scholarly journals Nilsson orbitals in quantum superintegrable systems

2020 ◽  
Vol 19 ◽  
pp. 27
Author(s):  
V. Blatzios ◽  
D. Bonatsos
Keyword(s):  
Binding Energies ◽  
Wave Functions ◽  
Irreducible Representations ◽  
Deformed Nuclei ◽  
Creation And Annihilation Operators ◽  
Neutron Interaction ◽  
Superintegrable Systems ◽  
Double Differences ◽  
Valence Proton

Recent studies [1] of the valence proton-neutron interaction through certain double differences of binding energies suggest that Nilsson orbitals with ΔK[ΔNΔn_zΔΛ] = 0[110] are responsible for large overlaps of wave functions in heavy deformed nuclei. We show that pairs of orbitals of this kind belong to neighboring irreducible representations of appropriate deformed U(3) algebras [2], being interconnected by deformed creation and annihilation operators. These deformed U(3) algebras correspond to oscillators with rational ratios of frequencies, which are examples of quantum superintegrable systems [3].

Representations of sl(3, IR) with half-integral spin bands

1976 ◽  
Vol 54 (11) ◽  
pp. 1114-1123 ◽  
Author(s):  
G. Rosensteel ◽  
D. J. Rowe
Keyword(s):  
Rare Earth ◽  
Harmonic Analysis ◽  
Principal Series ◽  
Algebraic Model ◽  
Wave Functions ◽  
Irreducible Representations ◽  
Deformed Nuclei ◽  
Rare Earth Nuclei ◽  
Integral Spin ◽  
Collective States

A series of irreducible representations of sl(3,IR) is constructed with half-integral spin bands which parallels the principal series of SL(3,IR). While the principal series for SL(3,IR) was shown by Weaver and Biedenharn to be applicable to even–even deformed nuclei, the series constructed here applies to odd mass nuclei. It is shown how parity is included in an SL(3,IR) algebraic model. A second (cuspidal parabolic) series of representations of SL(3,IR) is constructed, which is required for the harmonic analysis of wave functions on SL(3,IR), a necessary preliminary to the application of the results of the SL(3,IR) model in a full microscopic treatment of deformed nuclei. It is shown that the cuspidal parabolic series has undesirable properties for the description of collective states in rare-earth nuclei.

The binding energies of atomic nuclei III. Nuclear forces and the ground state of oxygen 16

1959 ◽  
Vol 253 (1273) ◽  
pp. 186-198 ◽  
Keyword(s):  
Binding Energy ◽  
Electron Scattering ◽  
Ground State ◽  
Binding Energies ◽  
Wave Functions ◽  
Unperturbed System ◽  
Core Radius ◽  
Nuclear Forces ◽  
Potential Core ◽  
Atomic Nuclei

The r. m. s. radius and the binding energy of oxygen 16 are calculated for several different internueleon potentials. These potentials all fit the low-energy data for two nucleons, they have hard cores of differing radii, and they include the Gammel-Thaler potential (core radius 0·4 fermi). The calculated r. m. s. radii range from 1·5 f for a potential with core radius 0·2 f to 2·0 f for a core radius 0·6 f. The value obtained from electron scattering experiments is 2·65 f. The calculated binding energies range from 256 MeV for a core radius 0·2 f to 118 MeV for core 0·5 f. The experimental value of binding energy is 127·3 MeV. The 25% discrepancy in the calculated r. m. s. radius may be due to the limitations of harmonic oscillator wave functions used in the unperturbed system.

scholarly journals Universality of excited three-body bound states in one dimension

2021 ◽  
Author(s):  
Lucas Happ ◽  
Matthias Zimmermann ◽  
Maxim A Efremov
Keyword(s):  
Excited States ◽  
Bound States ◽  
Space Dimension ◽  
Binding Energies ◽  
Wave Functions ◽  
One Dimension ◽  
Strong Indication ◽  
Body System ◽  
Weakly Bound ◽  
Three Body

Abstract We study a heavy-heavy-light three-body system confined to one space dimension in the regime where an excited state in the heavy-light subsystems becomes weakly bound. The associated two-body system is characterized by (i) the structure of the weakly-bound excited heavy-light state and (ii) the presence of deeply-bound heavy-light states. The consequences of these aspects for the behavior of the three-body system are analyzed. We find a strong indication for universal behavior of both three-body binding energies and wave functions for different weakly-bound excited states in the heavy-light subsystems.

On particle-like representations of the complete homogeneous Lorentz group

1973 ◽  
Vol 74 (1) ◽  
pp. 149-160 ◽  
Author(s):  
J. A. de Wet
Keyword(s):  
Lorentz Group ◽  
Wave Functions ◽  
Unitary Groups ◽  
Irreducible Representations ◽  
Electron Wave ◽  
Precise Form ◽  
Homogeneous Lorentz Group ◽  
The Many ◽  
Matrix Contraction

In two previous papers (1, 2) representations of the unitary groups U4, U2 were found which described some of the properties of nucleons and electrons. In particular, the many electron wave functions were constructed from the irreducible representations of U2 restricted to the proper orthochronous Lorentz group Lp. In this paper the irreducible representations of U4 found in (1) will be shown to be also irreducible representations of the complete homogeneous Lorentz group L0 and the techniques of matrix contraction employed in (2) will be used to find the precise form of the matrices of the infinitesimal ring.

Low-energy pion photoproduction from p-shell nuclei

1990 ◽  
Vol 68 (11) ◽  
pp. 1270-1278 ◽  
Author(s):  
C. Bennhold ◽  
L. Tiator ◽  
L. E. Wright
Keyword(s):  
Form Factors ◽  
Pion Photoproduction ◽  
Binding Energies ◽  
Wave Functions ◽  
Low Energy ◽  
Delta Resonance ◽  
Transverse Electromagnetic ◽  
Coulomb Effects ◽  
Correction Terms ◽  
Space Approach

Low-energy pion photoproduction off 6Li, 10B, and 14N has been reinvestigated in a DWIA framework that includes a number of improvements neglected in previous analyses. The production operator is based on Feynman diagrams and includes correction terms of order p2/M2 and higher. An s-channel delta resonance term is included with both longitudinal and transverse electromagnetic couplings. Rather than using on harmonic oscillator for the nucleon orbitals we employ Woods–Saxon wave functions that have been adjusted to fit electron-scattering form factors and single-particle binding energies. Furthermore, we include the Coulomb potential without approximation in our momentum-space approach. Using more realistic wave functions and including corrections to the production amplitude that have been neglected before leads to considerable improvement in the case of 10B and 14N when compared with existing data. The Coulomb effects are shown to change the cross section by about 30% close to threshold but are negligible at higher energies.

THE EFFECT OF TEMPERATURE IN SPHERICAL AND DEFORMED NUCLEI IN THE DHB APPROXIMATION

2007 ◽  
Vol 16 (09) ◽  
pp. 3032-3036 ◽  
Author(s):  
R. LISBOA ◽  
M. MALHEIRO ◽  
B. V. CARLSON
Keyword(s):  
Mean Value ◽  
Binding Energies ◽  
Effect Of Temperature ◽  
Positive Contribution ◽  
Pairing Interaction ◽  
Deformed Nuclei ◽  
Charge Radii ◽  
Hot Nuclei ◽  
The Mean ◽  
Spherical Nuclei

We present a DHB approximation for excited hot nuclei and calculate the pairing gaps, binding energies, entropy and radii of several spherical and deformed nuclei. We show that the binding energy decreases as the temperature increases, as we would expect from the positive contribution of the thermal energy of the nucleons. The neutron, proton and charge radii of spherical nuclei increase as the temperature increases, while for the deformed 168 Er nucleus these quantities decrease up to T = 2 MeV , the temperature at which the deformation disappears, and increase above this temperature. The pairing interaction is taken into account self-consistently and studied as a function of the temperature: for the even Tin isotopes, the mean value of the neutron pairing gap is almost zero already at T = 1 MeV .

The binding energies of s-shell nuclei

1969 ◽  
Vol 47 (24) ◽  
pp. 2825-2834 ◽  
Author(s):  
J. Law ◽  
R. K. Bhaduri
Keyword(s):  
Binding Energy ◽  
Long Range ◽  
Hard Core ◽  
Nucleon Nucleon ◽  
Interference Term ◽  
Binding Energies ◽  
Wave Functions ◽  
A Value ◽  
Range Part ◽  
Central Forces

We have calculated the binding energies of 4He and 3H with soft- and hard-core nucleon–nucleon potentials. With central forces, using harmonic-oscillator wave functions, we find that accurate results can be obtained by taking only the long-range part of the potential and its second-order perturbative term. When tensor forces are present, the long-range interference term is also included in the calculation. In this case, the method is not accurate and underbinds these nuclei by about 1 MeV per particle. Ignoring Coulomb forces, our method yields a value of 18.5 MeV for the binding energy of 4He with the Hamada–Johnston potential.

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