LOWER BOUNDS FOR THE BINDING ENERGIES OF N-PARTICLE SYSTEMS

1967 ◽  
Vol 45 (11) ◽  
pp. 3753-3760 ◽  
Author(s):  
S. Pruski
Keyword(s):  
Lower Bounds ◽  
State Energy ◽  
Nuclear Charge ◽  
Energy Levels ◽  
Binding Energies ◽  
Particle Systems ◽  
Fermion System ◽  
Close Approximation ◽  
Bounded Below ◽  
The Given

Two new families of lower bounds to the energy of an N-fermion system interacting via two-body forces are derived. They involve, respectively, energy levels of (N − 1)- and (N − 2)-particle systems associated with the given N-fermion system. The first is expected to give a fairly close approximation to the energy. In the case of an atom of nuclear charge Z with N electrons, the ground-state energy of this [Z, N] ion is bounded below by (N − 1)/(N − 2)2 times the sum of the N lowest energy levels of an associated ion [Z′, N′], with N′ = N − 1 and Z′ = Z(N − 2)/(N − 1).

A CORRELATION ESTIMATE WITH APPLICATIONS TO QUANTUM SYSTEMS WITH COULOMB INTERACTIONS

1994 ◽  
Vol 06 (05a) ◽  
pp. 977-997 ◽  
Author(s):  
GIAN MICHELE GRAF ◽  
JAN PHILIP SOLOVEJ
Keyword(s):  
Lower Bounds ◽  
Ground State ◽  
State Energy ◽  
Fock Space ◽  
Quantum Systems ◽  
Coulomb Interactions ◽  
Hartree Fock ◽  
Exchange Effects ◽  
Correlation Estimate ◽  
Bounded Below

We consider some two-body operators acting on a Fock space with either fermionic or no statistics. We prove that they are bounded below by one-body operators which mimic exchange effects. This allows us to compare two-body correlations of fermionic and bosonic systems with those in Hartree-Fock, respectively Hartree theory. Applications of the fermionic estimate yield lower bounds for the ground state energy of jellium at high densities and of molecules with large nuclear charges.

scholarly journals A New Piano-Stool Ruthenium(II) P-Cymene-Based Complex: Crystallographic, Hirshfeld Surface, DFT, and Luminescent Studies

Crystals ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 13
Author(s):  
Mohd. Muddassir ◽  
Abdullah Alarifi ◽  
Mohd. Afzal
Keyword(s):  
Density Functional ◽  
Weak Interactions ◽  
Energy Levels ◽  
Hirshfeld Surface ◽  
Binding Energies ◽  
Orbital Energy ◽  
Aminosalicylic Acid ◽  
Full Characterization

A new complex (Ru(η6-p-cymene)(5-ASA)Cl2) (1) where 5-ASA is 5-aminosalicylic acid has been prepared by reacting the ruthenium arene precursors ((η6-arene)Ru(μ-Cl)Cl)2, with the 5-ASA ligands in a 1:1 ratio. Full characterization of complex 1 was accomplished by elemental analysis, IR, and TGA following the structure obtained from a single-crystal X-ray pattern. The structural analysis revealed that complex 1 shows a “piano-stool” geometry with Ru-C (2.160(5)- 2.208(5)Å), Ru-N (2.159(4) Å) distances, which is similar to equivalents sister complex. Density functional theory (DFT) was used to calculate the significant molecular orbital energy levels, binding energies, bond angles, bond lengths, and spectral data (FTIR, NMR, and UV–VIS) of complex 1, consistent with the experimental results. The IR and UV–VIS spectra of complex 1 were computed using all of the methods and choose the most appropriate way to discuss. Hirshfeld surface analysis was also executed to understand the role of weak interactions such as H⋯H, C⋯H, C-H⋯π, and vdW interactions, which play a significant role in the crystal environment’s stability. Moreover, the luminescence results at room temperature show that complex 1 gives a more intense emission band positioned at 465 nm upon excitation at 330 nm makes it a suitable candidate for the building of photoluminescent material.

THE NATURAL PARTIAL ORDER ON LINEAR SEMIGROUPS WITH NULLITY AND CO-RANK BOUNDED BELOW

2014 ◽  
Vol 91 (1) ◽  
pp. 104-115 ◽  
Author(s):  
SUREEPORN CHAOPRAKNOI ◽  
TEERAPHONG PHONGPATTANACHAROEN ◽  
PONGSAN PRAKITSRI
Keyword(s):  
Semigroup Forum ◽  
Partial Order ◽  
Lower Bounds ◽  
Partial Orders ◽  
Natural Partial Order ◽  
Linear Transformations ◽  
Bounded Below

AbstractHiggins [‘The Mitsch order on a semigroup’, Semigroup Forum 49 (1994), 261–266] showed that the natural partial orders on a semigroup and its regular subsemigroups coincide. This is why we are interested in the study of the natural partial order on nonregular semigroups. Of particular interest are the nonregular semigroups of linear transformations with lower bounds on the nullity or the co-rank. In this paper, we determine when they exist, characterise the natural partial order on these nonregular semigroups and consider questions of compatibility, minimality and maximality. In addition, we provide many examples associated with our results.

Microwave spectrum and ground state energy levels of H217O

1975 ◽  
Vol 56 (1) ◽  
pp. 138-145 ◽  
Author(s):  
Frank C. De Lucia ◽  
Paul Helminger
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Energy Levels ◽  
Microwave Spectrum

scholarly journals Optimization of a k-covering of a bounded set with circles of two given radii

2021 ◽  
Vol 11 (1) ◽  
pp. 232-240
Author(s):  
Alexander V. Khorkov ◽  
Shamil I. Galiev
Keyword(s):  
Linear Programming ◽  
Numerical Method ◽  
Lower Bounds ◽  
Integer Linear Programming ◽  
Numerical Results ◽  
Programming Models ◽  
Bounded Set ◽  
The Given

Abstract A numerical method for investigating k-coverings of a convex bounded set with circles of two given radii is proposed. Cases with constraints on the distances between the covering circle centers are considered. An algorithm for finding an approximate number of such circles and the arrangement of their centers is described. For certain specific cases, approximate lower bounds of the density of the k-covering of the given domain are found. We use either 0–1 linear programming or general integer linear programming models. Numerical results demonstrating the effectiveness of the proposed methods are presented.

scholarly journals Nuclear Structure Evolution Reflected from Local Relations

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2253
Author(s):  
Man Bao ◽  
Qian Wei
Keyword(s):  
Nuclear Charge ◽  
Binding Energies ◽  
Structure Evolution ◽  
Α Decay ◽  
Charge Radii ◽  
Coexistence Phase ◽  
Nuclear Masses ◽  
Quadrupole Deformation Parameter ◽  
Nuclear Structures ◽  
Physical Quantities

The structure evolution of nuclei which are in connection with symmetry breaking is one of the important problems not only for nuclear structures, but also for astrophysics and the spectroscopy of exotic nuclei. Many physical quantities can provide useful information of a shell structure, such as nuclear masses and nuclear charge radii. This paper introduces three kinds of local relations, i.e., the NpNn scheme respectively for the quadrupole deformation parameter and the excitation energy of the first 2+, 4+, 6+ states, the (αN′n+N′p) relation for nuclear charge radii and α decay energies, and the so-called “nonpairing” relation for binding energies and nuclear charge radii. All these relations reflect the evolution of nuclear structures, involving shells, subshells, shape coexistence, phase transition and the Wigner effect. Some results from different models can be verified with each other.

Evaluation of AlGaAs/GaAs Heterointerface by Shubnikov-de Haas Oscillation Measurements

1986 ◽  
Vol 77 ◽  
Author(s):  
Kazumi Kasai ◽  
H. Tanaka ◽  
H. Itoh ◽  
T. Oh-Hori ◽  
M. Takikawa ◽  
...  
Keyword(s):  
Excited State ◽  
State Energy ◽  
Energy Levels ◽  
Interface Model ◽  
Dimensional Electron ◽  
Excited State Energy ◽  
Haas Oscillation ◽  
First Excited State ◽  
A New Technique

ABSTRACTThe measurement of Shubnikov-de Haas(SdH) oscillation is proposed as a new technique for evaluating the quality of a heterointerface. The first excited state of 2-dimensional electron energy levels is determined for several samples using the measurements of SdH oscillation. Lower values of the first excited state energy are found for the samples with a low mobility. The low value can be approximately explained in terms of graded interface model.

Lower Bounds to the Critical Rayleigh Number in Completely Confined Regions

1967 ◽  
Vol 34 (2) ◽  
pp. 308-312 ◽  
Author(s):  
M. Sherman ◽  
S. Ostrach
Keyword(s):  
Rayleigh Number ◽  
Lower Bounds ◽  
Body Force ◽  
Critical Rayleigh Number ◽  
Convective Motion ◽  
The Body ◽  
Maximum Dimension ◽  
Fixed Temperature ◽  
Boussinesq Fluid ◽  
The Given

A method is presented for estimating lower bounds to the minimum Rayleigh number that will induce a state of convective motion in a quasi-incompressible (Boussinesq) fluid where the temperature gradient is in the direction of the body force. The fluid is completely confined by fixed-temperature, rigid bounding walls. For any arbitrary region, the critical Rayleigh number is greater than 1558(h/D)4 where h is the maximum dimension of the given region in the direction of the body force and D is the diameter of an equal volume sphere. In certain simple geometrical configurations, improved lower-bound estimates are calculated.

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

Sign in / Sign up

Export Citation Format

Share Document