scholarly journals A Phenomenological Model for Hypernuclear Binding Energies

1961 ◽  
Vol 14 (2) ◽  
pp. 313 ◽  
Author(s):  
JW Olley
Keyword(s):  
Simple Model ◽  
Binding Energy ◽  
Phenomenological Model ◽  
Ground State ◽  
Mass Number ◽  
State Energy ◽  
Binding Energies ◽  
Potential Well ◽  
Nucleon Interaction ◽  
Experimental Values

The form of the dependence of the binding energy of the A-particle in hypernuclei on the mass number .A is of interest in obtaining empirical information about the hyperon-nucleon interaction. As an introductory calculation we considered the simple model in which the total A-nucleon interaction is replaced by a potential well V(r) in which the A moves and in which the only �effect of varying .A is to vary the radius but not the depth of the well. The binding energy of the A, B A' is then given by the ground state energy of a particle in this well. The aim of our calculations was to determine whether the present experimental values of B A defined a unique well sbape.

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.

scholarly journals Improvement in a phenomenological formula for ground state binding energies

2016 ◽  
Vol 25 (08) ◽  
pp. 1650046
Author(s):  
G. Gangopadhyay
Keyword(s):  
Binding Energy ◽  
Ground State ◽  
Magic Number ◽  
Substantial Improvement ◽  
Binding Energies ◽  
Mean Square ◽  
Mean Square Deviation ◽  
Neutron Magic Number ◽  
Experimental Values ◽  
New Formula

The phenomenological formula for ground state binding energy derived earlier [G. Gangopadhyay, Int. J. Mod. Phys. E 20 (2011) 179] has been modified. The parameters have been obtained by fitting the latest available tabulation of experimental values. The major modifications include a new term for pairing and introduction of a new neutron magic number at N = 160. The new formula reduced the root mean square deviation to 363[Formula: see text]keV, a substantial improvement over the previous version of the formula.

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.

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.

Ground-State Energy of an Exciton

1973 ◽  
Vol 51 (10) ◽  
pp. 1104-1108
Author(s):  
M. H. Hawton ◽  
P. K. Dubey ◽  
V. V. Paranjape
Keyword(s):  
Binding Energy ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Conventional Approach ◽  
Phonon Energy ◽  
Energy Ratio

We propose a method which differs from the conventional approach used by several authors for calculating the shift in the ground-state energy, E1s, of an exciton. Our approach allows us to obtain the shift for values of binding-energy-to-phonon-energy ratio, β2, which are not restricted to the range [Formula: see text], as is the case with earlier approaches. In the limit of small β, our result for E1s reduces to the expression derived by earlier authors.

Non-relativistic s-wave binding energies of Λ-particle in hypernuclei

2016 ◽  
Vol 31 (14) ◽  
pp. 1650084 ◽  
Author(s):  
A. Armat ◽  
H. Hassanabadi
Keyword(s):  
Experimental Data ◽  
Binding Energy ◽  
Analytical Solution ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Binding Energies ◽  
S Wave ◽  
Ground State Binding Energy ◽  
Type Interaction

In this work, the ground state binding energy of [Formula: see text]-particle in hypernuclei is investigated by using analytical solution of non-relativistic Schrödinger equation in the presence of a generalized Woods–Saxon-type interaction. The comparison with the experimental data is motivating.

Effects of Temperature and Hydrogen-Like Impurity on the Vibrational Frequency of the Polaron in RbCl Parabolic Quantum Dots

NANO ◽  
2016 ◽  
Vol 11 (03) ◽  
pp. 1650029 ◽  
Author(s):  
Wei Xiao ◽  
Jing-Lin Xiao
Keyword(s):  
Binding Energy ◽  
Ground State Energy ◽  
Ground State ◽  
Vibrational Frequency ◽  
State Energy ◽  
Impurity Potential ◽  
Ground State Binding Energy ◽  
Effects Of Temperature ◽  
Increasing Function ◽  
Coulombic Impurity Potential

The properties of an electron strongly coupled to longitudinal optical (LO) phonon in RbCl parabolic quantum dot (PQD) with a hydrogen-like impurity at the center were investigated at a finite temperature. We have obtained the vibrational frequency of a strong-coupling polaron in RbCl PQD by using linear combination operator method. We then calculate the effects of temperature, the Coulombic impurity potential and the effective confinement strength on the vibrational frequency by using unitary transformation and the quantum statistics theory methods. The influences of the temperature, the Coulombic impurity potential and the effective confinement strength on the ground state energy and the ground state binding energy are also analyzed. The strengths of these quantities increase with raising temperature. The vibrational frequency is an increasing function of the Coulombic impurity potential and the effective confinement strength. The ground state energy is an increasing function of the effective confinement strength, whereas it is a decreasing one of the Coulombic impurity potential. The ground state binding energy is an increasing function of the Coulombic impurity potential, whereas it is a decayed one of the effective confinement strength.

scholarly journals Quantum mechanics of particles trapped in a Lamé circle or Lamé sphere shaped potential well

2021 ◽  
Vol 67 (2 Mar-Apr) ◽  
pp. 206
Author(s):  
T. Isojärvi
Keyword(s):  
Quantum Mechanics ◽  
Excited State ◽  
Undergraduate Students ◽  
Ground State ◽  
State Energy ◽  
Potential Well ◽  
Step Potential ◽  
Time Stepping ◽  
Data Points ◽  
Well Depth

Ground state and 1st excited state energies and wave functions were calculated for systems of one or two electrons in a 2D and 3D potential well having a shape intermediate between a circle and a square or a sphere and a cube. One way to define such a potential well is with a step potential and a bounding surface of form |x| q +|y| q +|z| q = |r| q , which converts from a sphere to a cube when q increases from 2 to infinity. This kind of geometrical object is called a Lame surface. The calculations were done either with implicit finite difference time stepping in ´ the direction of negative imaginary time axis or with quantum diffusion Monte Carlo. The results demonstrate how the volume and depth of the potential well affect the E0 more than the shape parameter q does. Functions of two and three parameters were found to be sufficient for fitting an empirical graph to the ground state energy data points as a function of well depth V0 or exponent q. The ground state and first excited state energy of one particle in a potential well of this type appeared to be very closely approximated with an exponential function depending on q, when the well depth and area or volume was kept constant while changing the value of q. The model is potentially useful for describing quantum dots that deviate from simple geometric shapes, or for demonstrating methods of computational quantum mechanics to undergraduate students.

BINDING ENERGY OF A BOUND POLARON IN THE FINITE PARABOLIC QUANTUM WELL

2001 ◽  
Vol 15 (20) ◽  
pp. 827-835 ◽  
Author(s):  
FENG-QI ZHAO ◽  
XI XIA LIANG
Keyword(s):  
Binding Energy ◽  
Quantum Well ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Transition Energy ◽  
Energy Levels ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Bound Polaron

We have studied the effect of the electron–phonon interaction on the energy levels of the bound polaron and calculated the ground-state energy, the binding energy of the ground state, and the 1 s → 2 p ± transition energy in the GaAs/Al x Ga 1-x As parabolic quantum well (PQW) structure by using a modified Lee–Low–Pines (LLP) variational method. The numerical results are given and discussed. It is found that the contribution of electron–phonon interaction to the ground-state energy and the binding energy is obvious, especially in large well-width PQWs. The electron–phonon interaction should not be neglected.

scholarly journals A NEW PHENOMENOLOGICAL FORMULA FOR GROUND-STATE BINDING ENERGIES

2011 ◽  
Vol 20 (01) ◽  
pp. 179-190 ◽  
Author(s):  
G. GANGOPADHYAY
Keyword(s):  
Binding Energy ◽  
Single Particle ◽  
Ground State ◽  
Liquid Drop ◽  
Alpha Decay ◽  
Binding Energies ◽  
Present Calculation ◽  
Mean Square ◽  
Liquid Drop Model ◽  
The One

A phenomenological formula based on liquid drop model has been proposed for ground-state binding energies of nuclei. The effect due to bunching of single particle levels has been incorporated through a term resembling the one-body Hamiltonian. The effect of n–p interaction has been included through a function of valence nucleons. A total of 50 parameters has been used in the present calculation. The root mean square (r.m.s.) deviation for the binding energy values for 2140 nuclei comes out to be 0.376 MeV, and that for 1091 alpha decay energies is 0.284 MeV. The correspondence with the conventional liquid drop model is discussed.

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