Studies in jj -coupling. III. Nuclear energy levels

1952 ◽  
Vol 215 (1120) ◽  
pp. 120-132 ◽  
Keyword(s):  
Excited States ◽  
Ground State ◽  
Short Range ◽  
Nuclear Energy ◽  
Energy Levels ◽  
Wave Functions ◽  
Light Nuclei ◽  
Radial Dependence ◽  
Exchange Force ◽  
Very High

The wave functions for the configurations j n , with j = 3/2, 5/2 and 7/2, obtained in part II of this series according to the particular scheme of part I, are here used to obtain the central force energy matrices for nuclear configurations. The ordering of energy levels is studied as a function of the nature of the force with especial reference to its range, and the results are presented in the form of energy-level diagrams. The ordering of levels predicted to hold in parts I and II when forces are of short range is shown to occur with practical ranges; but for light nuclei in particular it is demonstrated that levels of very high angular momentum may sometimes occur near to the ground state. The results are found to be largely independent of the precise nature of the forces provided they are of reasonably short range and are attractive in the 1 S state of two like particles; for definiteness, however, the diagrams have been drawn for a Rosenfeld symmetrical exchange force of Gaussian radial dependence. The effect of using other types of central interaction is discussed qualitatively. The lowest excited states of even-even nuclei are seen to have a simple interpretation in jj -coupling.

DESCRIPTION OF E1 TRANSITION IN DOUBLY EVEN WELL-DEFORMED NUCLEI

1994 ◽  
Vol 03 (04) ◽  
pp. 1227-1250 ◽  
Author(s):  
V.G. SOLOVIEV ◽  
A.V. SUSHKOV ◽  
N. YU. SHIRIKOVA
Keyword(s):  
Experimental Data ◽  
Excited States ◽  
Ground State ◽  
Transition Probabilities ◽  
Wave Functions ◽  
Radial Dependence ◽  
Nuclear Model ◽  
Transition Rates ◽  
Deformed Nuclei ◽  
Dipole Interactions

One-phonon states with Kπ=0− and 1− are calculated within the RPA taking the isoscalar and isovector particle-hole and particle-particle octupole and isovector particlehole dipole interactions into account. General equations of the Quasiparticle-Phonon Nuclear Model are modified. The energies and wave functions of the nonrotational states below 2.3 MeV in 160Gd calculated within this model are in good overall agreement with experimental data. The E1 transition rates in several doubly even well-deformed nuclei are calculated. The influence of the radial dependence of the dipole and octupole interactions on E1 and E3 transition probabilities is investigated. It is shown that the fragmentation of one-phonon states below 2.3 MeV weakly affects the E1 transition rates from 1− states to the ground state. The fragmentation of one- and two-phonon states strongly affect B(E1) values of the transitions from 1− states with energy above 2.5 MeV to the ground states and between excited states. The results of calculating the E1 transition rates are compared with the relevant experimental data.

scholarly journals X-ray laser lines in nickel-like erbium

2016 ◽  
Vol 94 (8) ◽  
pp. 705-711
Author(s):  
Wessameldin S. Abdelaziz
Keyword(s):  
Ionization Potential ◽  
Excited States ◽  
Ground State ◽  
Energy Levels ◽  
Single Electron ◽  
Electron Densities ◽  
X Ray ◽  
Electron Excited States

Energy levels of 249 excited levels in nickel-like erbium are calculated using the 3s23p63d10 as a ground state and the single electron excited states from n = 3 to n = 4, 5 orbitals, calculations have been performed using FAC code (Gu. Astrophys. J. 582, 1241 (2003). doi:10.1086/344745 ). The populations are calculated over electron densities from 1020 to 1023 cm−3 and electron temperatures 1/2, 3/4 of the ionization potential of Ni-like Er. The gain coefficients of the transitions are calculated.

Evaluation of Luminescence Decay Measurements Probed on Pure and Doped Pt(IV) Hexahalogeno Complexes. II. Molecular Properties Obtained from Temperature Dependent Lifetime Curves

1997 ◽  
Vol 52 (5) ◽  
pp. 447-456
Author(s):  
Ingo Biertümpel ◽  
Hans-Herbert Schmidtke
Keyword(s):  
Excited States ◽  
Ground State ◽  
Energy Levels ◽  
Decay Rates ◽  
Rate Equations ◽  
Temperature Dependent ◽  
Lifetime Measurements ◽  
Thermally Activated ◽  
Ground State Energies ◽  
Higher Excited States

Abstract Lifetime measurements down to nearly liquid helium temperatures are used for determining energy levels and transition rates between excited levels and relaxations into the ground state. Energies are obtained from temperature dependent lifetimes by fitting experimental curves to model functions pertinent for thermally activated processes. Rates are calculated from solutions of rate equations. Similar parameters for pure and doped Pt(IV) hexahalogeno complexes indicate that excited levels largely belong to molecular units. Some of the rates between excited states are only somewhat larger than decay rates into the ground state, which is a consequence of the polyexponential decay measured also at low temperature (2 K). In the series of halogen complexes, the rates between spinorbit levels resulting from 3T1g increase from fluorine to bromine, although energy splittings become larger. Due to the decreasing population of higher excited states in this series, K^PtFö shows a tri-exponential, K2PtCl6 a bi-exponential and FoPtBr6 a mono-exponential decay. In the latter case the population density of higher excited states relaxes so fast that emission occurs primarily from the lowest excited Γ3(3T1g) level. Phase transitions and emission from chromophores on different sites can also be observed.

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.

Energies, radial expectation values, hyperfine structures of the ground state and highly excited states for C and O2+

2020 ◽  
Vol 34 (20) ◽  
pp. 2050197
Author(s):  
Chao Chen
Keyword(s):  
Excited States ◽  
Ground State ◽  
Magnetic Coupling ◽  
Wave Functions ◽  
Coupling Constants ◽  
Future Research ◽  
Expectation Values ◽  
Radiative Transitions ◽  
Experimental Values ◽  
Hyperfine Structures

The Rayleigh–Ritz variational method with multiconfiguration interaction wave functions is used to calculate energies, radiative transitions and radial expectation values of the [Formula: see text] [Formula: see text] ground state and the [Formula: see text], [Formula: see text], [Formula: see text] highly excited states of C and [Formula: see text]. Hyperfine structure parameters and magnetic coupling constants of these states are also calculated in this work. The present calculations agree well with theoretical and experimental values available in the literature. Other data not reported in the literature are expected to offer valuable benchmarks for future research.

An Exciton Approach to the Excited States of Two Electron Atoms. II. Determination of Spectroscopic Parameters, Polarizabilities and Dispersion Coefficients of H-, He, Li+, Be2+ and Ne8+

1985 ◽  
Vol 38 (1) ◽  
pp. 11
Author(s):  
PE Schipper ◽  
B Martire
Keyword(s):  
Excited States ◽  
Ground State ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Exciton Model ◽  
Interaction Coefficients ◽  
Isoelectronic Series ◽  
Helium Isoelectronic Series ◽  
Good Agreement

The exciton model developed in an earlier paper is applied quantitatively to a description of the excited states of representative members of the helium isoelectronic series; viz. H-, He, Li+,Be2+ and Ne8+. The energies of the eight lowest excited states are in good agreement with experiment, for a relatively small (1s-4p) hydrogenic basis; the ground state is obtained with slightly less precision. Response properties including oscillator strengths, polarizabilities and dispersion interaction coefficients are also calculated. The method appears to be quantitatively sound, and, above all, leads to particularly simple interpretations of the wave functions and the energies.

DENSITY FUNCTIONAL STUDY ON THE PROTON ASSISTED ISOMERIZATION OF 1H-IMIDAZO(4,5-b)PYRIDINE DERIVATIVES

2012 ◽  
Vol 11 (03) ◽  
pp. 651-661 ◽  
Author(s):  
R. P. DEKA ◽  
C. MEDHI
Keyword(s):  
Excited States ◽  
Ground State ◽  
Density Functional ◽  
Energy Levels ◽  
Relative Energy ◽  
Functional Study ◽  
Pyridine Derivatives ◽  
Energy Gaps ◽  
Free Molecules ◽  
Pass Through

The proton assisted isomerization reactions of 1H-imidazo(4,5-b)pyridine (IMP) derivatives have been studied by using B3LYP/6-31G + (d,p) calculations, and the transition states of the reactions are analyzed with B3LYP/6-31+G(d,p) opt=qst3 route. It has been found that the prototropic transformation could be the feasible pathway of isomerization, since the energy gaps between the various protonated isomers are found closer compared to free molecules. The conversion of IMP-a1 to IMP-b1 may pass through several protrotopic isomerization, since the activation energy as well as the relative energy levels of these isomers are not small compared to other pathways. However, the results suggest that some of the reactions may take place simultaneously through protrotopic transformation. The relative variations of energy gaps in the excited states are smaller than the ground states. The protrotropic transformation in the excited states may be more feasible than the ground state.

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