scholarly journals U(6) dynamical and quasi-dynamical symmetry in strongly deformed heavy nuclei

2018 ◽  
Vol 194 ◽  
pp. 05002 ◽  
Author(s):  
H.G. Ganev
Keyword(s):  
State Space ◽  
Effective Charge ◽  
Good Description ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Microscopic Structure ◽  
Heavy Nuclei ◽  
Ground Band ◽  
Model Hamiltonian ◽  
Collective States

The low-lying collective states of the ground, β and γ bands in154Sm and238U are investigated within the framework of the microscopic proton-neutron symplectic model (PNSM). For this purpose, the model Hamiltonian is diagonalized in a U(6)-coupled basis, restricted to the symplectic state space spanned by the fully symmetric U(6) vectors. A good description of the energy levels of the three bands under consideration, as well as the intraband B(E2) transition strengths between the states of the ground band is obtained for the two nuclei without the use of an effective charge. The calculations show that when the collective quadrupole dynamics is covered already by the symplectic bandhead structure, as in the case of154Sm, the results show the presence of a very good U(6) dynamical symmetry. In the case of238U, when we have an observed enhancement of the intraband B(E2) transition strengths, then the results show small admixtures from the higher major shells and a highly coherent mixing of different irreps which is manifested by the presence of a good U(6) quasi-dynamical symmetry in the microscopic structure of the collective states under consideration.

Energy Levels and Electromagnetic Transition of 90-94mo Nuclei Using Ibm-1

2020 ◽  
pp. 149-152
Keyword(s):  
Experimental Data ◽  
Transition Probability ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Interacting Boson Model ◽  
Excitation Energies ◽  
Electromagnetic Transition ◽  
Boson Model ◽  
Energy States ◽  
Good Agreement

The energy states for the J , b , ɤ bands and electromagnetic transitions B (E2) values for even – even molybdenum 90 – 94 Mo nuclei are calculated in the present work of "the interacting boson model (IBM-1)" . The parameters of the equation of IBM-1 Hamiltonian are determined which yield the best excellent suit the experimental energy states . The positive parity of energy states are obtained by using IBS1. for program for even 90 – 94 Mo isotopes with bosons number 5 , 4 and 5 respectively. The" reduced transition probability B(E2)" of these neuclei are calculated and compared with the experimental data . The ratio of the excitation energies of the 41+ to 21+ states ( R4/2) are also calculated . The calculated and experimental (R4/2) values showed that the 90 – 94 Mo nuclei have the vibrational dynamical symmetry U(5). Good agreement was found from comparison between the calculated energy states and electric quadruple probabilities B(E2) transition of the 90–94Mo isotopes with the experimental data .

scholarly journals Chronicle of the discovery of the back-bending phenomenon in atomic nuclei: a personal recollection 50 years on

2021 ◽  
Vol 46 (1) ◽  
Author(s):  
Hans Ryde
Keyword(s):  
Nuclear Structure ◽  
Ground State ◽  
Energy Levels ◽  
Historical Context ◽  
Rotational Frequency ◽  
Heavy Nuclei ◽  
Atomic Nuclei ◽  
Key Points ◽  
The Moment ◽  
The Right

AbstractA chronicle describing the historical context and the development of ideas and experiments leading to the discovery of the back-bending phenomenon in rapidly rotating atomic nuclei some 50 years ago is presented. The moment of inertia of some atomic nuclei increases anomalously at a certain rotational frequency, revealing important clues to our understanding of nuclear structure. I highlight the decisive interactions and contacts between experimentalists and theorists, which created the right environment, allowing for the revelation of an undetected phenomenon in Nature. Finally, I reflect on the key points allowing for the discovery and particularly point to the importance of systematic surveys, which in this case investigated the energy levels in heavy nuclei of a large sample of elements, as well as to the accuracy of the measurements of the ground state levels made at the time.

Dynamical symmetry in heavy nuclei and complementarity of bosons and fermions

1994 ◽  
Vol 570 (1-2) ◽  
pp. 77-85 ◽  
Author(s):  
Da Hsuan Feng ◽  
Pan Xing-Wang
Keyword(s):  
Dynamical Symmetry ◽  
Heavy Nuclei

scholarly journals q-SYMMETRIES IN DNLS-AL CHAINS AND EXACT SOLUTIONS OF QUANTUM DIMERS

1999 ◽  
Vol 13 (26) ◽  
pp. 3087-3106
Author(s):  
DEMOSTHENES ELLINAS ◽  
PANAGIOTIS MANIADIS
Keyword(s):  
Recurrence Relations ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Spin Model ◽  
Rate Of Change ◽  
Nonlinearity Parameter ◽  
Hamilton Operator ◽  
Central Elements ◽  
Lowering Operators ◽  
Dynamical Algebra

Dynamical symmetries of Hamiltonians quantized models of discrete nonlinear Schrödinger chain (DNLS) and of Ablowitz–Ladik chain (AL) are studied. It is shown that for n-sites the dynamical algebra of DNLS Hamilton operator is given by the su(n) algebra, while the respective symmetry for the AL case is the quantum algebra suq(n). The q-deformation of the dynamical symmetry in the AL model is due to the non-canonical oscillator-like structure of the raising and lowering operators at each site. Invariants of motions are found in terms of Casimir central elements of su(n) and suq(n) algebra generators, for the DNLS and QAL cases respectively. Utilizing the representation theory of the symmetry algebras we specialize to the n=2 quantum dimer case and formulate the eigenvalue problem of each dimer as a nonlinear (q)-spin model. Analytic investigations of the ensuing three-term nonlinear recurrence relations are carried out and the respective orthonormal and complete eigenvector bases are determined. The quantum manifestation of the classical self-trapping in the QDNLS-dimer and its absence in the QAL-dimer, is analysed by studying the asymptotic attraction and repulsion respectively, of the energy levels versus the strength of nonlinearity. Our treatment predicts for the QDNLS-dimer, a phase-transition like behaviour in the rate of change of the logarithm of eigenenergy differences, for values of the nonlinearity parameter near the classical bifurcation point.

ADIABATIC TRANSPORT PROPERTIES AND BERRY’S PHASE IN HEISENBERG-ISING RING

1991 ◽  
Vol 05 (03) ◽  
pp. 497-507 ◽  
Author(s):  
V.E. KOREPIN ◽  
A.C.T. WU
Keyword(s):  
Boundary Conditions ◽  
Transport Properties ◽  
Effective Charge ◽  
Spin Chain ◽  
Energy Levels ◽  
Adiabatic Process ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain

In a recent paper, B. Sutherland and B.S. Shastry have constructed an adiabatic process for the Heisenberg spin chain (spin ½) with respect to a change of boundary conditions. In this paper we calculate Berry’s phase for this process. We also evaluate the dependence of energy levels on boundary conditions which permits us to calculate the effective charge-carrying mass.

NUCLEAR RADIATION WIDTHS

1957 ◽  
Vol 35 (5) ◽  
pp. 666-671 ◽  
Author(s):  
A. G. W. Cameron
Keyword(s):  
Nuclear Energy ◽  
Energy Levels ◽  
Nuclear Radiation ◽  
Heavy Nuclei ◽  
Level Spacing ◽  
Excitation Energies ◽  
Average Deviation ◽  
Radiative Transitions ◽  
Logarithmic Average ◽  
Large Level

The total radiation widths of nuclear energy levels have been computed using the new level spacing formula of T. D. Newton. The only adjustable constant in this calculation is a normalizing factor, which was determined by comparison with observed radiation widths. The logarithmic average deviation of the observed radiation widths from the calculated values is then equal to a factor 1.37. Radiation widths computed for a series of nuclei close to the valley of beta stability at excitation energies corresponding to the energy release in neutron capture are presented. It is found that in heavy nuclei with large level spacings the radiation widths of electric dipole transitions to the ground state can exceed that computed from the above considerations. This accounts for the unusual nature of the radiative transitions in lead.

Tight Binding Modelling of Energy Band Structure in Nitride Heterostructures

2008 ◽  
Vol 8 (2) ◽  
pp. 540-548 ◽  
Author(s):  
Özden Akıncı ◽  
H. Hakan Gürel ◽  
Hilmi Ünlü
Keyword(s):  
Electronic Structure ◽  
Band Structure ◽  
Valence Band ◽  
Nearest Neighbor ◽  
Good Description ◽  
Energy Levels ◽  
Tight Binding ◽  
Binding Theory ◽  
Orbit Splitting ◽  
Atomic Energy Levels

We studied the electronic structure of group III–V nitride ternary/binary heterostructures by using a semi-empirical sp3s* tight binding theory, parametrized to provide accurate description of both valence and conductions bands. It is shown that the sp3s* basis, along with the second nearest neighbor (2NN) interactions, spin-orbit splitting of cation and anion atoms, and nonlinear composition variations of atomic energy levels and bond length of ternary, is sufficient to describe the electronic structure of III–V ternary/binary nitride heterostructures. Comparison with experiment shows that tight binding theory provides good description of band structure of III–V nitride semiconductors. The effect of interface strain on valence band offsets in the conventional Al1−xGaxN/GaN and In1−xGaxN/GaN and dilute GaAs1−xNx/GaAs nitride heterostructures is found to be linear function of composition for the entire composition range (0 ≤ x ≤ 1) because of smaller valence band deformations.

scholarly journals An analytical solution of Bohr's collective hamiltonian

1983 ◽  
Vol 6 (4) ◽  
pp. 803-809
Author(s):  
M. K. El-Adawi ◽  
H. A. Ismail ◽  
S. A. Shalaby ◽  
E. M. Sayed
Keyword(s):  
Analytical Solution ◽  
Energy Levels ◽  
Analytic Form ◽  
Collective Hamiltonian ◽  
Simple Analytic Form ◽  
Collective States

The collective states of126Xe,128Xe,130Xe, and130Be,52<z,N≤116are studied using Bohr's Collective Hamiltonian and a simple analytic form for the potential. The energy levels are calculated for this model and the results are compared with previously published experimental and calculated values.

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.

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