On the microscopic shell-model version of the Bohr-Mottelson collective model

Ganev, H. G.

doi:10.1088/1674-1137/ace67f

Cited by 3 publications

(10 citation statements)

References 42 publications

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“…Recently, a microscopic shell-model version of the BM model was formulated [40,41] within the framework of the microscopic proton-neutron symplectic model (PNSM) of nuclear collective motion with dynamical algebra. This version provides an interesting and relevant shell-model symplectic-based framework to explore the nature of the observed nuclear collective dynamics.…”

Section: S P(12 R)mentioning

confidence: 99%

“…The many-particle states in the microscopic shellmodel version of the BM model are classified by the following dynamical symmetry chain [40,41]: 1) 6) SO (2) where below the different subgroups are given the quantum numbers that characterize their irreducible representations. The quantum numbers and p define the oscillator shell structure.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…Thus, the standard harmonic oscillator basis states with even (odd) values ( ) are related [55] to the basis states through the expression with . The quantum numbers define the deformation of nuclear system and are related to the and quantum numbers υ and ν by the following expression [40]:…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…q denotes a multiplicity label in the reduction and its values, defining different quasibands, are given by . Based on chain (5), the monopole-quadrupole nuclear dynamics splits into radial and orbital motions, and the wave functions of the microscopic SM version of the BM model are as follows [40]:…”

Section: Theoretical Frameworkmentioning

confidence: 99%

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Proton-neutron symplectic model description of ¹⁰⁶Cd

Ganev

2024

Chinese Phys. C

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Microscopic shell-model description of the low-lying collectivestates in the weakly deformed nucleus $^{106}$Cd within the recentlyproposed microscopic version of the Bohr-Mottelson model is given. Agood description of the excitation energies of the lowest ground,$\gamma$, and $\beta$ quasibands is obtainedwithout the involvement of adjustable kinetic energy term. The$\gamma$ degrees of freedom are shown to play a crucial role in thedescription of spectroscopy of this nucleus. A modified $SU(3)$preserving high-order interaction is used to produce a$\gamma$-unstable type of the odd-even staggering, observedexperimentally between the states of the quasi-$\gamma$ band. Thepresent approach allows to describe the observedintraband and interband quadrupole collectivity. The resultsobtained in present work suggest a different interpretation of thefundamental question concerning the nature of low-energy vibrationsand the emergence of deformation and collectivity in the weakly deformed atomic nuclei.

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Section: S P(12 R)mentioning

confidence: 99%

Section: Theoretical Frameworkmentioning

confidence: 99%

Section: Theoretical Frameworkmentioning

confidence: 99%

Section: Theoretical Frameworkmentioning

confidence: 99%

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Proton-neutron symplectic model description of ¹⁰⁶Cd

Ganev

2024

Chinese Phys. C

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“…Recently, the BM model was embedded [16,17] into the two-component shell-model theory within the framework of the PNSM. It was demonstrated that a microscopic shellmodel version of the BM model is defined by one of dynamical symmetry chains of the PNSM.…”

Section: Introductionmentioning

confidence: 99%

Shell-model representations of the microscopic version of the Bohr–Mottelson collective model

Ganev

2024

Commun. Theor. Phys.

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The structure of the irreducible collective spaces of the group$Sp(12,R)$, which many-particle nuclear states are classifiedaccording to the chain $Sp(12,R) \supset U(6) \supset SO(6) \supsetSU_{pn}(3) \otimes SO(2) \supset SO(3)$ of the proton-neutronsymplectic model (PNSM), is considered in detail. This chain of thePNSM was recently shown to correspond to a microscopic shell-model version ofthe Bohr-Mottelson collective model. The construction of therelevant shell-model representations of the $Sp(12,R)$ group alongthis chain is considered for three nuclei with varying collectiveproperties and from different mass regions. It is shown that the$SU_{pn}(3)$ basis states of the $Sp(12,R)$ representationsbelonging to $SO(6)$ irreps with seniority$\upsilon \geq \upsilon_{0}$, with $v_{0}$ denoting the maximalseniority $SO(6)$ irrep contained in the $Sp(12,R)$ bandhead, arealways Pauli allowed, but organized in a different way intodifferent $SO(6)$ shells. This is in contrast to the case of fillingthe levels of the standard three-dimensional harmonic oscillator andusing the plethysm operation. Although the $SU_{pn}(3)$ multipletswith $\upsilon < \upsilon_{0}$ are not all Pauli forbidden, it issafe to discard them. The results obtained in the present work areimportant for the practical application of the microscopic versionof the Bohr-Mottelson collective model.

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Microscopic shell-model description of irrotational-flow dynamics in ¹⁰²Pd

Ganev

2024

Chinese Phys. C

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The structure of the low-lying collective excitations in $^{102}$Pdis studied within the recently proposed microscopic shell-modelversion of the Bohr-Mottelson (BM) collective model. A gooddescription of the excitation energies of the lowest ground,$\gamma$, and $\beta$ bands, as well as the staggering functionbetween the collective states of the $\gamma$ band and some otherenergy-dependent quantities, is obtained. The low-energy intrabandand interband quadrupole dynamics is reasonably well describedwithin the present proton-neutron sympletic based shell-modelapproach without the use of an effective charge and compared withthe predictions of some other nuclear stricture models. The obtainedresults of the present work shed light on the question of theexistence of irrotational-flow type quadrupole dynamics, which lieson the ground of the original BM model of quantized vibrations andsurface-wave rotations in atomic nuclei.

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On the microscopic shell-model version of the Bohr-Mottelson collective model

Cited by 3 publications

References 42 publications

Proton-neutron symplectic model description of ¹⁰⁶Cd

Proton-neutron symplectic model description of ¹⁰⁶Cd

Shell-model representations of the microscopic version of the Bohr–Mottelson collective model

Microscopic shell-model description of irrotational-flow dynamics in ¹⁰²Pd

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On the microscopic shell-model version of the Bohr-Mottelson collective model

Cited by 3 publications

References 42 publications

Proton-neutron symplectic model description of 106Cd

Proton-neutron symplectic model description of 106Cd

Shell-model representations of the microscopic version of the Bohr–Mottelson collective model

Microscopic shell-model description of irrotational-flow dynamics in 102Pd

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Proton-neutron symplectic model description of ¹⁰⁶Cd

Proton-neutron symplectic model description of ¹⁰⁶Cd

Microscopic shell-model description of irrotational-flow dynamics in ¹⁰²Pd