Ground-State Binding Energies of Three Identical Particles Which Interact via Three Mutual Morse Potentials

1972 ◽  
Vol 28 (2) ◽  
pp. 71-74 ◽  
Author(s):  
H. Krüger
Keyword(s):  
Ground State ◽  
Binding Energies ◽  
Identical Particles ◽  
Morse Potentials

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.

TWO-OSCILLATOR BASIS EXPANSION FOR THE SOLUTION OF RELATIVISTIC MEAN FIELD EQUATIONS

2000 ◽  
Vol 09 (06) ◽  
pp. 507-520
Author(s):  
S. V. S. SASTRY ◽  
ARUN K. JAIN ◽  
Y. K. GAMBHIR
Keyword(s):  
Ground State ◽  
Mean Field ◽  
Surface Region ◽  
Binding Energies ◽  
Basis Functions ◽  
Field Equations ◽  
Basis Expansion ◽  
Relativistic Mean Field ◽  
Mean Field Equations ◽  
Spherical Nuclei

In the relativistic mean field (RMF) calculations usually the basis expansion method is employed. For this one uses single harmonic oscillator (HO) basis functions. A proper description of the ground state nuclear properties of spherical nuclei requires a large (around 20) number of major oscillator shells in the expansion. In halo nuclei where the nucleons have extended spatial distributions, the use of single HO basis for the expansion is inadequate for the correct description of the nuclear properties, especially that of the surface region. In order to rectify these inadequacies, in the present work an orthonormal basis composed of two HO basis functions having different sizes is proposed. It has been shown that for a typical case of (A=11) the ground state constructed using two-HO wave functions extends much beyond the second state or even third excited state of the single HO wave function. To demonstrate its usefulness explicit numerical RMF calculations have been carried out using this procedure for a set of representative spherical nuclei ranging from 16 O to 208 Pb . The binding energies, charge radii and density distributions have been correctly reproduced in the present scheme using a much smaller number of major shells (around 10) in the expansion.

The Spectroscopy of 198O11 and the 187N11 Ground State

1983 ◽  
Vol 36 (6) ◽  
pp. 825
Author(s):  
Raymond K Sheline
Keyword(s):  
Ground State ◽  
Sudden Change ◽  
Binding Energies ◽  
Ground State Spin ◽  
System A ◽  
State Spin

The spectroscopies of 190 and 21 Ne (both eleven-neutron systems) are compared. The 1-+ [211 iJ, t+ [220il and t- [lOttl bands are observed in both nuclei. On the basis of these similarities 190 is assumed to be a prolate rotor like 21 Ne. If then the recently studied IBN ground state is also considered to be a deformed system (a one-proton hole in the 190 nucleus), both the 1- ground state spin and the sudden change in the systematics of the two-neutron binding energies can be understood.

BUILT-IN ELECTRIC FIELD EFFECT ON DONOR IMPURITIES IN STRAINED WURTZITE GaN/AlGaN ASYMMETRIC DOUBLE QUANTUM WELLS

2012 ◽  
Vol 26 (26) ◽  
pp. 1250172 ◽  
Author(s):  
JUN ZHU ◽  
SHI LIANG BAN ◽  
SI HUA HA
Keyword(s):  
Variational Method ◽  
Electric Field ◽  
Quantum Wells ◽  
Ground State ◽  
Field Effect ◽  
Binding Energies ◽  
Double Quantum ◽  
Electric Field Effect ◽  
Material Parameters ◽  
Asymmetric Double Quantum Wells

The ground state binding energies of donor impurities in strained [0001]-oriented wurtzite GaN / Al x Ga 1-x N asymmetric double quantum wells are investigated using a variational method combined with numerical computation. The built-in electric field due to the spontaneous and strain-induced piezoelectric polarization and the strain modification on material parameters are taken into account. The variations of binding energies versus the width of central barrier, the ratio of two well widths, and the impurity position are presented, respectively. It is found that the built-in electric field causes a mutation of binding energies with increasing the width of central barrier to some value. The results for symmetrical double quantum wells and without the built-in electric field are also discussed for comparison.

Binding Energies of Organic Charge-Transfer Complexes Calculated by First-Principles Methods

1998 ◽  
Vol 63 (8) ◽  
pp. 1223-1244 ◽  
Author(s):  
Cordula Rauwolf ◽  
Achim Mehlhorn ◽  
Jürgen Fabian
Keyword(s):  
Density Functional Theory ◽  
Charge Transfer ◽  
Ground State ◽  
Density Functional ◽  
Binding Energies ◽  
Basis Set ◽  
Dispersion Energy ◽  
Functional Theory ◽  
Basis Set Superposition Error ◽  
Donor And Acceptor

Weak interactions between organic donor and acceptor molecules resulting in cofacially-stacked aggregates ("CT complexes") were studied by second-order many-body perturbation theory (MP2) and by gradient-corrected hybrid Hartree-Fock/density functional theory (B3LYP exchange-correlation functional). The complexes consist of tetrathiafulvalene (TTF) and related compounds and tetracyanoethylene (TCNE). Density functional theory (DFT) and MP2 molecular equilibrium geometries of the component structures are calculated by means of 6-31G*, 6-31G*(0.25), 6-31++G**, 6-31++G(3df,2p) and 6-311G** basis sets. Reliable molecular geometries are obtained for the donor and acceptor compounds considered. The geometries of the compounds were kept frozen in optimizing aggregate structures with respect to the intermolecular distance. The basis set superposition error (BSSE) was considered (counterpoise correction). According to the DFT and MP2 calculations laterally-displaced stacks are more stable than vertical stacks. The charge transfer from the donor to the acceptor is small in the ground state of the isolated complexes. The cp-corrected binding energies of TTF/TCNE amount to -1.7 and -6.3 kcal/mol at the DFT(B3LYP) and MP2(frozen) level of theory, respectively (6-31G* basis set). Larger binding energies were obtained by Hobza's 6-31G*(0.25) basis set. The larger MP2 binding energies suggest that the dispersion energy is underestimated or not considered by the B3LYP functional. The energy increases when S in TTF/TCNE is replaced by O or NH but decreases with substitution by Se. The charge-transferred complexes in the triplet state are favored in the vertical arrangement. Self-consistent-reaction-field (SCRF) calculations predicted a gain in binding energy with solvation for the ground-state complex. The ground-state charge transfer between the components is increased up to 0.8 e in polar solvents.

GROUND STATE PROPERTIES OF EXTREME NEUTRON RICH ISOTOPES OBSERVED: A RELATIVISTIC MEAN FIELD APPROACH

2011 ◽  
Vol 20 (11) ◽  
pp. 2293-2303 ◽  
Author(s):  
PROVASH MALI
Keyword(s):  
Ground State ◽  
Mean Field ◽  
Mass Region ◽  
Binding Energies ◽  
Droplet Model ◽  
Shell Effects ◽  
Relativistic Mean Field ◽  
Ground State Properties ◽  
Neutron Rich Isotopes ◽  
Good Agreement

The ground state properties namely the binding energy, the root mean square (rms) radius (neutron, proton and charge) and the deformation parameter of 45 newly identified neutron-rich isotopes in the A~71–152 mass region have been predicted in the relativistic mean filed (RMF) framework along with the Bardeen–Cooper–Schrieffer (BCS) type of pairing. Validity of the RMF results with the NL3 effective force are tested for odd-A Zn and Rh isotopic chains without taking the time reversal symmetry breaking effects into consideration. The RMF prediction on the binding energies are in good agreement with the empirical/finite-range droplet model calculation. The shell effects on the rms radii of odd-A Zn and Rh isotopes are nicely reproduced. The possibility of shape-coexistence in the newly identified nuclei is discussed.

The binding energies of the hydrogen isotopes

1938 ◽  
Vol 34 (3) ◽  
pp. 365-374 ◽  
Author(s):  
A. H. Wilson
Keyword(s):  
Wave Equation ◽  
Binding Energy ◽  
Potential Energy ◽  
Ground State ◽  
Hydrogen Isotope ◽  
Hydrogen Isotopes ◽  
Binding Energies ◽  
Variation Method

The wave equation for the deuteron in its ground state is solved on the assumption that the mutual potential energy of a neutron and a proton is of the form r−1e−λr. The binding energy of the hydrogen isotope H3 is calculated approximately by the variation method.

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