Lower bounds for the ground states of the He-isoelectronic series

1981 ◽  
Vol 59 (11) ◽  
pp. 1668-1669 ◽  
Author(s):  
Serafin Fraga
Keyword(s):  
Kinetic Energy ◽  
Lower Bounds ◽  
Ground State ◽  
Ground States ◽  
Numerical Results ◽  
Hartree Fock ◽  
Electron Atom ◽  
Isoelectronic Series

A formulation, based on the concept of null local kinetic energy regions, has been developed for the determination of lower bounds for the ground state of a two-electron atom. Numerical results, obtained from Hartree–Fock functions, are presented for the elements He through Kr of the two-electron series.

scholarly journals Stimulated Processes in a Half-collision

1986 ◽  
Vol 5 (6) ◽  
pp. 393-406
Author(s):  
H. H. Telle
Keyword(s):  
Kinetic Energy ◽  
Quantum State ◽  
Ground State ◽  
Diatomic Molecules ◽  
Dye Laser ◽  
Interatomic Potentials ◽  
Repulsive Potential ◽  
Induced Absorption ◽  
Tunable Dye Laser

Selective photodissociation of diatomic molecules is used to prepare the separating species in a well defined quantum state with narrowly determined final kinetic energy of the particles. During the course of separation to products the repulsive potential is probed by a tunable dye laser, that is by induced absorption in case the dissociation proceeds on a potential leading to ground state products, or by induced emission or absorption for all other cases. The determination of interatomic potentials from the observed spectra is discussed.

scholarly journals EXACT GROUND STATES OF CORRELATED ELECTRONS ON PENTAGON CHAINS

2013 ◽  
Vol 27 (14) ◽  
pp. 1330009 ◽  
Author(s):  
ZSOLT GULÁCSI
Keyword(s):  
Kinetic Energy ◽  
Band Structure ◽  
Ground State ◽  
Ground States ◽  
Coulomb Repulsion ◽  
Positive Semidefinite ◽  
Flat Band ◽  
Correlated Electrons ◽  
Density Region ◽  
Hubbard Interaction

We construct a class of exact ground states for correlated electrons on pentagon chains in the high density region and discuss their physical properties. In this procedure the Hamiltonian is first cast in a positive semidefinite form using composite operators as a linear combination of creation operators acting on the sites of finite blocks. In the same step, the interaction is also transformed to obtain terms which require for their minimum eigenvalue zero at least one electron on each site. The transformed Hamiltonian matches the original Hamiltonian through a nonlinear system of equations whose solutions place the deduced ground states in restricted regions of the parameter space. In the second step, nonlocal product wave functions in position space are constructed. They are proven to be unique ground states which describe non-saturated ferromagnetic and correlated half metallic states. These solutions emerge when the strength of the Hubbard interaction Ui is site-dependent inside the unit cell. In the deduced phases, the interactions tune the bare dispersive band structure such to develop an effective upper flat band. We show that this band flattening effect emerges for a broader class of chains and is not restricted to pentagon chains. For the characterization of the deduced solutions, uniqueness proofs, exact ground state expectation values for long-range hopping amplitudes and correlation functions are also calculated. The study of physical reasons which lead to the appearance of ferromagnetism has revealed a new mechanism for the emergence of an ordered phase, described here in detail. This works as follows: starting from a completely dispersive bare band structure, the interactions quench the kinetic energy, hence the ordered phase is obtained solely by a drastic decrease of the interaction energy. Since Ui are site dependent, this determinative decrease is obtained by a redistribution of the double occupancy di such to attain small di where the on-site Coulomb repulsion Ui is high, and vice versa. The kinetic energy quench leads to the upper effective flat band, whose role is to enhance by its degeneracy the switching to the ordered phase dictated and stabilized by the interactions present. It is shown that for this phenomenon to occur, a given degree of complexity is needed for the chain, and the mechanism becomes inactive when the Ui interactions are homogeneous, or are missing from the ground state wave function.

Perturbation treatment of the Hartree–Fock equations for the ground states of the boron-like ions

1969 ◽  
Vol 47 (7) ◽  
pp. 699-705 ◽  
Author(s):  
C. S. Sharma ◽  
R. G. Wilson
Keyword(s):  
Ground State ◽  
Atomic System ◽  
Ground States ◽  
Great Accuracy ◽  
Second Order ◽  
Expectation Values ◽  
Third Order ◽  
First Order ◽  
Hartree Fock ◽  
The Third

The first-order Hartree–Fock and unrestricted Hartree–Fock equations for the ground state of a five electron atomic system are solved exactly. The solutions are used to evaluate the corresponding second-order energies exactly and the third-order energies with great accuracy. The first-order terms in the expectation values of 1/r, r, r2, and δ(r) are also calculated.

An Exciton Approach to the Excited States of Two Electron Atoms. II. Determination of Spectroscopic Parameters, Polarizabilities and Dispersion Coefficients of H-, He, Li+, Be2+ and Ne8+

1985 ◽  
Vol 38 (1) ◽  
pp. 11
Author(s):  
PE Schipper ◽  
B Martire
Keyword(s):  
Excited States ◽  
Ground State ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Exciton Model ◽  
Interaction Coefficients ◽  
Isoelectronic Series ◽  
Helium Isoelectronic Series ◽  
Good Agreement

The exciton model developed in an earlier paper is applied quantitatively to a description of the excited states of representative members of the helium isoelectronic series; viz. H-, He, Li+,Be2+ and Ne8+. The energies of the eight lowest excited states are in good agreement with experiment, for a relatively small (1s-4p) hydrogenic basis; the ground state is obtained with slightly less precision. Response properties including oscillator strengths, polarizabilities and dispersion interaction coefficients are also calculated. The method appears to be quantitatively sound, and, above all, leads to particularly simple interpretations of the wave functions and the energies.

scholarly journals Existence of Infinitely Many Distinct Solutions to the Quasirelativistic Hartree-Fock Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-20 ◽  
Author(s):  
M. Enstedt ◽  
M. Melgaard
Keyword(s):  
Riemannian Manifold ◽  
Kinetic Energy ◽  
Ground State ◽  
Multiple Solutions ◽  
Density Operator ◽  
Coulomb Systems ◽  
Total Charge ◽  
Hartree Fock ◽  
Noncompact Riemannian Manifold ◽  
Semilinear Elliptic

We establish existence of infinitely many distinct solutions to the semilinear elliptic Hartree-Fock equations forN-electron Coulomb systems with quasirelativistic kinetic energy−α−2Δxn+α−4−α−2for thenthelectron. Moreover, we prove existence of a ground state. The results are valid under the hypotheses that the total chargeZtotofKnuclei is greater thanN−1and thatZtotis smaller than a critical chargeZc. The proofs are based on a new application of the Fang-Ghoussoub critical point approach to multiple solutions on a noncompact Riemannian manifold, in combination with density operator techniques.

Electronic Structure of the Transition Elements

1973 ◽  
Vol 51 (6) ◽  
pp. 644-647
Author(s):  
K. M. S. Saxena ◽  
S. Fraga
Keyword(s):  
Electronic Structure ◽  
Excited States ◽  
Ground State ◽  
Ground States ◽  
Negative Ions ◽  
State Function ◽  
Transition Elements ◽  
Hartree Fock ◽  
Positive Ions ◽  
Single Set

Numerical Hartree–Fock functions have been determined for the ground states and first excited states of the configurations 3dN4s0 and 3dN4s2 for the negative ions, neutral atoms, and first four positive ions of all the transition elements. The validity of the approximation, embodied in the use of a single set of parameters determined from the ground state function of a configuration for the prediction of the spectroscopic levels arising from it, has been examined in detail in the case of Fe I, 3d64s2, where independent calculations have been carried out for all the excited states.

scholarly journals EXISTENCE OF GROUND STATES FOR NEGATIVE IONS AT THE BINDING THRESHOLD

2014 ◽  
Vol 26 (01) ◽  
pp. 1350021 ◽  
Author(s):  
JACOPO BELLAZZINI ◽  
RUPERT L. FRANK ◽  
ELLIOTT H. LIEB ◽  
ROBERT SEIRINGER
Keyword(s):  
Ground State ◽  
Nuclear Charge ◽  
Ground States ◽  
Negative Ions ◽  
Critical Value ◽  
Electron Atom

As the nuclear charge Z is continuously decreased an N-electron atom undergoes a binding-unbinding transition. We investigate whether the electrons remain bound and whether the radius of the system stays finite as the critical value Zc is approached. Existence of a ground state at Zc is shown under the condition Zc < N - K, where K is the maximal number of electrons that can be removed at Zc without changing the energy.

ON THE EVALUATION OF THE RIGOROUS ELECTROSTATIC POTENTIAL/ATOMIC ENERGY RELATIONSHIP

2007 ◽  
Vol 06 (04) ◽  
pp. 761-788
Author(s):  
ABRAHAM F. JALBOUT
Keyword(s):  
Electrostatic Potential ◽  
Ground State ◽  
Density Functional ◽  
Nuclear Charge ◽  
Electrostatic Potentials ◽  
Atomic Energy ◽  
Hartree Fock ◽  
Isoelectronic Series ◽  
Neutral Ground

A series of atomic energy formulas that relate atomic energies to the electrostatic potentials V0 at nuclei are obtained by a series of polynomial and series fits of V0 versus nuclear charge (Z). Density functional and Hartree–Fock V0 are used for a series of fits that involve an isoelectronic series of anions, cations, and neutral ground state atoms to approximate atomic energies. Comparisons to the exact energies were performed in order to demonstrate the efficacy of the rigorous expressions.

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 On the Evaluation of the Specific Mass Shift in the Ground States of Members of the He Isoelectronic Series

1979 ◽  
Vol 34 (12) ◽  
pp. 1538-1540
Author(s):  
Subal Saha ◽  
Sankar Sengupta
Keyword(s):  
Ground State ◽  
Pauli Principle ◽  
Mass Shift ◽  
Specific Mass ◽  
Expectation Values ◽  
Hartree Fock ◽  
Isoelectronic Series ◽  
Order Energy ◽  
Specific Mass Shift ◽  
State Configuration

Abstract A variation-perturbation method to calculate the specific mass shift in the ground state configuration of members of the He isoelectronic series is proposed. Through minimization of the second order energy, completely coupled and correlated orbitals are obtained in the Hartree Fock approximation. The influence of the Pauli principle and the electrostatic interaction on the motion of the electrons are automatically included while estimating the specific mass shift. This procedure also enables expectation values of the operator r1 · r2 to be calculated easily.

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