scholarly journals Расчеты релятивистских, корреляционных, ядерных и квантово-электродинамических поправок к энергии и потенциалу ионизации основного состояния гелиеподобных ионов

2020 ◽  
Vol 128 (1) ◽  
pp. 24
Author(s):  
И.И. Тупицын ◽  
С.В. Безбородов ◽  
А.В. Малышев ◽  
Д.В. Миронова ◽  
В.М. Шабаев
Keyword(s):  
Total Energy ◽  
Quantum Electrodynamic ◽  
Ground State ◽  
Finite Size ◽  
Wave Functions ◽  
Ionization Potentials ◽  
Recoil Effect ◽  
Finite Mass ◽  
Variational Calculations ◽  
Field Shift

In this work, nonrelativistic and relativistic variational calculations of the energies and ionization potentials of the ground state of helium-like ions for the nuclear charges in the range Z = 2 − 20 were performed.the leading corrections to the total energy were calculated including the contribution of electronic correlations, relativistic and quantum-electrodynamic (QED) corrections, and the contributions of the finite size ofnucleus (field shift) and the finite mass of the nucleus (recoil effect). Relativistic сalculations of the wave functions were performed using the Dirac-Coulomb-Breit (DCB) Hamiltonian.

WAVE FUNCTIONS FOR THE GROUND STATE OF THE He2 MOLECULE

1967 ◽  
Vol 45 (1) ◽  
pp. 137-143 ◽  
Author(s):  
Gene P. Barnett
Keyword(s):  
Total Energy ◽  
Ground State ◽  
Good Description ◽  
Wave Functions ◽  
Nonlinear Parameters ◽  
Open Shells ◽  
Interatomic Separation ◽  
Complete Set ◽  
The One

One- and two-configuration wave functions have been calculated for the He2 molecule over a range of interatomic separation from 3/4 to 6 atomic units. The one-electron basis consists of σ-type elliptical orbitals with the nonlinear parameters varied to minimize the total energy. The functions are formed with completely open shells and the complete set of singlet spin functions. The results give a good description of the system and compare favorably with other calculations.

LOWEST-ORDER CONSTRAINED VARIATIONAL CALCULATIONS FOR TWO-DIMENSIONAL LIQUID 3He

2013 ◽  
Vol 12 (07) ◽  
pp. 1350061 ◽  
Author(s):  
G. H. BORDBAR ◽  
F. FATEMI ◽  
M. T. MOHAMADI SABET
Keyword(s):  
Total Energy ◽  
Cluster Expansion ◽  
Ground State ◽  
Bound State ◽  
Energy Functional ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Lennard Jones ◽  
Pair Potentials ◽  
Variational Calculations

We have used the lowest-order constrained variational (LOCV) method based on the cluster expansion of the energy functional to calculate some ground state properties of two-dimensional liquid 3 He at zero temperature employing the Lennard-Jones and Aziz pair potentials. We have seen that the total energy increases by increasing density. It is shown that the two-dimensional liquid 3 He system has no self-bound state.

scholarly journals Target space entanglement in quantum mechanics of fermions and matrices

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Sotaro Sugishita
Keyword(s):  
Mutual Information ◽  
Ground State ◽  
Entanglement Entropy ◽  
Algebraic Approach ◽  
Upper Bounds ◽  
Wave Functions ◽  
Target Space ◽  
Single Interval ◽  
Area Law ◽  
Formula Expression

Abstract We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are N log 2 for N particles or an N × N matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as $$ \frac{1}{3} $$ 1 3 log N in the large N model. We obtain an analytical $$ \mathcal{O}\left({N}^0\right) $$ O N 0 expression of the mutual information for two intervals in the large N expansion.

scholarly journals NUMERICAL STUDY OF CHARGE AND STATISTICS OF LAUGHLIN QUASIPARTICLES

1999 ◽  
Vol 14 (04) ◽  
pp. 537-557 ◽  
Author(s):  
HEIDI KJØNSBERG ◽  
JAN MYRHEIM
Keyword(s):  
Numerical Study ◽  
Finite Size ◽  
Expected Value ◽  
Wave Functions ◽  
Numerical Calculations ◽  
Filling Fraction ◽  
Slow Convergence ◽  
Berry Phases ◽  
Size Correction ◽  
Finite Size Correction

We present numerical calculations of the charge and statistics, as extracted from Berry phases, of the Laughlin quasiparticles, near filling fraction 1/3, and for system sizes of up to 200 electrons. For the quasiholes our results confirm that the charge and statistics parameter are e/3 and 1/3, respectively. For the quasielectron charge we find a slow convergence towards the expected value of -e/3, with a finite size correction for N electrons of approximately -0.13e/N. The statistics parameter for the quasielectrons has no well defined value even for 200 electrons, but might possibly converge to 1/3. The anyon model works well for the quasiholes, but requires singular two-anyon wave functions for modelling two Laughlin quasielectrons.

STRUCTURE, STABILITY, AND ELECTRONIC PROPERTIES OF LARGE FULLERENES

1993 ◽  
Vol 07 (26) ◽  
pp. 4305-4329 ◽  
Author(s):  
C.Z. WANG ◽  
B.L. ZHANG ◽  
K.M. HO ◽  
X.Q. WANG
Keyword(s):  
Total Energy ◽  
Electronic Properties ◽  
Ground State ◽  
Relative Stability ◽  
Chemical Reactivity ◽  
Structure Stability ◽  
Quantum Mechanical ◽  
Efficient Scheme ◽  
Ground State Structures ◽  
Fullerene Clusters

The recent development in understanding the structures, relative stability, and electronic properties of large fullerenes is reviewed. We describe an efficient scheme to generate the ground-state networks for fullerene clusters. Combining this scheme with quantum-mechanical total-energy calculations, the ground-state structures of fullerenes ranging from C 20 to C 100 have been studied. Fullerenes of sizes 60, 70, and 84 are found to be energetically more stable than their neighbors. In addition to the energies, the fragmentation stability and the chemical reactivity of the clusters are shown to be important in determining the abundance of fullerene isomers.

scholarly journals Electromagnetic transition form factors of baryons in a relativistic Faddeev approach

2018 ◽  
Vol 181 ◽  
pp. 01013 ◽  
Author(s):  
Reinhard Alkofer ◽  
Christian S. Fischer ◽  
Hèlios Sanchis-Alepuz
Keyword(s):  
Ground State ◽  
Bound States ◽  
Body Wave ◽  
Form Factors ◽  
Wave Functions ◽  
Electromagnetic Form Factors ◽  
Transition Form ◽  
Electromagnetic Transition ◽  
Three Body ◽  
Gluon Interaction

The covariant Faddeev approach which describes baryons as relativistic three-quark bound states and is based on the Dyson-Schwinger and Bethe-Salpeter equations of QCD is briefly reviewed. All elements, including especially the baryons’ three-body-wave-functions, the quark propagators and the dressed quark-photon vertex, are calculated from a well-established approximation for the quark-gluon interaction. Selected previous results of this approach for the spectrum and elastic electromagnetic form factors of ground-state baryons and resonances are reported. The main focus of this talk is a presentation and discussion of results from a recent investigation of the electromagnetic transition form factors between ground-state octet and decuplet baryons as well as the octet-only Σ0 to Λ transition.

The binding energies of atomic nuclei III. Nuclear forces and the ground state of oxygen 16

1959 ◽  
Vol 253 (1273) ◽  
pp. 186-198 ◽  
Keyword(s):  
Binding Energy ◽  
Electron Scattering ◽  
Ground State ◽  
Binding Energies ◽  
Wave Functions ◽  
Unperturbed System ◽  
Core Radius ◽  
Nuclear Forces ◽  
Potential Core ◽  
Atomic Nuclei

The r. m. s. radius and the binding energy of oxygen 16 are calculated for several different internueleon potentials. These potentials all fit the low-energy data for two nucleons, they have hard cores of differing radii, and they include the Gammel-Thaler potential (core radius 0·4 fermi). The calculated r. m. s. radii range from 1·5 f for a potential with core radius 0·2 f to 2·0 f for a core radius 0·6 f. The value obtained from electron scattering experiments is 2·65 f. The calculated binding energies range from 256 MeV for a core radius 0·2 f to 118 MeV for core 0·5 f. The experimental value of binding energy is 127·3 MeV. The 25% discrepancy in the calculated r. m. s. radius may be due to the limitations of harmonic oscillator wave functions used in the unperturbed system.

LONG RANGE FORCES BETWEEN HYDROGEN MOLECULES

1955 ◽  
Vol 33 (11) ◽  
pp. 668-678 ◽  
Author(s):  
F. R. Britton ◽  
D. T. W. Bean
Keyword(s):  
Wave Function ◽  
Long Range ◽  
Ground State ◽  
Close Agreement ◽  
Van Der Waals ◽  
Wave Functions ◽  
Numerical Factor ◽  
Hydrogen Molecules ◽  
Static Quadrupole

Long range forces between two hydrogen molecules are calculated by using methods developed by Massey and Buckingham. Several terms omitted by them and a corrected numerical factor greatly change results for the van der Waals energy but do not affect their results for the static quadrupole–quadrupole energy. By using seven approximate ground state H2 wave functions information is obtained regarding the dependence of the van der Waals energy on the choice of wave function. The value of this energy averaged over all orientations of the molecular axes is found to be approximately −11.0 R−6 atomic units, a result in close agreement with semiempirical values.

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