Model Potential Energy Research Articles

Relativistic energies for diatomic molecule nucleus motions with the spin symmetry

Abstract The analytical solutions of the Dirac equation with the spin symmetry for the improved Manning–Rosen potential energy model have been explored. We present the bound state energy equation and the corresponding upper and lower radial wave functions. The degeneracy between the two states of the spin doublet for the nucleus motions of the X 1 Σ + state of SiF+ molecule has been observed. When the vector potential is equal to the scalar potential, the relativistic effect of the nuclear motion leads to a little decrease in the vibrational energies, while to an increase in those if the vector potential is greater than the scalar potential.

A comparison of interatomic potentials for modeling tungsten–hydrogen–helium plasma–surface interactions

We compare the hydrogen and helium clustering characteristics of three interatomic potential energy models intended for simulation of plasma-facing materials for fusion applications. Our simulations compare a Finnis–Sinclair potential and two different Tersoff-style bond order potentials created by Juslin et al. (2005) and Li et al. (2011), respectively, with respect to both helium and hydrogen clustering behavior in tungsten. We find significant differences between the Juslin and Li potentials in terms of both hydrogen and helium clustering behavior as well as the spatial distribution of hydrogen below the surface. These simulations are an important test on the road to more accurate models of gas clustering and surface evolution of tungsten divertors in ITER and other plasma devices.

D-dimensional energies for lithium dimer and silicon carbide radical

By using the supersymmetric shape invariance approach, we solve the Schrödinger equation with the modified Rosen–Morse potential energy model in D spatial dimensions. We find that the inter-dimensional degeneracy symmetry exists for the molecular system represented by the modified Rosen–Morse potential energy model. The rotation-vibrational energies for the 61Πu state of the 7Li2 molecule and the X3Π state of the SiC radical are observed to increase as D increases in the presence of a fixed vibrational quantum number and rotational quantum number. It is found that the behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system for these two molecular states.

Relationship of the deformed hyperbolic Kratzer-like and Tietz potential energy models for diatomic molecules

Taking the dissociation energy and the equilibrium bond length as explicit parameters, we construct an improved form of the deformed hyperbolic Kratzer-like potential function for diatomic molecules. We show that the deformed hyperbolic Kratzer-like potential model is equivalent to the Tietz potential model for diatomic molecules. We observe that the Tietz potential is superior to the Morse potential in reproducing the interaction potential energy curve for the 23Πg state of the 7Li2 molecule.

Molecular Spinless Energies of the Modified Rosen-Morse Potential Energy Model

We solve the Klein-Gordon equation with the modified Rosen-Morse potential energy model. The bound state energy equation has been obtained by using the supersymmetric shape invariance approach. The relativistic vibrational transition frequencies for the 6 1 Πu state of the 7 Li2 molecule have been computed by using the modified Rosen-Morse potential model. The calculated relativistic vibrational transition frequencies are in good agreement with the experimental RKR values.

D-dimensional energies for scandium monoiodide

We solve the Schrodinger equation with the Morse potential energy model in \(D\) spatial dimensions. The bound state rotation–vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. For a fixed vibrational quantum number and various rotational quantum numbers, the energies for the \(\hbox {X}^{1}\Sigma ^{+}\) state of ScI molecule increase as \(D\) increases. We observe that the behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system. The dimensional scaling method resembles a translation transformation from the higher dimensions to the actual three dimensions.

Nonequilibrium dynamics of a two-defect system under severe load.

In the framework of a two-defect model, based on a variation of the Landau technique, the kinetics of structural defect generation in solids under severe external load is investigated. The approach is based on a special form of kinetic equation in terms of internal energy, which is applied here to the description of an important practical problem of fine-grained structure formation in metals under severe plastic deformation. It unifies strengthening curves over the entire range of deformation, including the Hall-Petch and linear strengthening sections.

Fission-fragment charge yields: Variation of odd-even staggering with element number, energy, and charge asymmetry

Background: Fission-fragment charge-yield distributions exhibit a pronounced odd-even staggering. For actinide nuclei the staggering decreases with increasing proton number and with increasing excitation energy. In our calculations of fission yields [Phys. Rev. Lett. 106, 132503 (2011)] we obtained charge-yield distributions for a number of actinide nuclides by means of random walks on tabulated five-dimensional potential-energy surfaces. However, because the potential-energy model treats the system as a single, compound system during all stages of the fission process, in which individual fragment properties do not appear, no odd-even staggering appeared in the calculated yield curves.Purpose: We have recently become aware that in the experimental data displayed in Fig. 1 in the above paper, there is a remarkable similarity in the odd-even staggering in fission of $^{240}\mathrm{Pu}$ at thermal neutron energy and fission of $^{234}\mathrm{U}$ in photon-induced fission at around 11 MeV. We discuss how this similarity and how the variation in the magnitude of the odd-even staggering for three Th isotopes with charge asymmetry and isotope can be qualitatively understood based on strongly damped shape evolution on our calculated five-dimensional potential-energy surfaces.Methods: We conduct random walks on our tabulated five-dimensional potential-energy surfaces and study the difference between the total compound-nucleus energy and the potential energy for the different systems from saddle to scission. Under the strong-damping assumption this difference is the internal excitation energy. We also determine this quantity for different charge splits, symmetric and asymmetric.Results: We find that the magnitude of the odd-even staggering in the charge distribution in the several cases studied here correlates well, inversely, with the excitation energy above the potential-energy surface in the postsaddle region.Conclusions: Because the observed magnitude of the odd-even staggering correlates well with excitation energy over the region where the individual character of the fission fragments emerges, the Brownian shape-motion method can be expected to reproduce this feature, provided a potential-energy model is developed that accounts for how the nascent fragment properties are expressed in the calculated potential-energy surfaces.

Relationship of the Williams-Poulios and Manning-Rosen Potential Energy Models for Diatomic Molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved form of the Williams-Poulios potential energy model. It is found that the negative Williams-Poulios potential model is equivalent to the Manning-Rosen potential model for diatomic molecules. We observe that the Manning-Rosen potential is superior to the Morse potential in reproducing the interaction potential energy curves for the \({{a}^{3} \Sigma_{{\rm u}}^{+}}\) state of the 6Li2 molecule and the \({{X}^{1} \sum^{+}}\) state of the SiF+ molecule.

Synthesis and photoelectric properties of visible sensitive SnS2-linked graphene composites

SnS2-linked graphene (SnS2-rGO) was synthesized from graphene and SnCl2 under mild reducing conditions. X-ray diffraction and transmission electron microscopy of the SnS2-rGO samples confirmed the presence of SnS2 nanoplates that were highly dispersed and well linked onto the thin layered graphene. The SnS2-rGO was introduced as a working electrode into dye-sensitized solar cells (DSSCs) because of its good transparency and electric conductivity. The SnS2-rGO was mixed with p-25 TiO2 powders to make an anode electrode of DSSCs. The graphene and SnS2 exhibited a synergistic effect. Compared to p-25 TiO2-double layered DSSC, the SnS2-rGO-TiO2(upper)/TiO2(bottom) double layered anode film enhanced the energy conversion efficiency considerably; the efficiency for the 1.0 wt.% SnS2-rGO-TiO2(top)/TiO2(bottom)-DSSC was approximately 5.47%. A potential energy model for electron transfer among TiO2, SnS2-rGO-TiO2, and dye was suggested on the basis of ultraviolet–visible spectroscopy and cyclic voltammetry which showed a good relationship with the photovoltaic efficiency.

D-dimensional energies for sodium dimer

We solve the Schrödinger equation with the improved Tietz potential energy model in D spatial dimensions. The D-dimensional rotation–vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. The rotation–vibrational energies for the A1∑u+ and C1Пu states of the Na2 molecule increase as D increases in the presence of a fixed vibrational quantum number and rotational quantum number. It is observed that the behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system. We find that the D-dimensional scaling method resembles a translation transformation from the higher dimensions to the three dimensions.

D-dimensional energies for cesium and sodium dimers

We solve the Schrödinger equation with the improved Rosen−Morse potential energy model in D spatial dimensions. The D-dimensional rotation-vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. The energies for the 33[Formula: see text]g+ state of the Cs2 molecule and the 51Δg state of the Na2 molecule increase as D increases in the presence of fixed vibrational quantum number and various rotational quantum numbers. We observe that the change in behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system.

Solutions of the Klein-Gordon equation with the improved Manning-Rosen potential energy model in D dimensions

We solve the Klein-Gordon equation with the improved Manning-Rosen potential energy model in D spatial dimensions. The relativistic bound state energy equation and the unnormalized radial wave functions have been obtained. For fixed vibrational quantum number and various rotational quantum numbers, the relativistic energies for the a 3 Σ + states of the 7Li2 molecule increase as D increases. We observe that the change behavior of the relativistic vibrational energies in higher dimensions remains similar to that of the three-dimensional system.

Diatomic molecule energies of the modified Rosen−Morse potential energy model

We solve the Schrödinger equation with the modified Rosen−Morse empirical potential model to obtain rotation-vibrational energy spectra and unnormalized radial wave functions. The vibrational energy levels calculated with the modified Rosen−Morse potential model for the 61Πu state of the 7Li2 molecule and the X3Π state of the SiC radical are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential model.

Molecular energies of the improved Tietz potential energy model

We solve the Schrödinger equation with the improved Tietz empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The vibrational energy levels predicted by using the improved Tietz potential model for the 51Δgstate and C1Πustate of the Na2molecule are in good agreement with the experimental Rydberg−Klein−Rees data.

D-dimensional energies for lithium dimer

We solve the Schrödinger equation with the improved Manning–Rosen potential energy model in D spatial dimensions. The bound state rotation-vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. For fixed vibrational quantum number and various rotational quantum numbers, the energies for the a3Σu+ states of 7Li2 molecule increase as D increases. We observe that the change behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system.

Molecular energies of the improved Rosen−Morse potential energy model

We solve the Schrödinger equation with the improved Rosen−Morse empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The interaction potential energy curves for the 33Σg+ state of the Cs2 molecule and the 51Δg state of the Na2 molecule are modeled by employing the improved Rosen−Morse potential and the Morse potential. Favourable agreement for the improved Rosen−Morse potential is found in comparing with the Rydberg−Klein−Rees potential. The vibrational energy levels predicted by using the improved Rosen−Morse potential for the 33Σg+ state of Cs2 and the 51Δg state of Na2 are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential.

Molecular Spinless Energies of the Morse Potential Energy Model

We solve the Klein-Gordon equation with the Morse empirical potential energy model. The bound state energy equation has been obtained in terms of the supersymmetric shape invariance approach. The relativistic vibrational transition frequencies for the <TEX>$X^1{\sum}^+$</TEX> state of ScI molecule have been computed by using the Morse potential model. The calculated relativistic vibrational transition frequencies are in good agreement with the experimental RKR values.

Molecular spinless energies of the improved Tietz potential energy model

We solve the Klein-Gordon equation with the improved Tietz empirical potential energy model. The bound state energy equation has been obtained by using the supersymmetric shape invariance approach. The relativistic vibrational transition frequencies for the \(C^{1}\Pi_{u}\) state of Na2 molecule have been computed by using the improved Tietz potential model. The relativistic vibrational transition frequencies are in good agreement with the experimental RKR values.

High resolution infrared spectra of H2–Xe and D2–Xe van der Waals complexes

Spectra of weakly-bound hydrogen–xenon complexes are studied in equilibrium gas mixtures at relatively high spectral resolution (0.04 cm−1) using a long-path (112 m), low-temperature (140 K) absorption cell and a Fourier transform infrared spectrometer. The data cover the regions of the H2 and D2 fundamental stretching vibrations in the mid-infrared (λ ∼ 2.4, 3.3 μm), and are greatly improved compared to the only previous observation. The results serve as a stringent experimental benchmark for testing theoretical hydrogen–xenon intermolecular potential energy models, as well as forming the basis for deriving an improved semi-empirical potential.