scholarly journals MESIC MOLECULES OF LIGHT NUCLEI IN THE OSCILLATOR REPRESENTATION

1994 ◽  
Vol 09 (23) ◽  
pp. 2083-2095
Author(s):  
M. DINEYKHAN ◽  
G.V. EFIMOV
Keyword(s):  
Ground State ◽  
Hydrogen Isotopes ◽  
Binding Energies ◽  
Critical Values ◽  
Light Nuclei ◽  
Oscillator Representation ◽  
Representation Method ◽  
Oscillator Representation Method

The mesic molecules (HμNZ), where H is the hydrogen isotopes (p, d, t) and NZ are nuclei with charges Z=2, 3, 4, …and masses MZ=2Zmp, are studied. The energy values of the ground state for the mesic molecules of light nuclei have been calculated by using the oscillator representation method. The dependence of the binding energies of the muonic molecules on nuclear charges and the critical values of nuclear charges are obtained.

scholarly journals Oscillator Representation and Generalized van der Waals Hamiltonians

1997 ◽  
Vol 12 (16) ◽  
pp. 1193-1207
Author(s):  
M. Dineykhan
Keyword(s):  
Hydrogen Atom ◽  
Excited States ◽  
Ground State ◽  
Van Der Waals ◽  
Bound State ◽  
Oscillator Strengths ◽  
Uniform Electric Field ◽  
Oscillator Representation ◽  
Representation Method ◽  
Oscillator Representation Method

The oscillator representation method is extended to calculate the energy spectrum of bound state systems described by axially symmetrical potentials in the parabolic system coordinates. In particular, it is applied to calculate the energy of the ground and excited states of the hydrogen atom in the uniform electric field and van der Waals field. The method gives the perturbation formulas for the analytic spectrum of the hydrogen atom in the generalized van der Waals field and defines oscillator strengths for transitions from the ground state to the perturbed manifold n=10, m=0.

A NONPERTURBATIVE CALCULATION FOR THE EFFECTIVE POTENTIAL OF THE $\left(\frac{g}{4}\phi^{4}-J\phi\right)_{1+1}$ SCALAR FIELD THEORY USING THE OSCILLATOR REPRESENTATION METHOD WITH BOREL RESUMMATION

2007 ◽  
Vol 22 (06) ◽  
pp. 1265-1278
Author(s):  
ABOUZEID M. SHALABY ◽  
S. T. EL-BASYOUNY
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Phase Transition ◽  
Scalar Field ◽  
External Magnetic Field ◽  
Effective Potential ◽  
Oscillator Representation ◽  
Constructive Field Theory ◽  
Representation Method ◽  
Oscillator Representation Method

We established a resummed formula for the effective potential of [Formula: see text] scalar field theory that can mimic the true effective potential not only at the critical region but also at any point in the coupling space. We first extend the effective potential from the oscillator representation method, perturbatively, up to g3 order. We supplement perturbations by the use of a resummation algorithm, originally due to Kleinert, Thoms and Janke, which has the privilege of using the strong coupling as well as the large coupling behaviors rather than the conventional resummation techniques which use only the large order behavior. Accordingly, although the perturbation series available is up to g3 order, we found a good agreement between our resummed effective potential and the well-known features from constructive field theory. The resummed effective potential agrees well with the constructive field theory results concerning existing and order of phase transition in the absence of an external magnetic field. In the presence of the external magnetic field, as in magnetic systems, the effective potential shows nonexistence of phase transition and gives the behavior of the vacuum condensate as a monotonic increasing function of J, in complete agreement with constructive field theory methods.

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.

LEVEL DENSITIES IN LIGHTER NUCLEI

1965 ◽  
Vol 43 (7) ◽  
pp. 1248-1258 ◽  
Author(s):  
A. Gilbert ◽  
F. S. Chen ◽  
A. G. W. Cameron
Keyword(s):  
Excitation Energy ◽  
Ground State ◽  
Shell Structure ◽  
Mass Number ◽  
State Energy ◽  
Binding Energies ◽  
Light Nuclei ◽  
Cumulative Number ◽  
Additional Consideration ◽  
Level Densities

There has been discussion in the literature as to whether the cumulative number of levels in light nuclei varies more nearly as exp(const. [Formula: see text]) or exp(const. E), where E is the excitation energy. The question is examined in this paper. It is found that if one constructs "step diagrams" by plotting the cumulative number versus the energy, both formulas represent the data almost equally well. However, additional consideration of levels counted above neutron and proton binding energies shows that exp(const. [Formula: see text]) fails badly to represent the data, whereas exp(const. E) continues to give good fits. In either case E may be measured above an arbitrary ground-state energy E0. If the satisfactory formula is written in the form exp(E–E0)/T, then it is found that the dependence of the slope on mass number may be expressed in approximately the form T−1 = 0.0165A MeV−1, but there are significant deviations from this relation apparently related to shell structure. The intercepts E0 are quite variable but are roughly clustered according to the oddness or evenness of the neutron and proton numbers of the nucleus.

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.

Calculation of ground-state energies of muonic molecules of hydrogen isotopes confined to a two-dimensional region

1990 ◽  
Vol 41 (7) ◽  
pp. 4049-4051 ◽  
Author(s):  
I. C. da Cunha Lima ◽  
M. Fabbri ◽  
A. Ferreira da Silva ◽  
A. Troper
Keyword(s):  
Ground State ◽  
Hydrogen Isotopes ◽  
Two Dimensional ◽  
Ground State Energies
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