Matrix elements in the SU(1,1) 
					
	    
	    
	   
               SO(6) limit of the proton-neutron symplectic model

Ganev, H. G.

doi:10.1088/1674-1137/ac1c67

Cited by 9 publications

(10 citation statements)

References 55 publications

(122 reference statements)

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“…2, the theoretical predictions for the intraband yrast transition strengths are compared with the experimental results [12] and some other nuclear models, whose data are extracted from Refs. [12,25,39]. We observe that the almost linear behavior, characteristic of irrotational-flow quadrupole dynamics of BM type, is well reproduced by the present approach up to , with the exception of only the transition strength being slighly underestimated.…”

Section: Sl(6 R)supporting

confidence: 66%

“…Similar parametrization is used in Ref. [39], where the five-dimensional collective Hamiltonian, based on the relativistic covariant density functional theory, is applied to the yrast band tidal-wave collective mode in Pd.…”

Section: Applicationmentioning

confidence: 99%

“…Practically, to a given K band in the Elliott basis corresponds a band in and theoretical intraband values in Weisskopf units between the states of the ground band in Pd. Theoretical predictions of the five-dimensional collective Hamiltonian based on the relativistic self-consistent mean field without (5DCH) and with (5DCH*) spin-dependent moment of inertia [39], the interacting boson model (IBM) [25], the general collective model (GCM) [25], and the cranking + shell-correction tilted-axis cranking (WS-SCTAC) [12] semiclassical calculations are provided as well. No effective charge is used in the cases of PNSM, WS-SCTAC, 5DCH, and 5DCH*.…”

Section: Su(3)mentioning

confidence: 99%

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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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Section: Sl(6 R)supporting

confidence: 66%

Section: Applicationmentioning

confidence: 99%

Section: Su(3)mentioning

confidence: 99%

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

Ganev

2024

Chinese Phys. C

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“…It is convenient, however, to keep all six collective variables or those equivalent to them and use (29). Including the radial degrees of freedom, the microscopic analog of the generalized quadrupolemonopole BM Hamiltonian can be written in the form…”

Section: Formentioning

confidence: 99%

“…This expression is the same as Eq. ( 25); therefore, using (19), we can obtain the final result (29) with the useful identifications for the angular momentum operators in the intrinsic frame and irrotational-flow moments of inertia .…”

Section: Gcm(3)mentioning

confidence: 99%

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

Ganev

2023

Chinese Phys. C

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Recently proposed microscopic shell-model version of theBohr-Mottelson (BM) collective model is considered in more detail incoordinate representation. The latter possesses a clear andtransparent physical meaning, which allows to reveal some featuresof the new version of the collective model missed in the previousformulation. The relationships to the original BM model areconsidered, as well as between the different limiting submodels ofthe microscopic version of the BM model, which closely resemble therelationships of the original Wilets-Jean and rotor models. Thekinematically correct many-particle wave functions of themicroscopic version of the BM model, conserving the experimentallyobserved integrals of motion, are presented as consisting ofcollective irrotational-flow and intrinsic components $-$ in accordwith the original BM unified model. The general BM Hamiltonian isobtained as a contraction limit of the microscopic many-particlenuclear Hamiltonian, or, alternatively, by restricting the latter tothe scalar $O(m)$ irreducible collective space.

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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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Matrix elements in the SU(1,1) SO(6) limit of the proton-neutron symplectic model

Cited by 9 publications

References 55 publications

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

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

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

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

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Matrix elements in the SU(1,1) SO(6) limit of the proton-neutron symplectic model

Cited by 9 publications

References 55 publications

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

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

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

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

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

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