Highest weight irreducible representations favored by nuclear forces within SU(3)-symmetric fermionic systems

The consequences of the attractive, short-range nucleon-nucleon (NN) interaction on the wave functions of nuclear models bearing the SU(3) symmetry are reviewed. The NN interaction favors the most symmetric spatial SU(3) irreducible representation (irrep), which corresponds to the maximal spatial overlap among the fermions. The consideration of the highest weight (hw) irreps in nuclei and in alkali metal clusters, leads to the prediction of a prolate to oblate shape transition beyond the mid–shell region. Subsequently, the consequences of the use of the hw irreps on the binding energies and two-neutron separation energies in the rare earth region are discussed within the proxy-SU(3) scheme, by considering a very simple Hamiltonian, containing only thethree dimensional (3D) isotropic harmonic oscillator (HO) term and the quadrupole-quadrupole interaction. This Hamiltonian conserves the SU(3) symmetry and treats the nucleus as a rigid rotator.

Download Full-text

Why nuclear forces favor the highest weight irreducible representations of the fermionic SU(3) symmetry

The European Physical Journal A ◽

10.1140/epja/s10050-021-00395-x ◽

2021 ◽

Vol 57 (3) ◽

Author(s):

Andriana Martinou ◽

Dennis Bonatsos ◽

K. E. Karakatsanis ◽

S. Sarantopoulou ◽

I. E. Assimakis ◽

...

Keyword(s):

Irreducible Representations ◽

Nuclear Forces ◽

Highest Weight

Download Full-text

Application of AdS/CFT in Nuclear Physics

Advances in High Energy Physics ◽

10.1155/2014/863268 ◽

2014 ◽

Vol 2014 ◽

pp. 1-19 ◽

Cited By ~ 4

Author(s):

M. R. Pahlavani ◽

R. Morad

Keyword(s):

Nuclear Physics ◽

Decay Constant ◽

Nucleon Nucleon ◽

Binding Energies ◽

Coupling Constants ◽

Light Nuclei ◽

Nuclear Models ◽

Holographic Qcd ◽

Gauge Gravity ◽

Gravity Duality

We review some recent progress in studying the nuclear physics especially nucleon-nucleon (NN) force within the gauge-gravity duality, in context of noncritical string theory. Our main focus is on the holographic QCD model based on the AdS6background. We explain the noncritical holography model and obtain the vector-meson spectrum and pion decay constant. Also, we study the NN interaction in this frame and calculate the nucleonmeson coupling constants. A further topic covered is a toy model for calculating the light nuclei potential. In particular, we calculate the light nuclei binding energies and also excited energies of some available excited states. We compare our results with the results of other nuclear models and also with the experimental data. Moreover, we describe some other issues which are studied using the gauge-gravity duality.

Download Full-text

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

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1959.0187 ◽

1959 ◽

Vol 253 (1273) ◽

pp. 186-198 ◽

Cited By ~ 12

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.

Download Full-text

The symmetric group and the method of diatomics in molecules: an application to small lithium clusters

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1973.0048 ◽

1973 ◽

Vol 333 (1592) ◽

pp. 69-87 ◽

Cited By ~ 63

Keyword(s):

Alkali Metal ◽

Symmetric Group ◽

Metal Clusters ◽

Basis Functions ◽

Basis Set ◽

Irreducible Representations ◽

Secular Equations ◽

Alkali Metal Clusters ◽

Lithium Clusters

A new ‘most economical’ algorithm for the construction of diatomics in molecules secular equations is described. The method does not require the basis functions to be written down explicitly, since overlap may be factored out of the equations entirely. The theory is presented in detail for the particular case of homogeneous alkali metal clusters. A knowledge of the irreducible representations of the symmetric group for the Jahn-Serber basis set is necessary. The irreducible representations are derived by a genealogical procedure. Some preliminary calculations are presented for the molecules Li 3 through Li 6 , Li + 3 and Li + 4 . The lithium clusters are found to be stable with respect to all possible dissociations, and the i.ps of Li 3 and Li 4 are in agreement with the trends for the species Na 3 , Na 4 , K 3 , K 4 , etc., whose i.ps have been measured experimentally.

Download Full-text

Wigner SU(4) symmetry, clustering, and the spectrum of $$^{12}$$C

The European Physical Journal A ◽

10.1140/epja/s10050-021-00586-6 ◽

2021 ◽

Vol 57 (9) ◽

Author(s):

Shihang Shen ◽

Timo A. Lähde ◽

Dean Lee ◽

Ulf-G. Meißner

Keyword(s):

Excited States ◽

Ground State ◽

Nucleon Nucleon ◽

Irreducible Representations ◽

Spin Orbit ◽

Hoyle State ◽

Nucleon Interaction ◽

Model Calculations ◽

Nucleon Nucleon Interaction ◽

Spin Orbit Interactions

AbstractWe present lattice calculations of the low-lying spectrum of $$^{12}$$ 12 C using a simple nucleon–nucleon interaction that is independent of spin and isospin and therefore invariant under Wigner’s SU(4) symmetry. We find strong signals for all excited states up to $$\sim 15$$ ∼ 15 MeV above the ground state, and explore the structure of each state using a large variety of $$\alpha $$ α cluster and harmonic oscillator trial states, projected onto given irreducible representations of the cubic group. We are able to verify earlier findings for the $$\alpha $$ α clustering in the Hoyle state and the second $$2^+$$ 2 + state of $$^{12}$$ 12 C. The success of these calculations to describe the full low-lying energy spectrum using spin-independent interactions suggest that either the spin-orbit interactions are somewhat weak in the $$^{12}$$ 12 C system, or the effects of $$\alpha $$ α clustering are diminishing their influence. This is in agreement with previous findings from ab initio shell model calculations.

Download Full-text

NUCLEAR FORCES AND NUCLEAR MODELS

Modern Atomic and Nuclear Physics ◽

10.1142/9789814277167_0012 ◽

2010 ◽

pp. 488-559

Keyword(s):

Nuclear Forces ◽

Nuclear Models

Download Full-text

Nuclear Forces and Nuclear Models

Modern Atomic and Nuclear Physics ◽

10.1142/9789814307697_0011 ◽

2010 ◽

pp. 71-75

Keyword(s):

Nuclear Forces ◽

Nuclear Models

Download Full-text

Note on Weight Spaces of Irreducible Linear Representations

Canadian Mathematical Bulletin ◽

10.4153/cmb-1968-045-2 ◽

1968 ◽

Vol 11 (3) ◽

pp. 399-403 ◽

Cited By ~ 2

Author(s):

F. W. Lemire

Keyword(s):

Irreducible Representation ◽

Weight Function ◽

Wide Class ◽

Irreducible Representations ◽

Weight Space ◽

Closed Field ◽

One Dimensional ◽

Highest Weight ◽

Linear Representations ◽

Finite Dimensional

Let L denote a finite dimensional, simple Lie algebra over an algebraically closed field F of characteristic zero. It is well known that every weight space of an irreducible representation (ρ, V) admitting a highest weight function is finite dimensional. In a previous paper [2], we have established the existence of a wide class of irreducible representations which admit a one-dimensional weight space but no highest weight function. In this paper we show that the weight spaces of all such representations are finite dimensional.

Download Full-text