A group theoretical approach to the many nucleon problem

1971 ◽  
Vol 70 (3) ◽  
pp. 485-496 ◽  
Author(s):  
J. A. de Wet
Keyword(s):  
Angular Momentum ◽  
Theoretical Approach ◽  
Ground State ◽  
Mass Number ◽  
Energy Levels ◽  
Quantum Numbers ◽  
The Many ◽  
Special Case ◽  
Ground State Energies ◽  
Good Agreement

Representations of the four-dimensional unitary group U4 were considered long ago by Wigner(1)as a model for nuclear isobaric multiplets. However, the Hamiltonian did not include the components of isospin which together with the spin coordinates are known to label the nuclear states. In this paper we shall find representations characterized by the eigenvalues of angular momentum J, isospin T and parity π, and will find mass relations which give good agreement with the experimental energy levels of Li6 and Be8 labelled by the same quantum numbers. The representations found by Wigner give good results for the ground state energies, or masses, of all the nuclei up to a mass number of A = 110(2), and we shall derive Wigner's representations as a special case. In fact, unless these are satisfied it is impossible for particle-like representations of U4 to exist!

scholarly journals THE METHOD OF INCREMENTS — A WAVEFUNCTION-BASED AB-INITIO CORRELATION METHOD FOR SOLIDS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2204-2214 ◽  
Author(s):  
BEATE PAULUS
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Ground State ◽  
Infinite System ◽  
Correlation Energy ◽  
Correlation Method ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Good Agreement

The method of increments is a wavefunction-based ab initio correlation method for solids, which explicitly calculates the many-body wavefunction of the system. After a Hartree-Fock treatment of the infinite system the correlation energy of the solid is expanded in terms of localised orbitals or of a group of localised orbitals. The method of increments has been applied to a great variety of materials with a band gap, but in this paper the extension to metals is described. The application to solid mercury is presented, where we achieve very good agreement of the calculated ground-state properties with the experimental data.

scholarly journals FOUR-PARTICLE ANYON EXCITON: BOSON APPROXIMATION

1995 ◽  
Vol 09 (02) ◽  
pp. 123-133 ◽  
Author(s):  
M. E. Portnoi ◽  
E. I. Rashba
Keyword(s):  
Angular Momentum ◽  
Electron Density ◽  
Ground State ◽  
Hypergeometric Functions ◽  
Energy Levels ◽  
Confluent Hypergeometric Functions ◽  
Full Symmetry ◽  
Hole Confinement ◽  
Boson Approximation

A theory of anyon excitons consisting of a valence hole and three quasielectrons with electric charges –e/3 is presented. A full symmetry classification of the k = 0 states is given, where k is the exciton momentum. The energy levels of these states are expressed by quadratures of confluent hypergeometric functions. It is shown that the angular momentum L of the exciton ground state depends on the distance between the electron and hole confinement planes and takes the values L = 3n, where n is an integer. With increasing k the electron density shows a spectacular splitting on bundles. At first a single anyon splits off of the two-anyon core, and finally all anyons become separated.

Evaluation of Luminescence Decay Measurements Probed on Pure and Doped Pt(IV) Hexahalogeno Complexes. II. Molecular Properties Obtained from Temperature Dependent Lifetime Curves

1997 ◽  
Vol 52 (5) ◽  
pp. 447-456
Author(s):  
Ingo Biertümpel ◽  
Hans-Herbert Schmidtke
Keyword(s):  
Excited States ◽  
Ground State ◽  
Energy Levels ◽  
Decay Rates ◽  
Rate Equations ◽  
Temperature Dependent ◽  
Lifetime Measurements ◽  
Thermally Activated ◽  
Ground State Energies ◽  
Higher Excited States

Abstract Lifetime measurements down to nearly liquid helium temperatures are used for determining energy levels and transition rates between excited levels and relaxations into the ground state. Energies are obtained from temperature dependent lifetimes by fitting experimental curves to model functions pertinent for thermally activated processes. Rates are calculated from solutions of rate equations. Similar parameters for pure and doped Pt(IV) hexahalogeno complexes indicate that excited levels largely belong to molecular units. Some of the rates between excited states are only somewhat larger than decay rates into the ground state, which is a consequence of the polyexponential decay measured also at low temperature (2 K). In the series of halogen complexes, the rates between spinorbit levels resulting from 3T1g increase from fluorine to bromine, although energy splittings become larger. Due to the decreasing population of higher excited states in this series, K^PtFö shows a tri-exponential, K2PtCl6 a bi-exponential and FoPtBr6 a mono-exponential decay. In the latter case the population density of higher excited states relaxes so fast that emission occurs primarily from the lowest excited Γ3(3T1g) level. Phase transitions and emission from chromophores on different sites can also be observed.

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.

Energy spectrum for trigonometric Pöschl–Teller potential

2012 ◽  
Vol 90 (12) ◽  
pp. 1259-1265 ◽  
Author(s):  
Babatunde James Falaye
Keyword(s):  
Bound State ◽  
Asymptotic Iteration Method ◽  
Generalized Hypergeometric Functions ◽  
Short Range Potential ◽  
Energy Eigenvalues ◽  
Molecular Potential ◽  
Quantum Numbers ◽  
Special Case ◽  
Arbitrary Quantum ◽  
Good Agreement

We present analytical solutions of the Schrödinger equation for the trigonometric Pöschl–Teller molecular potential by using a proper approximation to the centrifugal term within the framework of the asymptotic iteration method. We obtain analytic forms for the energy eigenvalues and the bound state eigenfunction solutions are obtained in terms of the generalized hypergeometric functions. Energy eigenvalues for a few diatomic molecules are calculated for arbitrary quantum numbers n and ℓ with various values of parameter α. We also studied special case ℓ = 0 and found that the results are in good agreement with findings of other methods for short-range potential.

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).

scholarly journals Symmetry reduction of tensor networks in many-body theory

2020 ◽  
Vol 56 (10) ◽  
Author(s):  
A. Tichai ◽  
R. Wirth ◽  
J. Ripoche ◽  
T. Duguet
Keyword(s):  
Angular Momentum ◽  
State Of The Art ◽  
Symmetry Reduction ◽  
Reduced Form ◽  
Many Body ◽  
Systematic Account ◽  
Many Body Theory ◽  
Quantum Numbers ◽  
The Many ◽  
Body Theory

AbstractThe ongoing progress in (nuclear) many-body theory is accompanied by an ever-rising increase in complexity of the underlying formalisms used to solve the stationary Schrödinger equation. The associated working equations at play in state-of-the-art ab initio nuclear many-body methods can be analytically reduced with respect to angular-momentum, i.e. SU(2), quantum numbers whenever they are effectively employed in a symmetry-restricted context. The corresponding procedure constitutes a tedious and error-prone but yet an integral part of the implementation of those many-body frameworks. Indeed, this symmetry reduction is a key step to advance modern simulations to higher accuracy since the use of symmetry-adapted tensors can decrease the computational complexity by orders of magnitude. While attempts have been made in the past to automate the (anti-) commutation rules linked to Fermionic and Bosonic algebras at play in the derivation of the working equations, there is no systematic account to achieve the same goal for their symmetry reduction. In this work, the first version of an automated tool performing graph-theory-based angular-momentum reduction is presented. Taking the symmetry-unrestricted expressions of a generic tensor network as an input, the code provides their angular-momentum-reduced form in an error-safe way in a matter of seconds. Several state-of-the-art many-body methods serve as examples to demonstrate the generality of the approach and to highlight the potential impact on the many-body community.

THE EFFECT OF A VARYING MAGNETIC FIELD ON THE DIRAC FERMION SPECTRUM OF GRAPHENE

2011 ◽  
Vol 25 (03) ◽  
pp. 365-370 ◽  
Author(s):  
M. R. SETARE ◽  
D. JAHANI
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Ground State ◽  
Uniform Magnetic Field ◽  
Energy Levels ◽  
Single Layer ◽  
The Other ◽  
Dirac Fermion ◽  
Zero Energy ◽  
Special Case

We examine the effect of a magnetic field that varies inversely as the square of distance on the Dirac fermion spectrum of graphene, a single layer of graphite. We find that unlike the case of the uniform magnetic field for which zero-energy modes exhibit half the degeneracy of the other levels in the energy spectrum, the ground state in this case, as well as the other energy levels, is doubly degenerate. We also get zero-energy solutions for the special case of ky = 0.

scholarly journals Study of Nuclear Structure for 36Si Isotope by Using Shell Model with Several Interactions

2020 ◽  
Vol 18 ◽  
pp. 58-65
Author(s):  
Ali K. Hasan ◽  
Wafaa Al-mudhafar
Keyword(s):  
Angular Momentum ◽  
Shell Model ◽  
Transition Probability ◽  
Energy Levels ◽  
Model Space ◽  
Nuclear Shell Model ◽  
Process Compatibility ◽  
Nuclear Shell ◽  
Level 2 ◽  
Good Agreement

In this study, the nuclear shell model was applied to calculate the energy levels and reduced electric quadruple transition probability B(E2) for 36Si isotope using the OXBASH code within (1d3/2, 2s1/2, 2p3/2, 1f7/2) model space and using (HASN, ZBM2 and VPTH) interactions, As this isotope contains eight neutrons outside 28Si  core in the region and when comparing the results of this study with the values. Available process compatibility was acceptable. There was good agreement at level 2+1, and angular momentum and parity were confirmed for levels 4+, 6+, and for all interactions, and the value of B(E2) corresponds well with the only practical value available for the transition .

scholarly journals Environment of Er Doped in a-Si:H and Its Relation with Photoluminescence Spectra

2006 ◽  
Vol 910 ◽  
Author(s):  
Minoru Kumeda ◽  
Yoshitaka Sekizawa ◽  
Akiharu Morimoto ◽  
Tatsuo Shimizu
Keyword(s):  
Angular Momentum ◽  
Ground State ◽  
Photoluminescence Spectrum ◽  
Energy Levels ◽  
Field Potential ◽  
Photoluminescence Spectra ◽  
Stark Splitting ◽  
Oxygen Ions ◽  
Structural Fluctuation ◽  
Er Doped

AbstractThe crystal-field potential at the Er3+ ion surrounded by six oxygen ions is expanded in terms of polynomials. After converting it into equivalent angular momentum operators, the Stark-splitting of the 4I15/2 ground state of the Er3+ ion is calculated. Influence of the change in the environment of the Er3+ ion on the shift of the energy levels is investigated and compared with the observed Er photoluminescence spectrum in a-Si:H. The scattering of the calculated energy levels by the structural fluctuation around the Er3+ ion is also compared with the linewidth of the component photoluminescence lines.

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