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Intrinsic and collective structure in the interacting boson model

Nuclear Physics

Annals of PhysicsSep 1, 19870 citations

Intrinsic and collective structure in the interacting boson model

A. Leviatan

Annals of PhysicsNov 1, 198762 citations

Relationship between the Bohr Collective Hamiltonian and the Interacting-Boson Model

Joseph N. Ginocchio, Michael W. Kirson

WORLD SCIENTIFIC eBooksDec 1, 19880 citations

Microscopic foundation of the interacting boson model

Cheng-Li Wu, D.H. Feng, Jin-Quan Chen +1 more

An effective boson Hamiltonian is derived from the original Hamiltonian of a many-fermion system. The results show that when the intrinsic motion of bosons is collective and the excitation energies of the system are small, the effective boson-boson interaction can be reduced to a two-body interaction while for odd systems or systems with uncorrelated fermions, there is an additional two-body boson-fermion interaction. Both these interactions can be calculated from the original fermion-fermion ones. Thus, the microscopic foundation of the interacting boson model is established without recourse to mapping procedures.NUCLEAR STRUCTURE Interacting boson model, boson fermion hybrid representation, microscopic foundation.An effective boson Hamiltonian is derived from the original Hamiltonian of a many-fermion system. The results show that when the intrinsic motion of bosons is collective and the excitation energies of the system are small, the effective boson-boson interaction can be reduced to a two-body interaction while for odd systems or systems with uncorrelated fermions, there is an additional two-body boson-fermion interaction. Both these interactions can be calculated from the original fermion-fermion ones. Thus, the microscopic foundation of the interacting boson model is established without recourse to mapping procedures.NUCLEAR STRUCTURE Interacting boson model, boson fermion hybrid representation, microscopic foundation.

Physical Review CJul 1, 19822 citations

An intrinsic-state formalism for the Interacting Boson-Fermion Model with configuration mixing

E. Maya-Barbecho, J. E. García-Ramos

In this letter, we present the intrinsic state formalism of the Interacting Boson-Fermion Model incorporating both 0p-0h and 2p-2h (regular and intruder) configurations. The framework allows to deal with the unpaired fermion in either a single-j or multi-j orbital and is applicable to both axial and triaxial nuclear shapes. The formalism is applied to a schematic transitional region where regular and intruder configurations coexist and cross. We show that the boson-fermion part of the Hamiltonian can either enhance or suppress the emergence of a type II Quantum Phase Transition.In this letter, we present the intrinsic state formalism of the Interacting Boson-Fermion Model incorporating both 0p-0h and 2p-2h (regular and intruder) configurations. The framework allows to deal with the unpaired fermion in either a single-j or multi-j orbital and is applicable to both axial and triaxial nuclear shapes. The formalism is applied to a schematic transitional region where regular and intruder configurations coexist and cross. We show that the boson-fermion part of the Hamiltonian can either enhance or suppress the emergence of a type II Quantum Phase Transition.

arXiv:2507.05650Physics Letters BJul 15, 20255 citations

Magnetic and superconducting competition within the Hubbard dimer. Exact solution

M. Matlak, T. Słomska, B. Grabiec

Abstract We express the Hubbard dimer Hamiltonian $ H_{d} = {\textstyle \sum \nolimits ^{16} _{\alpha = 1} }E_{\alpha}\vert E_{\alpha}\rangle \langle E_{\alpha}\vert $ in the second quantization with theuse of the Hubbard and spin operators. We consider the case of positive and negative U. We decompose the resulting Hamiltonian into several parts collecting all the terms belonging to the same energy level. Such a decomposition visualizes explicitely all intrinsic interactions competing together and deeply hidden in the original form of the dimer Hamiltonian. Among them are competitive ferromagnetic and antiferromagnetic interactions. There are also hopping terms present which describe Cooper pairs hopping between sites 1 and 2 with positive and negative coupling constants (similar as in Kulik–Pedan, Penson–Kolb models). We show that the competition between intrinsic interactions strongly depends on the model parametrs and the averaged occupation number of electrons n ∈ [0, 4] resulting in different regimes of the model (as e.g. t–J model regime, etc.). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)Abstract We express the Hubbard dimer Hamiltonian $ H_{d} = {\textstyle \sum \nolimits ^{16} _{\alpha = 1} }E_{\alpha}\vert E_{\alpha}\rangle \langle E_{\alpha}\vert $ in the second quantization with theuse of the Hubbard and spin operators. We consider the case of positive and negative U. We decompose the resulting Hamiltonian into several parts collecting all the terms belonging to the same energy level. Such a decomposition visualizes explicitely all intrinsic interactions competing together and deeply hidden in the original form of the dimer Hamiltonian. Among them are competitive ferromagnetic and antiferromagnetic interactions. There are also hopping terms present which describe Cooper pairs hopping between sites 1 and 2 with positive and negative coupling constants (similar as in Kulik–Pedan, Penson–Kolb models). We show that the competition between intrinsic interactions strongly depends on the model parametrs and the averaged occupation number of electrons n ∈ [0, 4] resulting in different regimes of the model (as e.g. t–J model regime, etc.). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

physica status solidi (b)Jan 17, 20051 citation

Resolution of Any Interacting-Boson-Model Hamiltonian into Intrinsic and Collective Parts

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