Low-lying collective bands in the even tungsten isotopes 180–186W

1989 ◽  
Vol 67 (5) ◽  
pp. 479-484 ◽  
Author(s):  
R. Sahu
Keyword(s):  
Wave Function ◽  
Angular Momentum ◽  
Quadrupole Interaction ◽  
Asymmetry Parameter ◽  
Degrees Of Freedom ◽  
Energy Levels ◽  
Wave Functions ◽  
Electromagnetic Properties ◽  
Matrix Elements ◽  
Rigid Model

The γ-rigid model has been used to study the energy levels and the electromagnetic properties of 180, 182, 184, 186W. In this model, the intrinsic wave functions are obtained using the pairing plus the quadrupole–quadrupole interaction Hamiltonian of Baranger and Kumar. Good angular momentum states are projected approximately from such a triaxially symmetric intrinsic wave function. This model assumes the nucleus to be γ rigid but soft in the β degrees of freedom. The asymmetry parameter γ for a given nucleus is extracted using the experimental energies of the first 2+ and second 2+ states within the framework of the Davydov–Filippov model. The symmetry parameter β for each J state is determined from the minimization of the projected energy. The calculated energy levels of the ground and the 7 band, the B(E2) values, the electromagnetic moments, the E2 and E4 matrix elements, and the B(E2) ratios agree quite well with experimental results.

SPATIAL CORRELATIONS OF CHAOTIC WAVE FUNCTIONS

1996 ◽  
Vol 10 (03n05) ◽  
pp. 69-80 ◽  
Author(s):  
VLADIMIR N. PRIGODIN ◽  
NOBUHIKO TANIGUCHI
Keyword(s):  
Wave Function ◽  
Joint Distribution ◽  
Energy Levels ◽  
Density Fluctuations ◽  
Wave Functions ◽  
Spatial Correlations ◽  
Large Fluctuations ◽  
Amplitude Correlation ◽  
Universal Law ◽  
Function Density

The statistics of the spatial correlations of eigenfunctions is investigated in chaotic systems with or without time-reversal symmetry. It is rigorously shown that wave functions corresponding to different energy levels are uncorrelated in space. At a given eigenstate, we find that though the background of wave function density fluctuates strongly, there exist the long-standing Friedel oscillations in wave function intensity. The joint distribution of the intensity at two separate space points is presented by the universal law with one parameter — the average amplitude correlation. This distribution encompasses two different regions: One with an independent joint distribution for small values of density fluctuations, and the other showing an increasing spatial correlation for the large fluctuations.

Dirac Bound States of the Killingbeck Potential Under External Magnetic Fields

2015 ◽  
Vol 70 (7) ◽  
pp. 499-505 ◽  
Author(s):  
Zahra Sharifi ◽  
Fateme Tajic ◽  
Majid Hamzavi ◽  
Sameer M. Ikhdair
Keyword(s):  
Wave Function ◽  
Magnetic Fields ◽  
Ground State ◽  
Bound States ◽  
State Energy ◽  
Potential Model ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
Ansatz Method

AbstractThe Killingbeck potential model is used to study the influence of the external magnetic and Aharanov–Bohm (AB) flux fields on the splitting of the Dirac energy levels in a 2+1 dimensions. The ground state energy eigenvalue and its corresponding two spinor components wave functions are investigated in the presence of the spin and pseudo-spin symmetric limit as well as external fields using the wave function ansatz method.

Exact solutions to solitonic profile mass Schrödinger problem with a modified Pöschl–Teller potential

2016 ◽  
Vol 31 (04) ◽  
pp. 1650017 ◽  
Author(s):  
Shishan Dong ◽  
Qin Fang ◽  
B. J. Falaye ◽  
Guo-Hua Sun ◽  
C. Yáñez-Márquez ◽  
...  
Keyword(s):  
Wave Function ◽  
Exact Solutions ◽  
Ground State ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Wave Functions ◽  
Numerical Calculations ◽  
Potential Parameter ◽  
Heun Functions ◽  
Single Well

We present exact solutions of solitonic profile mass Schrödinger equation with a modified Pöschl–Teller potential. We find that the solutions can be expressed analytically in terms of confluent Heun functions. However, the energy levels are not analytically obtainable except via numerical calculations. The properties of the wave functions, which depend on the values of potential parameter [Formula: see text] are illustrated graphically. We find that the potential changes from single well to a double well when parameter [Formula: see text] changes from minus to positive. Initially, the crest of wave function for the ground state diminishes gradually with increasing [Formula: see text] and then becomes negative. We notice that the parities of the wave functions for [Formula: see text] also change.

scholarly journals General Framework for Calculating Spin–orbit Couplings Using Spinless One-Particle Density Matrices: Theory and Application to the Equation-of-Motion Coupled-Cluster Wave Functions

2019 ◽  
Author(s):  
Pavel Pokhilko ◽  
Evgeny Epifanovsky ◽  
Anna I. Krylov
Keyword(s):  
Degrees Of Freedom ◽  
Particle Density ◽  
Mean Field ◽  
Transition Density ◽  
Open Shell ◽  
Equation Of Motion ◽  
Wave Functions ◽  
Coupled Cluster ◽  
Spin Orbit ◽  
Matrix Elements

Standard implementations of non-relativistic excited-state calculations compute only one component of spin multiplets (i.e., Ms =0 triplets), however, matrix elements for all components are necessary for calculations of experimentally relevant spin-dependent quantities. To circumvent explicit calculations of all multiplet components, we employ Wigner–Eckart’s theorem. Applied to a reduced one-particle transition density matrix computed for a single multiplet component, Wigner–Eckart’s theorem generates all other spin–orbit matrix elements. In addition to computational efficiency, this approach also resolves the phase issue arising within Born–Oppenheimer’s separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculations of spin–orbit couplings using equation-of-motion coupled-cluster wave functions is presented. The two-electron contributions are included via the mean-field spin–orbit treatment. Intrinsic issues of constructing spin–orbit mean-field operators for open-shell references are discussed and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.

scholarly journals Hyperfine structure of muonic mesomolecules tdµ, tpµ, dpµ in variational method

2019 ◽  
Vol 222 ◽  
pp. 03011
Author(s):  
A.V. Eskin ◽  
V.I. Korobov ◽  
A.P. Martynenko ◽  
V.V. Sorokin
Keyword(s):  
Variational Method ◽  
Hyperfine Structure ◽  
Vacuum Polarization ◽  
Energy Levels ◽  
Computer Code ◽  
Wave Functions ◽  
Matrix Elements ◽  
Gaussian Form ◽  
Stochastic Variational Method ◽  
The Matrix

The hyperfine structure of energy levels of muonic molecules tdµ, tpµ and dpµ is calculated on the basis of stochastic variational method. The basis wave functions are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. Vacuum polarization, relativistic and nuclear structure corrections are taken into account to increase the accuracy. For numerical calculation, a computer code is written in the MATLAB system. Numerical values of energy levels of hyperfine structure in muonic molecules tdµ, tpµ and dpµ are obtained.

Numerical Methods for the Evaluation of the Löwdin α-Function

2005 ◽  
Vol 70 (8) ◽  
pp. 1035-1054 ◽  
Author(s):  
Nemanja Sovic ◽  
James D. Talman
Keyword(s):  
Wave Function ◽  
Angular Momentum ◽  
Numerical Methods ◽  
Rate Of Convergence ◽  
Wave Functions ◽  
Analytic Methods ◽  
Nuclear Attraction ◽  
Numerical Approaches ◽  
Löwdin Α Function

The problem of expanding an angular momentum wave function centered at one point in terms of angular momentum wave functions centered at another point is analysed. The emphasis is on obtaining methods that can be applied to functions that are defined numerically, in contrast to analytic methods. Three numerical approaches are described, and it is found that one leads to extremely accurate results. The question of the rate of convergence of the resulting series is discussed, and results of the application of the expansion to the calculation of nuclear attraction three-center integrals, and electron-electron four-center integrals are presented.

Investigation of isospin excited and mixed-symmetry states in even–even N = Z nuclei

2018 ◽  
Vol 27 (08) ◽  
pp. 1850065 ◽  
Author(s):  
Falih H. Al-Khudair
Keyword(s):  
Excited States ◽  
Degrees Of Freedom ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Systematic Investigation ◽  
Wave Functions ◽  
Mixed Symmetry ◽  
Mixed Symmetry States ◽  
Boson Model

Mixed-symmetry and isospin excited states are typical of the interacting boson model with isospin (IBM-3). With a view to look for such states, levels scheme of the IBM-3 dynamical symmetry is discussed. A systematic investigation in the proton and neutron degrees of freedom of the energy levels has been carried out. A sequence of isospin excitation bands has been identified. We have analyzed the wave functions and given the symmetrical labeling of the states. The transition probabilities between the isospin excitation states of model limits are analyzed in terms of isoscalar and isovector decompositions. The present calculations suggest that a combination of isospin excitation and mixed-symmetry states can provide substantial information on the structure of nuclear states. Calculations for [Formula: see text] and [Formula: see text] nuclei are presented and compared with the results of the shell model and available experimental data.

scholarly journals Color Confinement and Spatial Dimensions in the Complex-Sedenion Space

2017 ◽  
Vol 2017 ◽  
pp. 1-26 ◽  
Author(s):  
Zi-Hua Weng
Keyword(s):  
Wave Function ◽  
Complex Number ◽  
Degrees Of Freedom ◽  
Unit Vector ◽  
Wave Functions ◽  
Field Equations ◽  
Abelian Gauge ◽  
Color Confinement ◽  
Complex Quaternion ◽  
Spatial Dimensions

The paper aims to apply the complex-sedenions to explore the wave functions and field equations of non-Abelian gauge fields, considering the spatial dimensions of a unit vector as the color degrees of freedom in the complex-quaternion wave functions, exploring the physical properties of the color confinement essentially. J. C. Maxwell was the first to employ the quaternions to study the electromagnetic fields. His method inspires subsequent scholars to introduce the quaternions, octonions, and sedenions to research the electromagnetic field, gravitational field, and nuclear field. The application of complex-sedenions is capable of depicting not only the field equations of classical mechanics, but also the field equations of quantum mechanics. The latter can be degenerated into the Dirac equation and Yang-Mills equation. In contrast to the complex-number wave function, the complex-quaternion wave function possesses three new degrees of freedom, that is, three color degrees of freedom. One complex-quaternion wave function is equivalent to three complex-number wave functions. It means that the three spatial dimensions of unit vector in the complex-quaternion wave function can be considered as the “three colors”; naturally the color confinement will be effective. In other words, in the complex-quaternion space, the “three colors” are only the spatial dimensions, rather than any property of physical substance.

scholarly journals A LAGUERRE POLYNOMIAL ORTHOGONALITY AND THE HYDROGEN ATOM

2003 ◽  
Vol 01 (02) ◽  
pp. 177-188 ◽  
Author(s):  
CHARLES F. DUNKL
Keyword(s):  
Wave Function ◽  
Hydrogen Atom ◽  
Coulomb Potential ◽  
Elementary Proof ◽  
Laguerre Polynomial ◽  
Energy Levels ◽  
Laguerre Polynomials ◽  
Wave Functions ◽  
Radial Part ◽  
Meixner Polynomials

The radial part of the wave function of an electron in a Coulomb potential is the product of a Laguerre polynomial and an exponential with the variable scaled by a factor depending on the degree. This note presents an elementary proof of the orthogonality of wave functions with differing energy levels. It is also shown that this is the only other natural orthogonality for Laguerre polynomials. By expanding in terms of the usual Laguerre polynomial basis, an analogous strange orthogonality is obtained for Meixner polynomials.

scholarly journals WHY X(3915) IS SO NARROW AS A χc0(2P) STATE?

2013 ◽  
Vol 28 (28) ◽  
pp. 1350145 ◽  
Author(s):  
YUE JIANG ◽  
GUO-LI WANG ◽  
TIANHONG WANG ◽  
WAN-LI JU
Keyword(s):  
Wave Function ◽  
Quantum Chromodynamics ◽  
Decay Width ◽  
Babar Collaboration ◽  
Wave Functions ◽  
Final States ◽  
Full Width ◽  
Matrix Elements ◽  
Narrow Width ◽  
Open Question

New resonance X(3915) was identified as the charmonium χc0(2P) by BaBar Collaboration, but there still seems an open question of this assignment: why its full width is so narrow? To answer this question, we calculate the Okubo–Zweig–Iizuka (OZI)-allowed strong decays [Formula: see text], where X(3915) is assigned as a χc0(2P) state, and estimate its full width in the cooperating framework of 3P0 model and the Bethe–Salpeter (BS) method using the Mandelstam formalism, during which nonperturbative quantum chromodynamics (QCD) effects of the hadronic matrix elements are well-considered by overlapping integral over the relativistic Salpeter wave functions of the initial and final states. We find the node structure of χc0(2P) wave function resulting in the narrow width of X(3915) and show the dependence of the decay width on the variation of the initial mass of X(3915). We point out that the rate of [Formula: see text] is crucial to confirm whether X(3915) is the χc0(2P) state or not.

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