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.

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.

scholarly journals HADRON PRODUCTION IN NEUTRINO–NUCLEON INTERACTIONS AT HIGH ENERGIES

2003 ◽  
Vol 18 (04) ◽  
pp. 673-683
Author(s):  
M. T. HUSSEIN ◽  
N. M. HASSAN ◽  
W. ELHARBI
Keyword(s):  
Cross Sections ◽  
Particle Production ◽  
High Energy ◽  
Neutrino Energy ◽  
Wave Functions ◽  
Variation Method ◽  
Hypothetical Model ◽  
High Energies ◽  
Color Field

The multi-particle productions in neutrino–nucleon collisions at high energy are investigated through the analysis of the data of the experiment CERN-WA-025 at neutrino energy less than 260 GeV and the experiments FNAL-616 and FNAL-701 at energy range 120–250 GeV. The general features of these experiments are used as base to build a hypothetical model that views the reaction through a Feynman diagram of two vertices. The first of which concerns the weak interaction between the neutrino and the quark constituents of the nucleon. At the second vertex, a strong color field is assumed to play the role of particle production, which depend on the momentum transferred from the first vertex. The wave functions of the nucleon constituent quarks are determined using the variation method and relevant boundary conditions are applied to calculate the deep inelastic cross sections of the virtual diagram.

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.

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.

scholarly journals The interaction of light nuclei II-The binding energies of the nuclei H 1 3 and He 2 3

1935 ◽  
Vol 152 (877) ◽  
pp. 693-705 ◽  
Keyword(s):  
Binding Energy ◽  
Exact Solutions ◽  
Binding Energies ◽  
Light Nuclei ◽  
Attractive Force ◽  
Variation Method ◽  
Conspicuous Feature ◽  
Upper Limits ◽  
Available Information

The discovery of the light nuclei n 0 1 H 1 2 H 1 3 He 2 3 has provided additional and much-needed material on which to base and test any theory of the structure and interaction on nuclear particles. The properties of these nuclei which are best known are their masses, the latest values of which are the following: n 0 1 1·0083 H 1 2 2·0142 H 1 3 3·0161 He 2 3 3·0172, assuming the validity of the mass scheme proposed independently by Oliphant, Kempton, and Rutherford, and by Bethe (in which the results of the disintegration experiments are found to be consistent if the He 4 :O 16 ration is taken as 4·0034 :16). From these masses the binding energies of the nuclei, considered as combinations of neutrons and protons, may be obtained. We find, then, that H 1 2 = H 1 1 + n 0 1 - 2·1 x 10 6 e -volts, H 1 3 = H 1 1 + 2 n 0 1 - 8·1 x 10 6 e -volts, He 2 3 = 2H 1 1 + n 0 1 - 6·9 x 10 6 e -volts. The most conspicuous feature of these figures is that the binding energy of both H 1 3 and He 2 3 is considerably greater than twice of H 1 2 , and the question arises as to whether this cab be explained without introducing an attractive force between the neutrons in H 1 3 and between the protons in He 2 3 . In this paper we attempt to answer the question by applying the variation method to calculate the binding energies of H 1 3 and He 2 3 , use being made of all available information bearing on the form of the neutron-porton interaction. It is found that definite results cannot be obtained in this direction, but the calculations would seem to indicate that these additional attractive forces must be introduced, and, in any case, upper limits may be found for their magnitude. Before discussing these calculations it is important to examine the velocity of the variation method as applies to H 1 2 by comparing results obtained by its use with exact solutions.

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.

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.

scholarly journals Nonperturbative approach to the parton model

2016 ◽  
Vol 31 (06) ◽  
pp. 1650016 ◽  
Author(s):  
Yu. A. Simonov
Keyword(s):  
Nonperturbative Effects ◽  
Parton Model ◽  
String Tension ◽  
High Energy ◽  
Wave Functions ◽  
Parton Distributions ◽  
Text String ◽  
Preliminary Discussion ◽  
High Energy Scattering

In this paper, the nonperturbative parton distributions, obtained from the Lorentz contracted wave functions, are analyzed in the formalism of many-particle Fock components and their properties are compared to the standard perturbative distributions. We show that the collinear and IR divergencies specific for perturbative evolution treatment are absent in the nonperturbative version, however for large momenta [Formula: see text] (string tension), the bremsstrahlung kinematics is restored. A preliminary discussion of possible nonperturbative effects in DIS and high energy scattering is given, including in particular a possible role of multihybrid states in creating ridge-type effects.

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.

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