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تسجيل مستخدم جديدHighest weight irreducible representations favored by nuclear forces within SU(3)-symmetric fermionic systems
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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 the three 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.
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The consequences of the attractive, short-range nucleon-nucleon (NN) interaction on the wave functions of the Elliott SU(3) and the proxy-SU(3) symmetry are discussed. The NN interaction favors the most symmetric spatial SU(3) irreducible representat
ion, which corresponds to the maximal spatial overlap among the fermions. The percentage of the symmetric components out of the total in an SU(3) wave function is introduced, through which it is found, that no SU(3) irrep is more symmetric than the highest weight irrep for a certain number of valence particles in a three dimensional, isotropic, harmonic oscillator shell. The consideration of the highest weight irreps in nuclei and in alkali metal clusters, leads to the prediction of a prolate to oblate shape transition beyond the mid-shell region.
The SU(3) irreducible representations (irreps) are characterised by the (lambda, mu) Elliott quantum numbers, which are necessary for the extraction of the nuclear deformation, the energy spectrum and the transition probabilities. These irreps can be
calculated through a code which requires high computational power. In the following text a hand-writing method is presented for the calculation of the highest weight (h.w.) irreps, using two different sets of magic numbers, namely proxy-SU(3) and three-dimensional isotropic harmonic oscillator.
The inclusion of the three-nucleon forces (3NFs) in textit{ab initio} many-body approaches is a formidable task, due to the computational load implied by the treatment of their matrix elements. For this reason, practical applications have mostly been
limited to contributions where 3NFs enter as effective two-nucleon interactions. In this contribution, we derive the algebraic diagrammatic construction (ADC) working equations for a specific Feynman diagram of the self-energy that contains a fully irreducible three-nucleon force. This diagram is expected to be the most important among those previously neglected, because it connects dominant excited intermediate state configurations.
Violent nuclear collisions are open systems which require a non-equilibrium description when the process should be followed from the first instants. The heated system produced in the collision, can no more be treated within an independent-particle pi
cture and additional correlations should be taken into account: they rely to in-medium dissipation and phase-space fluctuations. Their interplay with the one-body collective behaviour activates the transport dynamics: large-amplitude fluctuations and bifurcations in a variety of mechanisms appear, from fusion to neck formation till eventually freezing out the system into several intermediate-mass clusters. Starting from fundamental concepts tested on nuclear matter, a microscopic description is built up to address violent processes occurring in heavy-ion collisions at Fermi energies and in spallation reactions, and it is applied to experimental observables.
The systematics of experimental energy differences between the levels of the ground state band and the gamma-1 band in even-even nuclei are studied as a function of the angular momentum L, demonstrating a decrease of the energy differences with incre
asing L, in contrast to what is seen in vibrational, gamma-unstable, and triaxial nuclei. After a short review of the relevant predictions of several simple collective models, it is shown that this decrease is caused in the framework of the proxy-SU(3) scheme by the same three-body and/or four body operators which break the degeneracy between the ground state band and the gamma-1 band, predicting in parallel the correct form of odd-even staggering within the gamma-1 bands.
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