Relativistic Energy States of the A-Particle in Hypernuclei Using Gaussian Potentials

1990 ◽  
Vol 45 (1) ◽  
pp. 14-16
Author(s):  
C. G. Koutroulos
Keyword(s):  
Dirac Equation ◽  
Excited States ◽  
Ground State ◽  
Vector Potential ◽  
Scalar Potential ◽  
Binding Energies ◽  
Relativistic Energy ◽  
Gaussian Form ◽  
Fourth Component ◽  
Potential Parameters

Abstract The Dirac equation with scalar potential and fourth component of vector potential of the Gaussian form is solved numerically for potential parameters obtained by a least squares fitting of the ground state binding energies of the A in a number of hypernuclei. The binding energies in the ground and excited states for various hypernuclei are determined. The spacings between the various levels are also given

Relativistic Ground and Excited State Energies of a/1-Particle in Hypernuclei Using Woods-Saxon Potentials

1989 ◽  
Vol 44 (12) ◽  
pp. 1234-1238 ◽  
Author(s):  
C. G. Koutroulos
Keyword(s):  
Excited State ◽  
Dirac Equation ◽  
Excited States ◽  
Ground State ◽  
Scalar Potential ◽  
Binding Energies ◽  
Fitting Procedure ◽  
Fourth Component ◽  
Potential Parameters ◽  
Good Agreement

Abstract The relativistic Dirac equation with a scalar potential and the fourth component of a vector potential of the Woods-Saxon shape is solved numerically for potential parameters obtained by a last squares fitting procedure of the ground state binding energies of the Λ in a number of hypernuclei and its binding energies in the ground and excited states (as well as the relevant spacings) for various hypcrnuclei are determined. The results are in very good agreement with the preliminary experimental ones given by Chrien on the basis of the (π+, K+) reaction on nuclei.

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

scholarly journals SOLUTION OF THE DIRAC EQUATION WITH NONCENTRAL THREE-VECTOR POTENTIAL

2006 ◽  
Vol 21 (07) ◽  
pp. 581-592 ◽  
Author(s):  
A. D. ALHAIDARI
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
Vector Potential ◽  
Radial Component ◽  
Wave Functions ◽  
Relativistic Energy ◽  
Dirac Oscillator ◽  
Spherical Coordinates ◽  
The One ◽  
Spinor Wave

We introduce coupling to three-vector potential in the (3+1)-dimensional Dirac equation. The potential is noncentral (angular-dependent) such that the Dirac equation separates completely in spherical coordinates. The relativistic energy spectrum and spinor wave functions are obtained for the case where the radial component of the vector potential is proportional to 1/r. The coupling presented in this work is a generalization of the one which was introduced by Moshinsky and Szczepaniak for the Dirac-oscillator problem.

scholarly journals Relativistic Expressions for the r.m.s. Radii of the λ-Particle Orbits in Hypernuclei and of the Corresponding Potential Energies

2020 ◽  
Vol 5 ◽  
pp. 125
Author(s):  
G. J. Papadopoulos ◽  
C. G. Koutroulos ◽  
M. E. Grypeos
Keyword(s):  
Mass Number ◽  
Scalar Potential ◽  
Energy Operator ◽  
Bound State ◽  
Expectation Value ◽  
Energy Eigenvalues ◽  
Particle Orbits ◽  
Analytic Expression ◽  
Fourth Component ◽  
Potential Parameters

The root mean square radii of the Λ-particle orbits in hypemuclei are calculated semi-analytically for every bound state, using the Dirac equation with a scalar potential Us{r) and the fourth component of a vector potential Uv{f) in the case of rectangular shapes of these potentials with the same radius R.ln addition an analytic expression of the expectation value of the corresponding potential energy operator is derived. For the above quantities, expressions of the energy eigenvalues in terms of the potential parameters are needed and approximate formulae may be used, in certain cases. The variation of these quantities with the mass number is also investigated and numerical calculations are performed.

TWO-CENTER PROBLEM FOR THE DIRAC EQUATION WITH A COULOMB AND SCALAR POTENTIAL

2007 ◽  
Vol 22 (18) ◽  
pp. 3123-3130
Author(s):  
V. V. BONDARCHUK ◽  
I. M. SHVAB ◽  
A. V. KATERNOGA
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Ground State ◽  
Scalar Potential ◽  
Scalar Coupling ◽  
Center Problem ◽  
Energy Term ◽  
Coupling Constant ◽  
Scalar Coupling Constant ◽  
Scalar Potentials

The ground state wave function and the energy term of a relativistic electron moving in the field of two fixed centers, when interaction of this particle with centers is described by two Coulomb and two Coulomb-like scalar potentials are calculated analytically by the LCAO method. Dependence of electron binding energy from value of scalar coupling constant was investigated using obtained analytic results.

scholarly journals Approximate treatment of the Dirac equation with scalar and vector potentials of rectangular shapes

2020 ◽  
Vol 4 ◽  
pp. 41
Author(s):  
M. E. Grypeos ◽  
C. G. Koutroulos ◽  
G. J. Papadopoulos
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Scalar Potential ◽  
Particle Energy ◽  
Vector Potentials ◽  
Wide Range ◽  
Analytic Expressions ◽  
Fourth Component ◽  
Approximate Treatment ◽  
Range Of Values

The Dirac equation with scalar potential Us(r) and fourth component of vector po­ tential Uv(r) is considered in the case of the rectangular shapes of these potentials with the same radius R and approximate analytic expressions are derived for the single-particle energy of bound states in certain cases. The results obtained with these expressions are compared with the corresponding "exact" results obtained by solving the eigenvalue equa­ tion numerically.It is found that very good results are obtained for the ground state and for quite a wide range of values of R with one of the proposed expressions. Even the corresponding non-relativistic version of this expession, has not been derived before, to our knowledge.

Dirac equation with some time-dependent electromagnetic terms

2016 ◽  
Vol 31 (23) ◽  
pp. 1650132 ◽  
Author(s):  
K. Saeedi ◽  
S. Zarrinkamar ◽  
H. Hassanabadi
Keyword(s):  
Electromagnetic Field ◽  
Dirac Equation ◽  
Linear Form ◽  
Vector Potential ◽  
Scalar Potential ◽  
Time Dependent ◽  
Exponential Form

We study the motion of relativistic fermions in a time-dependent electromagnetic field within the framework of Dirac equation. We consider the time-dependent scalar potential of the exponential form and the vector potential of linear form. We obtain the eigenfunctions and eigenvalues.

The Rotational Spectrum of 2,2-Dimethylthiirane

1993 ◽  
Vol 48 (11) ◽  
pp. 1102-1106 ◽  
Author(s):  
H. Hartwig ◽  
H. Dreizler
Keyword(s):  
Excited States ◽  
Ground State ◽  
Heavy Atom ◽  
Natural Abundance ◽  
Structure Parameters ◽  
Rotational Spectrum ◽  
Centrifugal Distortion ◽  
Centrifugal Distortion Constants ◽  
Potential Parameters

Abstract The rotational spectrum of 2,2-dimethylthiirane (isobutylene sulfide) has been assigned for the ground and torsionally excited states. The rotational and centrifugal distortion constants, as well as the potential parameters V3 and V´1 2 are determined. The ground state spectra of the 13C and 34S isotopomers were assigned in natural abundance and heavy atom structure parameters are given.

scholarly journals Root mean square radii of the Λ-particle orbits in hypernuclei using potentials of orthogonal shape in arelativistic treatment

2019 ◽  
Vol 3 ◽  
pp. 20
Author(s):  
C. G. Koutroulos ◽  
G. J. Papadopoulos
Keyword(s):  
Dirac Equation ◽  
Root Mean Square ◽  
Excited States ◽  
Ground State ◽  
Mean Square ◽  
Vector Potentials ◽  
Particle Orbits ◽  
Approximate Expressions

The root mean square radii of the Λ-particle orbits in hypernuclei are calculated in the ground and first excited states using the Dirac equation with scalar and vector potentials of orthogonal shape. An exact analytic and also approximate expressions are derived for the root mean square ra-' dius of the Λ orbit in its ground state. It is shown that <r >  2 1/2 1/3 ' varies linearly with A ' for the higer mass hypers 1/2 ^ nuclei, Our results in the ground state are compared with the results of Rayet and also with those of Daskaloyannis et. al.

Excited-State Dynamics in the RNA Nucleotide Uridine 5’-Monophosphate Investigated by Femtosecond Broadband Transient Absorption Spectroscopy

2019 ◽  
Author(s):  
Matthew M. Brister ◽  
Carlos Crespo-Hernández
Keyword(s):  
Excited State ◽  
Excited States ◽  
Ground State ◽  
Transient Absorption ◽  
Electronic Energy ◽  
Transient Absorption Spectroscopy ◽  
Electronic Relaxation ◽  
Vibrationally Excited ◽  
Excited State Dynamics ◽  
Π State

<p></p><p> Damage to RNA from ultraviolet radiation induce chemical modifications to the nucleobases. Unraveling the excited states involved in these reactions is essential, but investigations aimed at understanding the electronic-energy relaxation pathways of the RNA nucleotide uridine 5’-monophosphate (UMP) have not received enough attention. In this Letter, the excited-state dynamics of UMP is investigated in aqueous solution. Excitation at 267 nm results in a trifurcation event that leads to the simultaneous population of the vibrationally-excited ground state, a longlived <sup>1</sup>n<sub>O</sub>π* state, and a receiver triplet state within 200 fs. The receiver state internally convert to the long-lived <sup>3</sup>ππ* state in an ultrafast time scale. The results elucidate the electronic relaxation pathways and clarify earlier transient absorption experiments performed for uracil derivatives in solution. This mechanistic information is important because long-lived nπ* and ππ* excited states of both singlet and triplet multiplicities are thought to lead to the formation of harmful photoproducts.</p><p></p>

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