scholarly journals Ro-vibrational energies of cesium dimer and lithium dimer with molecular attractive potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
C. A. Onate ◽  
T. A. Akanbi ◽  
I. B. Okon
Keyword(s):  
Thermal Properties ◽  
Attractive Potential ◽  
Average Deviation ◽  
Radial Wave ◽  
Lithium Dimer ◽  
Temperature Parameter ◽  
Vibrational Energies ◽  
Experimental Values ◽  
Uvarov Method ◽  
Potential Parameters

AbstractAn approximate solution of the Schrӧdinger equation for a molecular attractive potential was obtained using the parametric Nikiforov–Uvarov method. The energy equation and the corresponding radial wave functions were calculated. The effects of the potential parameters on the energy eigenvalues were examined. The thermal properties under the molecular attractive potential were calculated and the behaviour of the thermal properties with the maximum quantum state (λ) and the temperature parameter (β) respectively, were studied. Using the molecular spectroscopic parameters, the Rydberg–Klein–Rees (RKR) of cesium dimer and lithium dimer were both obtained and compared with the experimental values. The RKR values of both cesium dimer and lithium dimer calculated aligned with the observed values. The deviation and average deviation of the RKR for each molecule were also calculated.

scholarly journals Vibrational energies of some diatomic molecules for a modified and deformed potential

2021 ◽  
Author(s):  
C. A. Onate ◽  
I. B. Okon ◽  
M. C. Onyeaju ◽  
O. Ebomwonyi
Keyword(s):  
Energy Equation ◽  
Potential Model ◽  
Radial Wave Function ◽  
Expectation Values ◽  
Radial Wave ◽  
Molecular Potential ◽  
Lithium Dimer ◽  
Sodium Dimer ◽  
Vibrational Energies ◽  
Uvarov Method

Abstract A molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov-Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.

scholarly journals Vibrational energies of some diatomic molecules for a modified and deformed potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
C. A. Onate ◽  
I. B. Okon ◽  
M. C. Onyeaju ◽  
O. Ebomwonyi
Keyword(s):  
Energy Equation ◽  
Potential Model ◽  
Radial Wave Function ◽  
Expectation Values ◽  
Radial Wave ◽  
Molecular Potential ◽  
Lithium Dimer ◽  
Sodium Dimer ◽  
Vibrational Energies ◽  
Uvarov Method

AbstractA molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov–Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.

Analytical solution of the Shredinger equation for the linear combination of the Manning-Rosen and the class of Yukawa potential

2021 ◽  
pp. 157-169
Author(s):  
G.A. Bayramova ◽  
Keyword(s):  
Analytical Solution ◽  
Bound States ◽  
Hypergeometric Functions ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Radial Wave ◽  
Rosen Potential ◽  
Analytical Expressions ◽  
Potential Parameters

In the present work, an analytical solution for bound states of the modified Schrödinger equation is found for the new supposed combined Manning-Rosen potential plus the Yukawa class. To overcome the difficulties arising in the case l ≠ 0 in the centrifugal part of the Manning-Rosen potential plus the Yukawa class for bound states, we applied the developed approximation. Analytical expressions for the energy eigenvalue and the corresponding radial wave functions for an arbitrary value l ≠ 0 of the orbital quantum number are obtained. And also obtained eigenfunctions expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are very sensitive to the choice of potential parameters.

scholarly journals The 7Be(p, ?)8B Cross Section at Low Energies

1980 ◽  
Vol 33 (2) ◽  
pp. 177 ◽  
Author(s):  
FC Barker
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Solar Neutrinos ◽  
Model Calculations ◽  
Spectroscopic Factors ◽  
Low Energies ◽  
Standard Values ◽  
Experimental Values ◽  
Parameter Values ◽  
Potential Parameters

The nonresonant part of the 7Be(p, )I)8B cross section at low energies is recalculated by means of a direct-capture potential model, using parameter values determined by fitting 7Li(n, n)7Li and 7Li(n, )I)8Li data. Standard values of the potential parameters and spectroscopic factors give values of the 7Li(n,)I) cross section that are too large. Modified values that fit the thermal-neutron capture cross section predict 7Be(p,)I) cross sections that are much less than the experimental values. Also, shell model calculations predict resonant 7Be(p,)I) cross sections that are smaller than the experimental values. It is suggested that the accepted experimental values of the 7Be(p, )I) cross section may be too large, perhaps due partly to an overlarge accepted value for the 7Li(d, p)8Li cross section, which has been used for normalization purposes. A decrease in the 7Be(p,)I) cross section would reduce the calculated detection rate of solar neutrinos and lessen the discrepancy with the measured value.

scholarly journals Structural, elastic, electronic and thermal properties of InAs: A study of functional density

2017 ◽  
Vol 26 (46) ◽  
Author(s):  
Víctor Mendoza-Estrada ◽  
Melissa Romero-Baños ◽  
Viviana Dovale-Farelo ◽  
William López-Pérez ◽  
Álvaro González-García ◽  
...  
Keyword(s):  
Thermal Properties ◽  
Density Functional ◽  
Experimental Studies ◽  
Debye Model ◽  
Band Gap Energy ◽  
Functional Theory ◽  
Zinc Blende ◽  
The Density Functional Theory ◽  
The Stability ◽  
Experimental Values

In this research, first-principles calculations were carried out within the density functional theory (DFT) framework, using LDA and GGA, in order to study the structural, elastic, electronic and thermal properties of InAs in the zinc-blende structure. The results of the structural properties (a, B0, ) agree with the theoretical and experimental results reported by other authors. Additionally, the elastic properties, the elastic constants (C11, C12 and C44), the anisotropy coefficient (A) and the predicted speeds of the sound ( , , and ) are in agreement with the results reported by other authors. In contrast, the shear modulus (G), the Young's modulus (Y) and the Poisson's ratio (v) show some discrepancy with respect to the experimental values, although, the values obtained are reasonable. On the other hand, it is evident the tendency of the LDA and GGA approaches to underestimate the value of the band-gap energy in semiconductors. The thermal properties (V, , θD yCV) of InAs, calculated using the quasi-harmonic Debye model, are slightly sensitive as the temperature increases. According to the stability criteria and the negative value of the enthalpy of formation, InAs is mechanically and thermodynamically stable. Therefore, this work can be used as a future reference for theoretical and experimental studies based on InAs.

Charge distributions and chemical effects. XXXI. Molecular energies of ethylenic compounds

1983 ◽  
Vol 61 (1) ◽  
pp. 197-205 ◽  
Author(s):  
M.-T. Béraldin ◽  
S. Fliszâr
Keyword(s):  
Zero Point ◽  
Enthalpies Of Formation ◽  
Average Deviation ◽  
Bond Forming ◽  
Chemical Effects ◽  
Nuclear Magnetic Resonance Spectra ◽  
Energy Formula ◽  
Standard Enthalpies Of Formation ◽  
Vibrational Energies ◽  
Proper Consideration

The energy formula describing bond contributions in terms of the charges carried by the bond-forming atoms is applied to ethylenic compounds. It is shown in what manner σ and π electrons can be treated within the framework of the bond energy theory giving the atomization energy of the vibrationless molecule at 0 K. Proper consideration of zero-point and thermal vibrational energies leads to standard enthalpies of formation. These calculations, which are carried out on the basis of, 13C nuclear magnetic resonance spectra, agree with their experimental counterparts, within experimental uncertainties (~0.3 kcal mol−1 average deviation).

Diatomic molecules energy spectra for the generalized Mobius square potential model

2020 ◽  
Vol 34 (21) ◽  
pp. 2050209
Author(s):  
U. S. Okorie ◽  
A. N. Ikot ◽  
M. U. Ibezim-Ezeani ◽  
Hewa Y. Abdullah
Keyword(s):  
Dissociation Energy ◽  
Approximation Scheme ◽  
Potential Model ◽  
Vibrational Energy ◽  
Diatomic Molecules ◽  
Energy Spectra ◽  
Equilibrium Bond Length ◽  
Quantum Numbers ◽  
Vibrational Energies ◽  
Potential Parameters

The modified version of the generalized Mobius square (GMS) potential has been obtained by employing the dissociation energy and equilibrium bond length as explicit parameters. The potential parameters have been defined in terms of the molecular parameters. The modified GMS potential has also been used to model internuclear interaction potential curves for different states of diatomic molecules. Also, we have obtained the rotational–vibrational energy spectra of the new GMS potential model, both analytically and numerically for the different diatomic molecules. This was done by employing a Pekeris-type approximation scheme and an appropriate coordinate transformation to solve the Schrodinger equation. Our results have been compared with the experimental Rydberg–Klein–Rees (RKR) data and its corresponding average absolute deviations in terms of the dissociation energy computed. The effects of the vibrational and rotational quantum numbers on the rotational–vibrational energies for the different states of the various diatomic molecules have also been discussed. This paper has shown to be highly relevant to the studies of thermodynamic and thermochemical functions of diatomic molecules.

Thermal transport property prediction of a CMC laminate from base materials properties and manufacturing porosities

2005 ◽  
Vol 461 (2063) ◽  
pp. 3575-3597 ◽  
Author(s):  
P. Del Puglia ◽  
M.A Sheikh ◽  
D.R Hayhurst
Keyword(s):  
Finite Element ◽  
Thermal Properties ◽  
Ceramic Matrix Composite ◽  
Unit Cell ◽  
Matrix Cracking ◽  
Thermal Transport Property ◽  
Materials Properties ◽  
Base Materials ◽  
Experimental Values

This paper reviews two publications of the authors. The first relates to the classification of manufacturing porosity of a ceramic matrix composite material DRL-XT and the second to the quantification of thermal property degradation, due to porosity, at the level of the fibre tow and matrix regions. The paper then shows how these degraded thermal properties can be used in macro unit cell finite element analyses to quantify the effect of manufacturing porosity on bulk composite thermal properties. The dominant porosity type is matrix cracking, which is responsible for a 25% reduction of in-plane bulk thermal conductivity. Key to the success of the approach is an accurate knowledge of thermal properties of the constituent materials. However, in their absence, it is shown how property bounds may be used coupled with: semi-inverse finite element unit cell modelling and experimental values of bulk composite thermal properties.

Theory of spin-orbit coupling in atoms, II. Comparison of theory with experiment

1963 ◽  
Vol 271 (1347) ◽  
pp. 565-578 ◽  
Keyword(s):  
Wave Functions ◽  
Coupling Constants ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Outer Electron ◽  
Coupling Constant ◽  
Radial Wave ◽  
Order Of Magnitude ◽  
Experimental Values

Results of calculations of the spin-orbit coupling constant for 2 p , 3 p , 4 p , and 3 d shell ions and atoms are presented. The calculations are based on a theory developed in a previous paper. Excellent agreement of this theory with experiment is obtained for the 2 p and 3 d shell ions, while calculations using the familiar < ∂ V / r ∂ r > expression for the coupling constant lie 10 to 20 % too high. The exchange terms discussed in the earlier paper make a contribution to the coupling constant of the same sign and order of magnitude as the ordinary shielding terms. For the 3 p and 4 p shell atoms, the calculated coupling constants based on the exact theory and on the < ∂ V / r ∂ r > expression both tend to lie below the experimental values. An explanation for this disagreement is suggested, based on the noded nature of the outer-electron radial wave functions for these atoms. The importance of the residual-spin-other-orbit interaction is discussed, and it is shown that ignoring the form of this interaction may lead to a large variation in the coupling constant within a configuration.

scholarly journals Research on calculation of grinding surface roughness

2022 ◽  
pp. 85-92
Author(s):  
Van Nga Tran Thi ◽  
Khanh Nguyen Lam ◽  
Cuong Nguyen Van
Keyword(s):  
Surface Roughness ◽  
Surface Hardness ◽  
Experimental Results ◽  
Grinding Wheel ◽  
Grinding Wheels ◽  
Machining Processes ◽  
Average Deviation ◽  
Proposed Model ◽  
Experimental Values ◽  
Tip Radius

In machining processes, grinding is often chosen as the final machining method. Grinding is often chosen as the final machining method. This process has many advantages such as high precision and low surface roughness. It depends on many parameters including grinding parameters, dressing parameters and lubrication conditions. In grinding, the surface roughness of a workpiece has a significant influence on quality of the part. This paper presents a study of the grinding surface roughness predictions of workpieces. Based on the previous studies, the study built a relationship between the abrasive grain tip radius and the Standard marking systems of the grinding wheel for conventional and superabrasive grinding wheels (diamond and CBN abrasive). Based on this, the grinding surface roughness was predicted. The proposed model was verified by comparing the predicted and experimental results. Appling the research results, the surface roughness when grinding three types of steel D3, A295M and SAE 420 with Al2O3 and CBN grinding wheels were predicted. The predicted surface roughness values were close to the experimental values, the average deviation between predictive results and experimental results is 15.11 % for the use of Al2O3 grinding wheels and 24.29 % for the case of using CBN grinding wheels. The results of the comparison between the predicted model and the experiment show that the method of surface roughness presented in this study can be used to predict surface roughness in each specific case. The proposed model was verified by comparing the predicted and measured results of surface hardness. This model can be used to predict the surface hardness when surface grinding

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