PHENOMENOLOGICAL RELATIVISTIC STUDY OF THE ENERGY OF A Λ IN ITS GROUND AND EXCITED STATES IN HYPERNUCLEI

1994 ◽  
Vol 03 (03) ◽  
pp. 939-951
Author(s):  
G.J. PAPADOPOULOS ◽  
C.G. KOUTROULOS ◽  
M.E. GRYPEOS
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Dirac Equation ◽  
Least Squares ◽  
Excited States ◽  
Energy Eigenvalue ◽  
Bound State ◽  
Small Component ◽  
Repulsive Potentials ◽  
Analytic Expressions

The binding energy BΛ of a Λ-particle in hypernuclei is studied by means of the Dirac equation with attractive and repulsive potentials of rectangular shapes and of the same radius. The energy eigenvalue equation in this case is obtained analytically for every bound state, as well as the large and small component of the wave function (for given BΛ). A first attempt is also made to investigate the possibility of deriving in particular cases approximate analytic expressions of BΛ for the excited states. Using various least squares fittings, numerical results for the binding energy of the Λ are given and comparisons and comments are also made.

scholarly journals PHENOMENOLOGICAL RELATIVISTIC STUDY OF THE ENERGY OF Α Λ IN ITS GROUND AND EXCITED STATES IN HYPERNUCLEI

2020 ◽  
Vol 2 ◽  
pp. 389
Author(s):  
G. J. Papadopoulos ◽  
C. G. Koutroulos ◽  
M. E. Grypeos
Keyword(s):  
Binding Energy ◽  
Dirac Equation ◽  
Excited States ◽  
Energy Eigenvalue ◽  
Bound State ◽  
Eigenvalue Equation ◽  
Repulsive Potentials

The binding energy B_Λ of a Λ-particle in hypernuclei is studied by means of the Dirac equation containing attractive and repulsive potentials of orthogonal shapes. The energy eigenvalue equation in this case is obtained analytically for every bound state. An attempt is also made to investigate the possibility of deriving in particular cases approximate ana­lytic expressions for B_Λ.

scholarly journals Calculation of Binding Energy and Wave Function for Exotic Hidden-Charm Pentaquark

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
F. Chezani Sharahi ◽  
M. Monemzadeh
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
The Other

In this study, pentaquark P c 4380 composed of a baryon Σ c , and a D ¯ ∗ meson is considered. Pentaquark is as a bound state of two-body systems composed of a baryon and a meson. The calculated potential will be expanded and replaced in the Schrödinger equation until tenth sentences of expansion. Solving the Schrödinger equation with the expanded potential of Pentaquark leads to an analytically complete approach. As a consequence, the binding energy E B of pentaquark P c and wave function is obtained. The results E B will be presented in the form of tables so that we can review the existence of pentaquark P c . Then, the wave function will be shown on diagrams. Finally, the calculated results are compared with the other obtained results, and the mass of observing pentaquark P c and the radius of pentaquark are estimated.

Effect of the Wigner–Dunkl algebra on the Dirac equation and Dirac harmonic oscillator

2018 ◽  
Vol 33 (25) ◽  
pp. 1850146 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W. S. Chung
Keyword(s):  
Functional Analysis ◽  
Wave Function ◽  
Dirac Equation ◽  
Harmonic Oscillator ◽  
Limit State ◽  
Energy Eigenvalue ◽  
Eigenvalue Equation ◽  
Reflection Symmetry ◽  
Analysis Method ◽  
One Dimensional

In this work, we study the Dirac equation and Dirac harmonic oscillator in one-dimensional via the Dunkl algebra. By using Dunkl derivative, we solve the momentum operator and Hamiltonian that include the reflection symmetry. Based on the concept of the Wigner–Dunkl algebra and the functional analysis method, we have obtained the energy eigenvalue equation and the corresponding wave function for Dirac harmonic oscillator and Dirac equation, respectively. It is shown all results in the limit state satisfied what we had expected before.

Exact Numerical Procedure for the Binding Energy of Hydrogen Impurities in Quantum Dots with Parabolic Confinements

2013 ◽  
Vol 475-476 ◽  
pp. 1355-1358
Author(s):  
Arnold Abramov
Keyword(s):  
Quantum Dots ◽  
Wave Function ◽  
Binding Energy ◽  
Quantum Dot ◽  
Excited States ◽  
Ground State ◽  
Qualitative Agreement ◽  
Numerical Procedure ◽  
Impurity States ◽  
Parabolic Confinement

In this paper we present exact numerical procedure to calculate the binding energy and wave function of impurity states in a quantum dot with parabolic confinement. The developed method allows control the accuracy of obtained results, as well as calculates the characteristics of not only ground state, but also of the excited states. Comparison of our results with data obtained by other methods is in quantitative and qualitative agreement. We studied the effects of impurity position on the binding energy.

scholarly journals A SIMPLE DIRAC WAVE FUNCTION FOR A COULOMB POTENTIAL WITH LINEAR CONFINEMENT

1999 ◽  
Vol 14 (34) ◽  
pp. 2409-2411 ◽  
Author(s):  
JERROLD FRANKLIN
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Dirac Equation ◽  
Coulomb Potential ◽  
Ground State ◽  
Linear Potential ◽  
Confining Potential ◽  
Lorentz Scalar ◽  
Dirac Wave Function ◽  
Scalar Part

A simple analytical solution is found to the Dirac equation for the combination of a Coulomb potential with a linear confining potential. An appropriate linear combination of Lorentz scalar and vector linear potentials, with the scalar part dominating, can be chosen to give a simple Dirac wave function. The binding energy depends only on the Coulomb strength and is not affected by the linear potential. The method works for the ground state, or for the lowest state with l=j-1/2, for any j.

APPROXIMATE BOUND DIRAC STATES FOR PSEUDOSCALAR HULTHÉN POTENTIAL

2013 ◽  
Vol 22 (06) ◽  
pp. 1350035
Author(s):  
M. HAMZAVI ◽  
A. A. RAJABI ◽  
F. KOOCHAKPOOR
Keyword(s):  
Dirac Equation ◽  
Energy Eigenvalue ◽  
Spin Symmetry ◽  
Bound State ◽  
Hulthén Potential ◽  
Energy Eigenvalues ◽  
Hulthen Potential ◽  
Approximate Analytical Solutions ◽  
Potential Parameters ◽  
Nu Method

In this paper, we present approximate analytical solutions of the Dirac equation with the pseudoscalar Hulthén potential under spin and pseudospin (p-spin) symmetry limits in (3+1) dimensions. The energy eigenvalues and corresponding eigenfunctions are given in their closed forms by using the Nikiforov–Uvarov (NU) method. Numerical results of the energy eigenvalue equations are presented to show the effects of the potential parameters on the bound-state energies.

Four-body bound state calculations using three-dimensional low-momentum effective interaction Vlow-k

2017 ◽  
Vol 26 (12) ◽  
pp. 1750083 ◽  
Author(s):  
M. Radin ◽  
H. Mohseni ◽  
F. Nazari ◽  
M. R. Hadizadeh
Keyword(s):  
Wave Function ◽  
Renormalization Group ◽  
Binding Energy ◽  
Effective Interaction ◽  
Three Dimensional ◽  
Bound State ◽  
Suzuki Method ◽  
Wide Range ◽  
Cutoff Dependence ◽  
Text Interaction

In this paper, we solve the coupled Yakubovsky integral equations for four-body (4B) bound state using the low-momentum effective two-body interaction [Formula: see text] in a three-dimensional (3D) approach, without using a partial wave (PW) decomposition. The renormalization group (RG) evolved interaction is constructed from spin-independent Malfliet–Tjon potential using the Lee–Suzuki method. The cutoff dependence of the 4B binding energy and wave function is investigated for a wide range of the momentum cutoff [Formula: see text] of [Formula: see text] interaction from 1.0 to 8.0[Formula: see text][Formula: see text].

Spin Separation and the Modified Dirac Equation

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Perturbation Expansion ◽  
Spin Dependence ◽  
Small Component ◽  
Hartree Fock ◽  
Shell System ◽  
Relativistic Corrections ◽  
Corrections To Electronic Structure ◽  
The One

In the preceding chapters, the theory for calculations based on the Dirac equation has been laid out in some detail. The discussion of the methods included a comparison with equivalent nonrelativistic methods, from which it is apparent that four-component calculations will be considerably more expensive than the corresponding nonrelativistic calculations—perhaps two orders of magnitude more expensive. For this reason, there have been many methods developed that make approximations to the Dirac equation, and it is to these that we turn in this part of the book. There are two elements of the Dirac equation that contribute to the large amount of work: the presence of the small component of the wave function and the spin dependence of the Hamiltonian. The small component is primarily responsible for the large number of two-electron integrals which, as will be seen later, contain all the lowest-order relativistic corrections to the electron–electron interaction. The spin dependence is incorporated through the kinetic energy operator and the correction to the electronic Coulomb interaction, and also through the coupling of the spin and orbital angular momenta in the atomic 2-spinors, which form a natural basis set for the solution of the Dirac equation. Spin separation has obvious advantages from a computational perspective. As we will show for several spin-free approaches below, a spin-free Hamiltonian is generally real, and therefore real spin–orbitals may be employed for the large and small components. The spin can then be factorized out and spin-restricted Hartree–Fock methods used to generate the one-electron functions. In the post-SCF stage, where the no-pair approximation is invoked, the transformation of the integrals from the atomic to the molecular basis produces a set of real molecular integrals that are indistinguishable from a set of nonrelativistic MO integrals, and therefore all the nonrelativistic correlation methods may be employed without modification to obtain relativistic spin-free correlated wave functions. In most cases, spin–free relativistic effects dominate the relativistic corrections to electronic structure. We will show later that in a perturbation expansion based on the nonrelativistic wave function, the spin-free effects for a closed-shell system enter in first order, whereas the spin-dependent effects make their first contribution in second order.

Insights into theoretical quantum chemistry from electron momentum spectroscopy

1996 ◽  
Vol 74 (11-12) ◽  
pp. 757-762 ◽  
Author(s):  
Ernest R. Davidson
Keyword(s):  
Hydrogen Bond ◽  
Wave Function ◽  
Binding Energy ◽  
Quantum Chemistry ◽  
Excited States ◽  
Momentum Density ◽  
Water Dimer ◽  
Basis Sets ◽  
Electron Momentum ◽  
Electron Momentum Spectroscopy

Most basis sets used in quantum chemistry are designed to get the correct charge and momentum density in the region important for covalent bonding. The (e,2e) cross section measured by electron momentum spectroscopy (EMS) emphasizes the low-momentum, large r, region of the wave function. Improving the description of this part of the wave function for water has resulted in good agreement with (e,2e) data. Because the hydrogen bond is sensitive to the long-range tail of the wave function, this has simultaneously led to an improved description of the hydrogen bond in the water dimer. The satellite region of the binding energy spectrum gives information about the excited states of the cation that is not available at present from any other form of spectroscopy. Calculations seeking agreement with the binding-energy spectra and the momentum distribution associated with satellite peaks have led to the most complete catalog of the cation excited states for ethylene. Here we report the assignment of the excited states based on the dominant part of the wave function rather than focusing on the small coefficients that describe the intensity borrowing from the primary holes. We also examine the adequacy of the assumption that every Dyson orbital is similar to one of the Hartree–Fock orbitals.

scholarly journals An event excess observed in the deeply bound region of the 12C (K−, p) missing-mass spectrum

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yudai Ichikawa ◽  
Junko Yamagata-Sekihara ◽  
Jung Keun Ahn ◽  
Yuya Akazawa ◽  
Kanae Aoki ◽  
...  
Keyword(s):  
Mass Spectrum ◽  
Binding Energy ◽  
Decay Channel ◽  
Peak Shift ◽  
Bound State ◽  
Elastic Peak ◽  
Missing Mass ◽  
Decay Modes ◽  
Kaon Momentum ◽  
First Time

Abstract We have measured, for the first time, the inclusive missing-mass spectrum of the $^{12}$C$(K^-, p)$ reaction at an incident kaon momentum of 1.8 GeV/$c$ at the J-PARC K1.8 beamline. We observed a prominent quasi-elastic peak ($K^-p \rightarrow K^-p$) in this spectrum. In the quasi-elastic peak region, the effect of secondary interaction is apparently observed as a peak shift, and the peak exhibits a tail in the bound region. We compared the spectrum with a theoretical calculation based on the Green’s function method by assuming different values of the parameters for the $\bar{K}$–nucleus optical potential. We found that the spectrum shape in the binding-energy region $-300 \, \text{MeV} < B_{K} < 40$ MeV is best reproduced with the potential depths $V_0 = -80$ MeV (real part) and $W_0 = -40$ MeV (imaginary part). On the other hand, we observed a significant event excess in the deeply bound region around $B_{K} \sim 100$ MeV, where the major decay channel of $K^- NN \to \pi\Sigma N$ is energetically closed, and the non-mesonic decay modes ($K^- NN \to \Lambda N$ and $\Sigma N$) should mainly contribute. The enhancement is fitted well by a Breit–Wigner function with a kaon-binding energy of 90 MeV and width 100 MeV. A possible interpretation is a deeply bound state of a $Y^{*}$-nucleus system.

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