ENERGY LEVELS IN THE STATISTICAL ATOM WITH EXCHANGE AND CORRELATION

1967 ◽  
Vol 45 (5) ◽  
pp. 1745-1754 ◽  
Author(s):  
Ashok Jain ◽  
Satish Kumar
Keyword(s):  
Ground State ◽  
Energy Levels ◽  
Argon Atom ◽  
Particle Energy ◽  
Single Particle Energy ◽  
Relativistic Generalization ◽  
Quantum Numbers ◽  
Different Types ◽  
Present Formalism ◽  
Experimental Values

In this paper, quantum numbers are introduced in a statistical model of atoms that includes the correlation and the exchange terms (TFDC model). Two different types of angular momentum assignments have been introduced into the model and, as an application of this, the single-particle energy levels of the argon atom in its ground state have been calculated. A simple relativistic generalization of the present formalism is discussed and is shown to give better agreement with experimental values. Finally, some suggestions for improvement of the present formalism are made.

Shell-Tunneling Spectroscopy of the Single-Particle Energy Levels of Insulating Quantum Dots

Nano Letters ◽  
2001 ◽  
Vol 1 (10) ◽  
pp. 551-556 ◽  
Author(s):  
E. P. A. M. Bakkers ◽  
Z. Hens ◽  
A. Zunger ◽  
A. Franceschetti ◽  
L. P. Kouwenhoven ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Single Particle ◽  
Energy Levels ◽  
Tunneling Spectroscopy ◽  
Particle Energy ◽  
Single Particle Energy

scholarly journals HARTREE–FOCK GROUND STATE OF THE COMPOSITE FERMION METAL

1995 ◽  
Vol 09 (14) ◽  
pp. 889-894
Author(s):  
PIOTR SITKO ◽  
LUCJAN JACAK
Keyword(s):  
Single Particle ◽  
Ground State ◽  
Particle Energy ◽  
Fermi Velocity ◽  
Exchange Term ◽  
Single Particle Energy ◽  
Composite Fermion ◽  
Hartree Fock ◽  
Logarithmic Interaction ◽  
Particle Exchange

Within the Hartree–Fock approximation the ground state of the composite fermion metal is found. We observe that the single-particle energy spectrum is dominated by the logarithmic interaction exchange term which leads to an infinite jump of the single-particle exchange at the Fermi momentum. It is shown that the Hartree–Fock result brings no corrections to the RPA Fermi velocity.

scholarly journals WHY HOLES ARE NOT LIKE ELECTRONS III: HOW HOLES IN THE NORMAL STATE TURN INTO ELECTRONS IN THE SUPERCONDUCTING STATE

2009 ◽  
Vol 23 (14) ◽  
pp. 3035-3057 ◽  
Author(s):  
J. E. HIRSCH
Keyword(s):  
Single Particle ◽  
Normal State ◽  
Superconducting State ◽  
Negative Charge ◽  
Energy Levels ◽  
Particle Energy ◽  
Point Of View ◽  
Electron Interaction ◽  
Single Particle Energy ◽  
The Difference

In recent work, we discussed the difference between electrons and holes in energy band in solids from a many-particle point of view, originating in the electron–electron interaction,1 and from a single particle point of view, originating in the electron–ion interaction.2 We proposed that superconductivity in solids only occurs when the Fermi level is close to the top of a band (hole carriers), that it originates in "undressing" of carriers from both the electron–electron and the electron–ion interaction, and that as a consequence holes in the normal state behave like electrons in the superconducting state.3 However, the connection between both undressing effects was left unclear, as was left unclear how the transformation from hole behavior to electron behavior occurs. Here, we clarify these questions by showing that the same electron–electron interaction physics that promotes pairing of hole carriers and undressing of carriers from the electron–electron interaction leads to undressing of carriers from the electron–ion interaction and transforms the behavior of carriers from hole-like to electron-like. A complete reorganization of the occupation of single-particle energy levels occurs. Furthermore this phenomenon is connected with the expulsion of negative charge that we predict to occur in superconductors. These unexpected connections support the validity of our theoretical framework, the theory of hole superconductivity, to explain superconductivity in solids.

The influence of environment upon the spectra of molecules in liquids and crystals

1960 ◽  
Vol 255 (1280) ◽  
pp. 5-21 ◽  
Keyword(s):  
Ground State ◽  
Electronic Excitation ◽  
Energy Levels ◽  
Rotational Energy ◽  
Intermolecular Distance ◽  
Pressure Broadening ◽  
Basic Difference ◽  
Solid States ◽  
Quantum Numbers ◽  
Electronic Ground

The effect on the spectrum of a molecule of the environment in which it is located depends upon the changes which the surroundings produce in the electronic, vibrational, rotational and nuclear energies of the upper and lower states of the molecule. Studies of the influence of environment in the gaseous, liquid or solid states can thus be made by any of the appropriate techniques listed in table 1, and it is clearly desirable in studying any one system to use as many different techniques as possible. A basic difference between the effect of environment on electronic and vibra­tional energy levels arises from the very much greater overlap of electron density with the environment that results from electronic excitation. Hence while for the consideration of changes which arise in the vibrational spectrum it is adequate to consider only the distortion of the curve relating the interaction energy to the intermolecular distance in the electronic ground state, for electronic spectra, how­ever, the changes in the potential curves in both upper and lower states must clearly be taken into account. Collisions between molecules in gases lead to the broadening of rotational energy levels, and much useful information on inter­molecular force fields has resulted from observations on pressure broadening of pure rotational lines in the microwave region. Both self-broadening and broadening by different foreign gases have been studied as well as the dependence of line half­width Δ v 1/2 on the rotational quantum numbers J and K (Townes & Schawlow 1955).

Periodic features of the statistical atom with exchange and correlation

1968 ◽  
Vol 46 (1) ◽  
pp. 1-13 ◽  
Author(s):  
F. C. Auluck ◽  
Ashok Jain ◽  
Satish Kumar
Keyword(s):  
Angular Momentum ◽  
Mass Velocity ◽  
Energy Levels ◽  
Analytic Form ◽  
Particle Energy ◽  
Relativistic Mass ◽  
Angular Momentum Quantum Number ◽  
Velocity Correction ◽  
Present Formalism ◽  
Exchange And Correlation

The periodic features of atoms are studied using a statistical model embellished with exchange and correlation. It is shown that the earlier results, obtained on the basis of the simple TF model, can be computed in an analytic form by using the Tietz approximation. Single-particle energy levels of neutral atoms are calculated following the approach outlined by us in an earlier publication (Jain and Kumar 1967), and are compared with those obtained by other methods. A new angular momentum assignment is proposed and is shown to give values of v(l, Z) (the number of electrons with orbital angular momentum quantum number l, in an atom of atomic number Z) which are in very close agreement with the empirical values. The relativistic mass–velocity correction is incorporated in the calculation of angular-momentum groups. Finally, some suggestions are made for improving the present formalism.

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