The binding energies of s-shell nuclei

1969 ◽  
Vol 47 (24) ◽  
pp. 2825-2834 ◽  
Author(s):  
J. Law ◽  
R. K. Bhaduri
Keyword(s):  
Binding Energy ◽  
Long Range ◽  
Hard Core ◽  
Nucleon Nucleon ◽  
Interference Term ◽  
Binding Energies ◽  
Wave Functions ◽  
A Value ◽  
Range Part ◽  
Central Forces

We have calculated the binding energies of 4He and 3H with soft- and hard-core nucleon–nucleon potentials. With central forces, using harmonic-oscillator wave functions, we find that accurate results can be obtained by taking only the long-range part of the potential and its second-order perturbative term. When tensor forces are present, the long-range interference term is also included in the calculation. In this case, the method is not accurate and underbinds these nuclei by about 1 MeV per particle. Ignoring Coulomb forces, our method yields a value of 18.5 MeV for the binding energy of 4He with the Hamada–Johnston potential.

NUCLEAR MATTER AND THE LONG-RANGE PART OF THE NUCLEON–NUCLEON POTENTIAL

1967 ◽  
Vol 45 (3) ◽  
pp. 1289-1295 ◽  
Author(s):  
J. M. Pearson
Keyword(s):  
Nuclear Matter ◽  
Long Range ◽  
Short Range ◽  
Hard Core ◽  
Nucleon Nucleon ◽  
Intermediate Region ◽  
Precise Form ◽  
Nucleon Potential ◽  
Range Part

Elementary nuclear-matter calculations are performed with five different central nucleon–nucleon potentials. These are all static with a hard core of radius 0.4 fm and an OPEP tail, but are characterized by vastly different forms in the intermediate region. It is concluded that nuclear matter is insensitive to the precise form of the central part of the nucleon–nucleon potential everywhere beyond the short-range repulsive region, provided the nucleon–nucleon data are well fitted.

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.

Smooth nucleon–nucleon interactions and meson theory

1968 ◽  
Vol 46 (8) ◽  
pp. 963-969 ◽  
Author(s):  
Pierre Desgrolard ◽  
J. M. Pearson ◽  
Gérard Saunier
Keyword(s):  
Nuclear Matter ◽  
Long Range ◽  
Short Range ◽  
Singlet State ◽  
Nucleon Nucleon ◽  
Second Order ◽  
Meson Theory ◽  
The One ◽  
Range Part ◽  
Short Range Correlations

Tabakin and Davies have shown that it is possible to fit the singlet-state nucleon–nucleon data with a potential that is smooth enough to give very small second-order terms in an ordinary perturbation–theoretic treatment of nuclear matter. However, their potential is unrealistic in that the requirements of meson theory are in no way satisfied in the long-range region. It is shown here that a potential whose long-range part conforms to the OBEP of Bryan and Scott can still be made to fit the phase shifts without increasing significantly the second-order terms. Thus, with meson theory being incapable of making an unequivocal statement about the short-range region, it will only be by resorting to the experimental evidence for short-range correlations in nuclei that one will be able to resolve the question as to whether or not an interaction as smooth as the one considered here can be regarded as "real" rather than merely "effective". In any event, the existence of such correlations cannot be inferred from the singlet nucleon–nucleon data.

The electrostatic calculation of molecurlar energies - III. The binding energies of saturated molecules

1954 ◽  
Vol 226 (1165) ◽  
pp. 193-205 ◽  
Keyword(s):  
Binding Energy ◽  
Valence Bond ◽  
Binding Energies ◽  
Wave Functions ◽  
Complex Molecules ◽  
Electron Orbital ◽  
Hydride Molecule ◽  
Paired Electron ◽  
Bond Functions ◽  
Good Agreement

A technique for calculating the binding energy of any saturated molecule is developed.The method is based on an application of the electrostatic theorem, discussed in earlier parts, to paired-electron orbital wave functions.These wave functions include both molecular-orbital and valence-bond functions as special cases.The resulting numerical computations are sufficiently simple to be carried through without approximation even for complex molecules. The method is applied to the lithium molecule and the lithium hydride molecule, and yields results in good agreement with experiment. The choice of wave functions for calculations on other molecules is discussed.

Binding energy of the triton

1951 ◽  
Vol 204 (1079) ◽  
pp. 476-488 ◽  
Keyword(s):  
Binding Energy ◽  
Magnetic Moments ◽  
Coulomb Repulsion ◽  
Coherent Scattering ◽  
High Energy ◽  
Binding Energies ◽  
Wave Functions ◽  
Variation Method ◽  
The Difference ◽  
High Energy Scattering

The variation method is employed to calculate the binding energy of the triton assuming charge-independent, two-body, Yukawa shape interactions between nucleons in which tensor forces are included. More complete trial wave functions are used than employed hitherto in such calculations, and it is found that an interaction of Yukawa shape with constants adjusted to fit the observed data on the binding energy, quadrupole moment and magnetic moment of the deuteron, the low-energy and high-energy scattering of neutrons by protons, the photodisintegration of the deuteron and the coherent scattering of slow neutrons gives an approximately correct binding energy for the triton. Calculations are also carried out with interactions of the same type but with different constants. The exchange character of the forces remains unimportant. It is confirmed that the difference in the binding energies of 3 H and 3 He can be ascribed to the effect of Coulomb repulsion between the protons in the latter nucleus. The wave functions found are used to compute the magnetic moments of the two nuclei but do not contain sufficient admixture of P component to explain the observed values.

PRESSURE EFFECT ON THE INTERFACE EXCITONS IN A TYPE-II ZnTe/CdSe HETEROJUNCTION

2003 ◽  
Vol 17 (27n28) ◽  
pp. 1425-1435 ◽  
Author(s):  
Z. Z. GUO ◽  
X. X. LIANG ◽  
S. L. BAN
Keyword(s):  
Binding Energy ◽  
Ground State ◽  
Pressure Effect ◽  
Light Hole ◽  
Binding Energies ◽  
Wave Functions ◽  
Type Ii ◽  
Band Bending ◽  
Effective Masses ◽  
Transfer Method

A variational method is used to study the ground-state binding energies of interface light-hole excitons in ZnTe/CdSe type-II heterojunctions under the influence of hydrostatic pressure. The finite triangle potential well approximation is introduced considering the band bending near the interface. The asymptotic transfer method is adopted to obtain the sub-band energies and wave functions of the electrons and light holes. The pressure influence on the band offsets, the effective masses and the dielectric constant are considered in the calculation. The obvious pressure-induced increase of the exciton binding energy is demonstrated and the influences of the pressure-depended parameters on the binding energy are compared.

A qualitative investigation of the wave functions of metallic uranium

1958 ◽  
Vol 247 (1249) ◽  
pp. 199-213 ◽  
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Binding Energies ◽  
Wave Functions ◽  
Atomic Sphere ◽  
Maximum Charge ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Negative Binding Energy ◽  
Metallic Uranium

The potential field and wave functions in metallic uranium have been calculated approximately by determining Hartree self-consistent fields for the four configurations (6 d ) 6 , (5 f ) 2 (6 d ) 2 (7 s ) 2 , (5 f ) 4 (6 d ) 2 , and (5 f ) 6 using the Wigner–Seitz boundary condition at the surface of the equivalent atomic sphere. In the self-consistent field obtained for each configuration, wave functions falling to zero at the surface of the sphere were evaluated for the outer electrons. The differences between the Hartree ∊-parameters for the two boundary conditions were used to give an indication of the relative band widths. The (5 f ) wave function has its principal maximum inside the (6 s ) (6 p ) shell, but is appreciable at the surface of the sphere and must participate in bonding. The binding energy of an electron in the (5 f ) wave function is 0.3934 rydbergs in the configuration (5 f ) 2 (6 d ) 2 (7 s ) 2 as given by the Hartree ∊-parameter. The (6 d ) function has its maximum charge density at the boundary and, with a binding energy of 0.1749 rydbergs in the same configuration, is likely to form a good metallic band. The (7 s ) function has a large negative binding energy and is not likely to occur. In the configuration (5 f ) 2 (6 d ) 2 (7 s ) 2 the band widths of the (5 f ), (6 d ) and (7 s ) functions are in the ratio 1:9∙8:22∙7. As the number of (5 f ) electrons is increased all the binding energies decrease and the band widths increase. At the same time the (6 s ) and (6 p ) functions are markedly perturbed, the functions (5 s ), (5 p ) and (5 d ) to a lesser extent.

A QUANTUM MONTE CARLO STUDY ON EXCITONIC COMPLEXES IN GaAs/AlGaAs QUANTUM WIRES

2001 ◽  
Vol 15 (28n30) ◽  
pp. 3985-3988 ◽  
Author(s):  
TAKUMA TSUCHIYA
Keyword(s):  
Monte Carlo ◽  
Binding Energy ◽  
Quantum Monte Carlo ◽  
Quantum Wires ◽  
Monte Carlo Study ◽  
Binding Energies ◽  
Wave Functions ◽  
Diffusion Monte Carlo ◽  
Biexciton Binding Energy ◽  
Diffusion Monte Carlo Method

Binding energies of biexcitons and charged excitons in GaAs/Al 0.3 Ga 0.7 As quantum wires were calculated by the diffusion Monte Carlo method. The binding energy for the negatively charged excitons is enhanced strongly, because of the mismatch of the electron and the hole wave functions. The resulting biexciton binding energy reproduces experimental results quite well.

A DFT study of spherands containing five anisyl groups — Highly preorganized to bind the alkali metal

2006 ◽  
Vol 84 (8) ◽  
pp. 1045-1049 ◽  
Author(s):  
Shabaan AK Elroby ◽  
Kyu Hwan Lee ◽  
Seung Joo Cho ◽  
Alan Hinchliffe
Keyword(s):  
Density Functional Theory ◽  
Binding Energy ◽  
Density Functional ◽  
Ionic Radius ◽  
Binding Energies ◽  
Cavity Size ◽  
X Ray Diffraction ◽  
Functional Theory ◽  
X Ray ◽  
Good Agreement

Although anisyl units are basically poor ligands for metal ions, the rigid placements of their oxygens during synthesis rather than during complexation are undoubtedly responsible for the enhanced binding and selectivity of the spherand. We used standard B3LYP/6-31G** (5d) density functional theory (DFT) to investigate the complexation between spherands containing five anisyl groups, with CH2–O–CH2 (2) and CH2–S–CH2 (3) units in an 18-membered macrocyclic ring, and the cationic guests (Li+, Na+, and K+). Our geometric structure results for spherands 1, 2, and 3 are in good agreement with the previously reported X-ray diffraction data. The absolute values of the binding energy of all the spherands are inversely proportional to the ionic radius of the guests. The results, taken as a whole, show that replacement of one anisyl group by CH2–O–CH2 (2) and CH2–S–CH2 (3) makes the cavity bigger and less preorganized. In addition, both the binding and specificity decrease for small ions. The spherands 2 and 3 appear beautifully preorganized to bind all guests, so it is not surprising that their binding energies are close to the parent spherand 1. Interestingly, there is a clear linear relation between the radius of the cavity and the binding energy (R2 = 0.999).Key words: spherands, preorganization, density functional theory, binding energy, cavity size.

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