arvanitis ◽  
F. Geniet ◽  
M. Iacomi ◽  
J.-L. Kneur ◽  
A. Neveu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
General Framework ◽  
Free Field ◽  
Variational Calculation ◽  
Final Point ◽  
Variational Calculations ◽  
Perturbative Renormalization ◽  
Good Agreement ◽  
Gross Neveu Model

We show how to perform systematically improvable variational calculations in the O(2N) Gross–Neveu model for generic N, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the perturbative renormalization group. The final point is a general framework for the calculation of nonperturbative quantities like condensates, masses, etc., in an asymptotically free field theory. For the Gross–Neveu model, the numerical results obtained from a "two-loop" variational calculation are in a very good agreement with exact quantities down to low values of N.

scholarly journals Effect of Electronic Correlations on the Electronic Structure, Magnetic and Optical Properties of the Ternary RCuGe Compounds with R = Tb, Dy, Ho, Er

Materials ◽  
2020 ◽  
Vol 13 (16) ◽  
pp. 3536
Author(s):  
Alexey V. Lukoyanov ◽  
Lubov N. Gramateeva ◽  
Yury V. Knyazev ◽  
Yury I. Kuz’min ◽  
Sachin Gupta ◽  
...  
Keyword(s):  
Optical Properties ◽  
Electronic Structure ◽  
Theoretical Calculations ◽  
Rare Earth Ions ◽  
Local Spin Density Approximation ◽  
Electron Correlations ◽  
Absorption Region ◽  
Densities Of States ◽  
Interband Light Absorption ◽  
Good Agreement

In this study, the ab initio and experimental results for RCuGe ternary intermetallics were reported for R = Tb, Dy, Ho, Er. Our theoretical calculations of the electronic structure, employing local spin density approximation accounting for electron–electron correlations in the 4f shell of Tb, Dy, Ho, Er ions were carried in DFT+U method. The optical properties of the RCuGe ternary compounds were studied at a broad range of wavelengths. The spectral and electronic characteristics were obtained. The theoretical electron densities of states were taken to interpret the experimental energy dependencies of the experimental optical conductivity in the interband light–absorption region. From the band calculations, the 4f shell of the rare-earth ions was shown to provide the major contribution to the electronic structure, magnetic and optical properties of the RCuGe intermetallics. The accounting for electron–electron correlations in Tb, Dy, Ho, Er resulted in a good agreement between the calculated and experimental magnetic and optical characteristics.

Rigorous quantum electrodynamics treatment of electron correlations in high-Z ions: Beyond the Breit and effective-potential approximations

2001 ◽  
Vol 81 (10) ◽  
pp. 1547-1555 ◽  
Author(s):  
V. A. Yerokhin ◽  
A. N. Artemyev ◽  
V. M. Shabaev ◽  
M. M. Sysak ◽  
O. M. Zherebtsov ◽  
...  
Keyword(s):  
Effective Potential ◽  
Quantum Electrodynamics ◽  
Electron Correlations

ANHARMONIC EFFECTIVE POTENTIAL, LOCAL FORCE CONSTANT AND EXAFS OF HCP CRYSTALS: THEORY AND COMPARISON TO EXPERIMENT

2008 ◽  
Vol 22 (29) ◽  
pp. 5155-5166 ◽  
Author(s):  
NGUYEN VAN HUNG ◽  
TONG SY TIEN ◽  
LE HAI HUNG ◽  
RONALD R. FRAHM
Keyword(s):  
Thermal Expansion ◽  
Fine Structure ◽  
Thermal Expansion Coefficient ◽  
Force Constant ◽  
Expansion Coefficient ◽  
Effective Potential ◽  
X Ray ◽  
X Ray Absorption ◽  
Analytical Expressions ◽  
Good Agreement

Anharmonic effective potential, Extended X-ray Absorption Fine Structure (EXAFS) and its parameters of hcp crystals have been theoretically and experimentally studied. Analytical expressions for the anharmonic effective potential, effective local force constant, three first cumulants, a novel anharmonic factor, thermal expansion coefficient and anhamonic contributions to EXAFS amplitude and phase have been derived. This anharmonic theory is applied to analyze the EXAFS of Zn and Cd at 77 K and 300 K, measured at HASYLAB (DESY, Germany). Numerical results are found to be in good agreement with experiment, where unnegligible anharmonic effects have been shown in the considered theoretical and experimental quantities.

Eigen function and corresponding eigen values of charge carriers in V-grooves quantum wires with variable width

2016 ◽  
Vol 30 (17) ◽  
pp. 1650103
Author(s):  
Ali Hossein Mohammad Zaheri
Keyword(s):  
Effective Potential ◽  
Quantum Wire ◽  
Quantum Wires ◽  
Wave Functions ◽  
Charge Carriers ◽  
Energy Spectra ◽  
Eigen Value ◽  
Eigen Values ◽  
Interface Geometry ◽  
Good Agreement

In this work, we have calculated analytically the energy spectra of electrons and holes in V-grooves quantum wires. To modify wire structure, we have used the equations which suggested in the work of Inoshita et al. We introduce a new effective potential scheme which is applicable and matchable with actual interface geometry of this groove of ridge quantum wires. By applying this effective potential and considering a suitable transformed coordinate that allows the decoupling of the two-dimensional wave functions, we have calculated eigen values of the charge carriers in three states as well as the wave functions. We found that by increasing the curvature at the top of quantum wire [Formula: see text] the energy eigen value decreases. Our results are in good agreement with the earlier investigations.

Theoretical Study of the Physisorption of CO on Metal Oxide Surfaces Using the KSCED-DFT Approach

1998 ◽  
Vol 63 (9) ◽  
pp. 1447-1459 ◽  
Author(s):  
Nathalie Vulliermet ◽  
Tomasz A. Wesolowski ◽  
Jacques Weber
Keyword(s):  
Metal Oxide ◽  
Frequency Shift ◽  
Electron Density ◽  
Effective Potential ◽  
Theoretical Study ◽  
Adsorbed Molecule ◽  
Theoretical Studies ◽  
Metal Oxide Surfaces ◽  
Stretching Vibration ◽  
Good Agreement

Theoretical studies on structure and stretching frequency of the CO molecule physisorbed on the MgO(100) or ZnO(1010) surfaces are reported. The properties of the adsorbed molecule were investigated by means of the recently developed formalism of Kohn-Sham equations with constrained electron density (KSCED). The KSCED method makes it possible to divide a large system into two subsystems and to study one of them using Kohn-Sham-like equations with an effective potential which takes into account the interactions between subsystems. This method (KSCED) was shown to be adequate to study the properties of the CO molecule adsorbed on the MgO(100) surface as reported in a previous paper (Wesolowski et. al.: J. Mol. Struct., THEOCHEM, in press). The effect of the interactions with the surface on the CO stretching frequency and geometry was analyzed for vertically bound (C-down) CO at the Zn-site of the ZnO(1010) surface. The ZnO(1010) surface was represented using several cluster models: Zn2+, (ZnO3)4-, or Zn9O9 embedded in a matrix of point charges. The KSCED frequency shift of the CO stretching vibration is blue-shifted and in good agreement with experiment.

Many-Electron Correlations in the Photoionization of a Nitrogen Atom

1974 ◽  
Vol 52 (4) ◽  
pp. 349-354 ◽  
Author(s):  
N. A. Cherepkov ◽  
L. V. Chernysheva ◽  
V. Radojević ◽  
I. Pavlin
Keyword(s):  
Nitrogen Atom ◽  
Cross Section ◽  
Cross Sections ◽  
Random Phase Approximation ◽  
Random Phase ◽  
Electron Correlations ◽  
Sum Rule ◽  
Hartree Fock ◽  
The Cross ◽  
Good Agreement

Photoionization cross sections for the outer shell of the nitrogen atom ground state are calculated in the single-particle Hartree–Fock approximation and, in order to take into account many-electron correlations, also in the Random Phase Approximation with Exchange (RPAE). To be able to apply the RPAE, its modification for the half-filled shell atom, such as nitrogen atom, is presented. Calculation of length and velocity forms of the cross section in both approximations are compared with the available experimental data, and a good agreement is obtained. It has been found that in the RPAE the influence of many-electron correlations in a nitrogen atom is not great, but it is very important since, in contrast to the Hartree–Fock approximation, it results in the validity of the sum rule and the coincidence of the length and velocity forms of the cross sections, in agreement with the requirement of the general theory. The angular distribution of photoelectrons is also calculated in the RPAE, which has not been measured so far.

scholarly journals Approximate l-States of the Manning-Rosen Potential by Using Nikiforov-Uvarov Method

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Sameer M. Ikhdair
Keyword(s):  
Jacobi Polynomials ◽  
Bound State ◽  
Potential Range ◽  
Quantum Numbers ◽  
Special Cases ◽  
Screening Parameter ◽  
Potential Case ◽  
Rosen Potential ◽  
Uvarov Method ◽  
Good Agreement

The approximately analytical bound state solutions of the l-wave Schrödinger equation for the Manning-Rosen (MR) potential are carried out by a proper approximation to the centrifugal term. The energy spectrum formula and normalized wave functions expressed in terms of the Jacobi polynomials are both obtained for the application of the Nikiforov-Uvarov (NU) method to the Manning-Rosen potential. To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary principal and orbital quantum numbers n and l with two different values of the potential screening parameter α. It is found that our results are in good agreement with the those obtained by other methods for short potential range, lowest values of orbital quantum number l, and α. Two special cases of much interest are investigated like the s-wave case and Hulthén potential case.

scholarly journals Extraction of Heart Rate Variability from Smartphone Photoplethysmograms

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Rong-Chao Peng ◽  
Xiao-Lin Zhou ◽  
Wan-Hua Lin ◽  
Yuan-Ting Zhang
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Autonomic Function ◽  
Clinical Tool ◽  
Nonlinear Parameters ◽  
First Derivative ◽  
Peak Point ◽  
Characteristic Points ◽  
Highly Correlated ◽  
Good Agreement

Heart rate variability (HRV) is a useful clinical tool for autonomic function assessment and cardiovascular diseases diagnosis. It is traditionally calculated from a dedicated medical electrocardiograph (ECG). In this paper, we demonstrate that HRV can also be extracted from photoplethysmograms (PPG) obtained by the camera of a smartphone. Sixteen HRV parameters, including time-domain, frequency-domain, and nonlinear parameters, were calculated from PPG captured by a smartphone for 30 healthy subjects and were compared with those derived from ECG. The statistical results showed that 14 parameters (AVNN, SDNN, CV, RMSSD, SDSD, TP, VLF, LF, HF, LF/HF, nLF, nHF, SD1, and SD2) from PPG were highly correlated (r>0.7,P<0.001) with those from ECG, and 7 parameters (AVNN, TP, VLF, LF, HF, nLF, and nHF) from PPG were in good agreement with those from ECG within the acceptable limits. In addition, five different algorithms to detect the characteristic points of PPG wave were also investigated: peak point (PP), valley point (VP), maximum first derivative (M1D), maximum second derivative (M2D), and tangent intersection (TI). The results showed that M2D and TI algorithms had the best performance. These results suggest that the smartphone might be used for HRV measurement.

Sign in / Sign up

Export Citation Format

Share Document