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 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.

scholarly journals The interaction of light nuclei III-The binding energies of He 4 , He 5 , Li 6 , and of nuclei of type 4 n

1936 ◽  
Vol 156 (889) ◽  
pp. 634-654 ◽  
Keyword(s):  
Short Range ◽  
Binding Energies ◽  
Potential Functions ◽  
Light Nuclei ◽  
Variation Method ◽  
Interaction Energies ◽  
Short Range Potential ◽  
Variational Treatment ◽  
Binding Forces ◽  
Repulsive Forces

The possibility of discussing nuclear structure in terms of neutrons and protons, and so avoiding the awkward difficulties associated with the behavioiur of electrons under nuclear conditions, has greatly stimulated interest in the binding energies of nuclei. Investigation of these energies leads to information about the nature an magnitude of the interactions between neutrons and protons. In a pervious paper, referred to henceforth as Paper I, we considered the binding energies of the nuclei composed of three particles ("ternary" nuclei) He 3 and H 3 . Assuming that the binding forces were of a two-body nature and taking simple short range potential functions to represent the interaction energies which were consistent with the observed mass of H 2 , the variation method was applied to determine the parameters in these potential functions. It was shown that it is improbable that the observed masses of the "ternary" nuclei could be explained without introducing attractive forces between like particles. Since then a more exact variational treatment, due to Thomas, has shown that these conclusions must be modified if the range of interaction between neutron and proton is less than 10 -13 cm. In such circumstances Thomas proved that the binding energies of the ternary nuclei would be greater than the observed, unless repulsions between like particles are included. For greater ranges of interaction the conclusions of Paper I are unaffected; namely, that for ranges of interaction less than 3 X 10- 13 cm the interaction between like particles is less than that between unlike, provided the range of interaction is substantially the same in both cases. The results may be summarized as follows: ( a ) For ranges of the two-body forces less than 10 -13 cm repulsive forces between like particles must exist.

scholarly journals The binding energies of very light nuclei

1947 ◽  
Vol 191 (1024) ◽  
pp. 61-82 ◽  
Keyword(s):  
Binding Energy ◽  
Cosmic Ray ◽  
Energy Difference ◽  
Binding Energies ◽  
Fair Agreement ◽  
Light Nuclei ◽  
Meson Mass ◽  
Triplet States ◽  
Many Body ◽  
Static Interaction

The static interaction of the Møller-Rosenfeld theory is used to calculate approximately the binding energies of the nuclei H 2 , H 3 , He 3 and He 4 . The value of the meson mass and of the two other parameters available in the theory are determined from a comparison with the observed binding energies of the H 3 nucleus and of the singlet and triplet states of the deuteron. The meson mass so determined is between 210 and 220 electron masses which is in fair agreement with cosmic-ray measurements. The binding energy of He 3 calculated from the energy difference H 3 – He 3 is also found to be in fair agreement with the observed value. The theoretical binding energy of He 4 is less than half the observed value, and it is suggested that in this nucleus there exists an additional many-body interaction.

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.

DYNAMICS OF DEEPLY BOUND ${\bar K}$ STATES

2007 ◽  
Vol 22 (02n03) ◽  
pp. 633-636 ◽  
Author(s):  
JIŘI MAREŠ ◽  
ELIAHU FRIEDMAN ◽  
AVRAHAM GAL
Keyword(s):  
Binding Energy ◽  
Mean Field ◽  
Binding Energies ◽  
Light Nuclei ◽  
Nucleus Interaction ◽  
Core Nucleus ◽  
Relativistic Mean Field ◽  
The Core ◽  
Wide Range ◽  
Rmf Model

Dynamical effects for [Formula: see text] deeply bound nuclear states are explored within a relativistic mean field (RMF) model. Varying the strength of [Formula: see text] - nucleus interaction, we cover a wide range of binding energies in order to evaluate the corresponding widths. A lower limit [Formula: see text] is placed on the width expected for binding energy in the range of [Formula: see text]. Substantial polarization of the core nucleus is found in light nuclei. We discuss the results of the FINUDA experiment at DAΦNE which presented evidence for deeply bound K- pp states in Li and 12 C .

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.

scholarly journals np-Pair Correlations in the Isovector Pairing Model

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1405
Author(s):  
Feng Pan ◽  
Yingwen He ◽  
Lianrong Dai ◽  
Chong Qi ◽  
Jerry P. Draayer
Keyword(s):  
Binding Energy ◽  
Occupation Number ◽  
Mean Field ◽  
Energy Difference ◽  
Binding Energies ◽  
Pair Correlations ◽  
Isospin Symmetry Breaking ◽  
Pairing Model ◽  
Proton Pairing ◽  
Spin Basis

A diagonalization scheme for the shell model mean-field plus isovector pairing Hamiltonian in the O(5) tensor product basis of the quasi-spin SUΛ(2) ⊗ SUI(2) chain is proposed. The advantage of the diagonalization scheme lies in the fact that not only can the isospin-conserved, charge-independent isovector pairing interaction be analyzed, but also the isospin symmetry breaking cases. More importantly, the number operator of the np-pairs can be realized in this neutron and proton quasi-spin basis, with which the np-pair occupation number and its fluctuation at the J = 0+ ground state of the model can be evaluated. As examples of the application, binding energies and low-lying J = 0+ excited states of the even–even and odd–odd N∼Z ds-shell nuclei are fit in the model with the charge-independent approximation, from which the neutron–proton pairing contribution to the binding energy in the ds-shell nuclei is estimated. It is observed that the decrease in the double binding-energy difference for the odd–odd nuclei is mainly due to the symmetry energy and Wigner energy contribution to the binding energy that alter the pairing staggering patten. The np-pair amplitudes in the np-pair stripping or picking-up process of these N = Z nuclei are also calculated.

Interfacial Adhesion of Cu to Self-Assembled Monolayers on SiO2

2001 ◽  
Vol 695 ◽  
Author(s):  
G. Cui ◽  
M. Lane ◽  
K. Vijayamohanan ◽  
G. Ramanath
Keyword(s):  
Binding Energy ◽  
Photoelectron Spectroscopy ◽  
Interfacial Adhesion ◽  
Adhesion Energy ◽  
Binding Energies ◽  
Self Assembled Monolayers ◽  
Chemical Binding ◽  
Barrier Materials ◽  
Assembled Monolayers ◽  
Self Assembled

ABSTRACTAs the critical feature size in microelectronic devices continues to decrease below 100 nm, new barrier materials of > 5 nm thickness are required. Recently we have shown that self-assembled monolayers (SAMs) are attractive candidates that inhibit Cu diffusion into SiO2. For SAMs to be used as barriers in real applications, however, they must also promote adhesion at the Cu/dielectric interfaces. Here, we report preliminary quantitative measurements of interfacial adhesion energy and chemical binding energy of Cu/SiO2 interfaces treated with nitrogen-terminated SAMs. Amine-containing SAMs show a ~10% higher adhesion energy with Cu, while interfaces with Cu-pyridine bonds actually show degraded adhesion, when compared with that of the reference Cu/SiN interface. However, X-ray photoelectron spectroscopy (XPS) measurements show that Cu-pyridine and Cu-amine interactions have a factor-of-four higher binding energy than that of Cu-N bonds at Cu/SiN interfaces. The lack of correlation between adhesion and chemical binding energies is most likely due to incomplete coverage of SAMs.

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 Combinatorial Library Designing and Virtual Screening of Cryptolepine Derivatives against Topoisomerase II by Molecular Docking

2020 ◽  
Author(s):  
Maria ◽  
Zahid Khan
Keyword(s):  
Molecular Docking ◽  
Cell Division ◽  
Binding Energy ◽  
Cancer Cells ◽  
Anticancer Agents ◽  
Combinatorial Library ◽  
Topoisomerase Ii ◽  
Computational Study ◽  
Binding Energies ◽  
Potential Inhibitors

AbstractComputational approaches have emerging role for designing potential inhibitors against topoisomerase 2 for treatment of cancer. TOP2A plays a key role in DNA replication before cell division and thus facilitates the growth of cells. This function of TOP2A can be suppressed by targeting with potential inhibitors in cancer cells to stop the uncontrolled cell division. Among potential inhibitors cryptolepine is more selective and has the ability to intercalate into DNA, effectively block TOP2A and cease cell division in cancer cells. However, cryptolepine is non-specific and have low affinity, therefore, a combinatorial library was designed and virtually screened for identification of its derivatives with greater TOP2A binding affinities.A combinatorial library of 31114 derivatives of cryptolepine was formed and the library was virtually screened by molecular docking to predict the molecular interactions between cryptolepine derivatives and TOP2A taking cryptolepine as standard. The overall screening and docking approach explored all the binding poses of cryptolepine for TOP2A to calculate binding energy. The compounds are given database number 8618, 907, 147, 16755, and 8186 scored lowest binding energies of −9.88kcal/mol, −9.76kcal/mol, −9.75kcal/mol, −9.73kcal/mol, and −9.72kcal/mol respectively and highest binding affinity while cryptolepine binding energy is −6.09kcal/mol. The good binding interactions of the derivatives showed that they can be used as potent TOP2A inhibitors and act as more effective anticancer agents than cryptolepine itself. The interactions of derivatives with different amino acid residues were also observed. A comprehensive understanding of the interactions of proposed derivatives with TOP2A helped for searching more novel and potent drug-like molecules for anticancer therapy. This Computational study suggests useful references to understand inhibition mechanisms that will help in the modification of TOP2A inhibitors.

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