Tunneling of a diatomic molecule

2006 ◽  
Vol 84 (6-7) ◽  
pp. 615-620 ◽  
Author(s):  
G L Goodvin ◽  
Mark RA Shegelski
Keyword(s):  
Binding Energy ◽  
Potential Barrier ◽  
Energy Levels ◽  
Three Dimensional ◽  
One Dimension ◽  
Vibrational States ◽  
Elegant Method ◽  
Initial States ◽  
Transmission Resonances ◽  
Homonuclear Molecule

We summarize our study of a diatomic homonuclear molecule incident upon a potential barrier in one dimension [G.L. Goodvin and M.R.A. Shegelski. Phys. Rev. A, 71, 032719 (2005).]. We study various initial states for the molecule and allow transitions between vibrational states of the molecule during the process of tunneling. By applying an elegant method to solve this problem, we show that transmission resonances occur in several cases and that adding more binding energy levels for the molecule can tend to decrease the probability of tunneling. We also discuss the extension of our results to more realistic three-dimensional and experimental systems.PACS Nos.: 34.20.Cf, 03.65.Xp, 34.20.Gj, 34.50.Pi

Reconstruction of Objects from their Projections Using Orthogonal Functions

1973 ◽  
Vol 31 ◽  
pp. 268-269
Author(s):  
Elrnar Zeitler
Keyword(s):  
Unit Area ◽  
Three Dimensional ◽  
One Dimension ◽  
Spatial Density ◽  
Dimensional Representation ◽  
Orthogonal Functions ◽  
Object A ◽  
Plane Normal ◽  
Dimensional Object ◽  
Spatial Density Distribution

Considering any finite three-dimensional object, a “projection” is here defined as a two-dimensional representation of the object's mass per unit area on a plane normal to a given projection axis, here taken as they-axis. Since the object can be seen as being built from parallel, thin slices, the relation between object structure and its projection can be reduced by one dimension. It is assumed that an electron microscope equipped with a tilting stage records the projectionWhere the object has a spatial density distribution p(r,ϕ) within a limiting radius taken to be unity, and the stage is tilted by an angle 9 with respect to the x-axis of the recording plane.

Energies and Electric Dipole Moments of the Bound Vibrational States of HN2+ and DN2+

2008 ◽  
Vol 73 (6-7) ◽  
pp. 873-897 ◽  
Author(s):  
Vladimír Špirko ◽  
Ota Bludský ◽  
Wolfgang P. Kraemer
Keyword(s):  
Dipole Moment ◽  
Nearest Neighbor ◽  
Energy Surface ◽  
Dipole Moments ◽  
Three Dimensional ◽  
Vibrational States ◽  
Spacing Distribution ◽  
Triatomic Molecules ◽  
Vibrational Levels ◽  
Different Levels

The adiabatic three-dimensional potential energy surface and the corresponding dipole moment surface describing the ground electronic state of HN2+ (Χ1Σ+) are calculated at different levels of ab initio theory. The calculations cover the entire bound part of the potential up to its lowest dissociation channel including the isomerization barrier. Energies of all bound vibrational and low-lying ro-vibrational levels are determined in a fully variational procedure using the Suttcliffe-Tennyson Hamiltonian for triatomic molecules. They are in close agreement with the available experimental numbers. From the dipole moment function effective dipoles and transition moments are obtained for all the calculated vibrational and ro-vibrational states. Statistical tools such as the density of states or the nearest-neighbor level spacing distribution (NNSD) are applied to describe and analyse general patterns and characteristics of the energy and dipole results calculated for the massively large number of states of the strongly bound HN2+ ion and its deuterated isotopomer.

scholarly journals SPECTRAL CORRELATIONS IN DISORDERED MESOSCOPIC METALS AND THEIR RELEVANCE FOR PERSISTENT CURRENTS

1996 ◽  
Vol 10 (28) ◽  
pp. 1397-1406 ◽  
Author(s):  
AXEL VÖLKER ◽  
PETER KOPIETZ
Keyword(s):  
Energy Levels ◽  
Three Dimensional ◽  
Average Density ◽  
Electron Interaction ◽  
Energy Window ◽  
Persistent Currents ◽  
Dependent Part ◽  
The Difference ◽  
Aharonov Bohm ◽  
Grand Canonical

We use the Lanczos method to calculate the variance σ2(E, ϕ) of the number of energy levels in an energy window of width E below the Fermi energy for noninteracting disordered electrons on a thin three-dimensional ring threaded by an Aharonov–Bohm flux ϕ. We confirm numerically that for small E the flux-dependent part of σ2(E, ϕ) is well described by the Altshuler–Shklovskii-diagram involving two Cooperons. However, in the absence of electron–electron interactions this result cannot be extrapolated to energies E where the energy-dependence of the average density of states becomes significant. We discuss consequences for persistent currents and argue that for the calculation of the difference between the canonical- and grand canonical current it is crucial to take the electron–electron interaction into account.

Dynamics of a composite system in a point source-induced space–time

2021 ◽  
pp. 2150144
Author(s):  
Abdullah Guvendi
Keyword(s):  
Point Source ◽  
Composite System ◽  
Dimensional Space ◽  
Energy Levels ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Space Time ◽  
Spin Coupling ◽  
Quantum Oscillator ◽  
Dimensional Space Time

We investigate the dynamics of a composite system ([Formula: see text]) consisting of an interacting fermion–antifermion pair in the three-dimensional space–time background generated by a static point source. By considering the interaction between the particles as Dirac oscillator coupling, we analyze the effects of space–time topology on the energy of such a [Formula: see text]. To achieve this, we solve the corresponding form of a two-body Dirac equation (fully-covariant) by assuming the center-of-mass of the particles is at rest and locates at the origin of the spatial geometry. Under this assumption, we arrive at a nonperturbative energy spectrum for the system in question. This spectrum includes spin coupling and depends on the angular deficit parameter [Formula: see text] of the geometric background. This provides a suitable basis to determine the effects of the geometric background on the energy of the [Formula: see text] under consideration. Our results show that such a [Formula: see text] behaves like a single quantum oscillator. Then, we analyze the alterations in the energy levels and discuss the limits of the obtained results. We show that the effects of the geometric background on each energy level are not same and there can be degeneracy in the energy levels for small values of the [Formula: see text].

Inner-product theory calculations for some rational potentials in a three-dimensional system

1996 ◽  
Vol 74 (1-2) ◽  
pp. 4-9
Author(s):  
M. R. M. Witwit
Keyword(s):  
Energy Levels ◽  
Three Dimensional ◽  
Inner Product ◽  
Dimensional System ◽  
Product Technique ◽  
Special Cases ◽  
Wide Range ◽  
Perturbation Parameters ◽  
Three Dimensional System ◽  
Range Of Values

The energy levels of a three-dimensional system are calculated for the rational potentials,[Formula: see text]using the inner-product technique over a wide range of values of the perturbation parameters (λ, g) and for various eigenstates. The numerical results for some special cases agree with those of previous workers where available.

scholarly journals Calculations with Reaction Matrices in the p?f Shell

1972 ◽  
Vol 25 (6) ◽  
pp. 651
Author(s):  
HN Comins ◽  
RGL Hewitt
Keyword(s):  
Binding Energy ◽  
Shell Model ◽  
Energy Levels ◽  
Model Reaction ◽  
Pauli Operator ◽  
Reaction Matrix

Elements of the shell-model reaction matrix have been calculated for the p-f shell with an exact treatment of the Pauli operator. These elements have been used in straightforward calculations of the energy levels of 42Ca and 42Sc and the binding energy of 40Ca.

Benzotriazacycle Cored Perylene Diimide Non-fullerene Acceptors for High-performance Organic Solar Cells

2021 ◽  
Vol 01 ◽  
Author(s):  
Min Deng ◽  
Zhenkai Ji ◽  
Xiaopeng Xu ◽  
Liyang Yu ◽  
Qiang Peng
Keyword(s):  
Solar Cells ◽  
Organic Solar Cells ◽  
High Performance ◽  
Energy Levels ◽  
Three Dimensional ◽  
Molecular Structures ◽  
Perylene Diimide ◽  
Photon Absorption ◽  
Optoelectronic Property ◽  
Design Synthesis

Background: Perylene diimide (PDI) is among the most investigated non-fullerene electron acceptor for organic solar cells (OSCs). Constructing PDI derivatives into three-dimensional propeller-like molecular structures is not only one of the viable routes to suppress the over aggregation tendency of the PDI chromophores, but also raises possibilities to tune and optimize the optoelectronic property of the molecules. Objective: In this work, we reported the design, synthesis, and characterization of three electron-accepting materials, namely BOZ-PDI, BTZ-PDI, and BIZ-PDI, each with three PDI arms linked to benzotrioxazole, benzotrithiazole, and benzotriimidazole based center cores, respectively. Method: The introduction of electron-withdrawing center cores with heteroatoms does not significantly complicate the synthesis of the acceptor molecules but drastically influences the energy levels of the propeller-like PDI derivatives. Result: The highest power conversion efficiency was obtained with benzoxazole-based BOZ-PDI reaching 7.70% for its higher photon absorption and charge transport ability. Conclusion: This work explores the utilization of electron-withdrawing cores with heteroatoms in the propeller-like PDI derivatives, which provides a handy tool to construct high-performance non-fullerene acceptor materials.

Some Properties of a Quartic Potential with a Finite Binding Energy

1978 ◽  
Vol 33 (12) ◽  
pp. 1581-1587
Author(s):  
R. N. Kesarwani ◽  
Y. P. Varshni
Keyword(s):  
Binding Energy ◽  
Potential Energy ◽  
Energy Function ◽  
Interparticle Distance ◽  
Potential Energy Function ◽  
Vibrational States ◽  
Third Order ◽  
Quartic Potential ◽  
The Third ◽  
Range Of Values

Abstract A potential energy function is proposed which exhibits a quartic dependence on (r - re), where re is the equilibrium interparticle distance, in the neighbourhood of re, and has a finite binding energy. To study the pattern of the eigenvalues, the WKBJ method is applied to the third order, and the relevant integrals are evaluated analytically. Results are shown graphically for a few sets of parameters. The number of vibrational states that the potential can support is determined for a range of values of the parameters. Some suggestions as to the possible applications of the proposed potential are also made.

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