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H. G. Ganev

Publications and source records attributed to H. G. Ganev.

At least 19 recordsLinked to original sources
arXiv2025

Extended multiconfigurational dynamical symmetry

An extended multiconfigurational dynamical symmetry (EMUSY) within the symplectic symmetry approach to clustering (SSAC) is proposed for the general case of multicluster nuclear systems. A characteristic property of the EMUSY is that it includes more general symplectic, i.e. number non-preserving, transformations which contain the standard number-preserving (unitary) multiconfigurational dynamical symmetry transformations as a special limiting case. In this way the EMUSY becomes able to connect various possible clusterizations of different multicluster type, as well as various many-particle configurations between the shell, collective and cluster models of nuclear structure. The theory is briefly illustrated using the nuclear system $^{24}$Mg as an example.

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arXiv2024

Symplectic symmetry approach to clustering in atomic nuclei: The case of $^{24}$Mg

Symplectic symmetry approach to clustering (SSAC) in atomic nuclei, recently proposed, is modified and further developed in more detail. It is firstly applied to the light two-cluster $^{20}$Ne + $α$ system of $^{24}$Mg, the latter exhibiting well developed low-energy $K^π = 0^{+}_{1}$, $K^π = 2^{+}_{1}$ and $K^π = 0^{-}_{1}$ rotational bands in its spectrum. A simple algebraic Hamiltonian, consisting of dynamical symmetry, residual and vertical mixing parts is used to describe these three lowest rotational bands of positive and negative parity in $^{24}$Mg. A good description of the excitation energies is obtain by considering only the $SU(3)$ cluster states restricted to the stretched many-particle Hilbert subspace, built on the leading Pauli allowed $SU(3)$ multiplet for the positive- and negative-parity states, respectively. The coupling to the higher cluster-model configurations allows to describe the known low-lying experimentally observed $B(E2)$ transition probabilities within and between the cluster states of the three bands under consideration without the use of an effective charge.

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arXiv2024

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

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 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 are always Pauli allowed for $\upsilon \geq \upsilon_{0}$, 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, as it was actually done in the practical applications.

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arXiv2022

Symplectic symmetry and clustering in atomic nuclei

A new symplectic-based shell-model approach to clustering in atomic nuclei is proposed by considering the simple system $^{20}$Ne. Its relation to the collective excitations of this system is mentioned as well. The construction of the Pauli allowed Hilbert space of the cluster states with maximal permutational symmetry is given for the $^{16}$O+$^{4}$He $\rightarrow$ $^{20}$Ne channel in the case of one-component many-particle nuclear system. The equivalence of the obtained cluster model space to that of the semi-microscopic algebraic cluster model is demonstrated.

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arXiv2021

Microscopic version of the Bohr-Mottelson model and its application

The shell-model coupling scheme of the proton-neutron symplectic model (PNSM), defined by the following dynamical symmetry chain $Sp(12,R) \supset SU(1,1) \otimes SO(6) \supset U(1) \otimes SU_{pn}(3) \otimes SO(2) \supset SO(3)$, is considered. It is shown that it corresponds to a microscopic version of the Bohr-Mottelson collective model which captures the original relationships between its exactly solvable submodel limits. This variant of the PNSM provides an interesting and relevant shell-model symplectic-based framework for exploring the nuclear collective dynamics. Some simple applications of the present theory to different nuclei with various collective properties are given.

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arXiv2020

Microscopic shell-model counterpart of the Bohr-Mottelson model

In the present paper we demonstrate that there exists a fully microscopic shell-model counterpart of the Bohr-Mottelson model by embedding the latter in the microscopic shell-model theory of atomic nucleus within the framework of the recently proposed fully microscopic proton-neutron symplectic model (PNSM). For this purpose, another shell-model coupling scheme of the PNSM is considered in which the basis states are classified by the algebraic structure $SU(1,1) \otimes SO(6)$. It is shown that the configuration space of the PNSM contains a six-dimensional subspace that is closely related to the configuration space of the generalized quadrupole-monopole Bohr-Mottelson model and its dynamics splits into radial and orbital motions. The group $SO(6)$ acting in this space, in contrast, e.g., to popular IBM, contains an $SU(3)$ subgroup which allows to introduce microscopic shell-model counterparts of the exactly solvable limits of the Bohr-Mottelson model that closely parallel the relationship of the original Wilets-Jean and rotor models. The Wilets-Jean-type dynamics in the present approach, in contrast to the original collective model formulation, is governed by the microscopic shell-model intrinsic structure of the symplectic bandhead which defines the relevant Pauli allowed $SO(6)$, and hence $SU(3)$, subrepresentations. The original Wilets-Jean dynamics of the generalized Bohr-Mottelson model is recovered for the case of closed-shell nuclei, for which the symplectic bandhead structure is trivially reduced to the scalar or equivalent to it irreducible representation.

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arXiv2014

The proton-neutron symplectic model of nuclear collective motions

A proton-neutron symplectic model of collective motions, based on the non-compact symplectic group $Sp(12,R)$, is introduced by considering the symplectic geometry of the two-component many-particle nuclear system. The possible classical collective motions are determined by different dynamical groups that can be constructed from the symplectic generators. The relation of the $Sp(12,R)$ irreps with the shell-model classification of the basis states is considered by extending of the state space to the direct product space of $SU_{p}(3) \otimes SU_{n}(3)$ irreps, generalizing in this way the Elliott's $SU(3)$ model for the case of two-component system. The $Sp(12,R)$ model appears then as a natural multi-major-shell extension of the generalized proton-neutron $SU(3)$ scheme which takes into account the core collective excitations of monopole and quadrupole, as well as dipole type associated with the giant resonance vibrational degrees of freedom. Each $Sp(12,R)$ irreducible representation is determined by a symplectic bandhead or an intrinsic $U(6)$ space which can be fixed by the underlying proton-neutron shell-model structure, so the theory becomes completely compatible with the Pauli principle. It is shown that this intrinsic $U(6)$ structure is of vital importance for the appearance of the low-lying collective bands with both the positive and negative parity. The full range of low-lying collective states can then be described by the microscopically based intrinsic $U(6)$ structure, renormalized by coupling to the giant resonance vibrations.

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arXiv2014

Simultaneous description of low-lying positive and negative parity bands in heavy even-even nuclei

The low-lying spectra including the first few excited positive and negative parity bands of some heavy even-even nuclei from the rare earth and actinide mass regions are investigated within the framework of the symplectic Interacting Vector Boson Model with Sp(12,$R$) dynamical symmetry group. Symplectic dynamical symmetries allow the change of the number of excitation quanta or phonons building the collective states providing for larger representation spaces and richer subalgebraic structures to incorporate more complex nuclear spectra. The theoretical predictions for the energy levels and the electromagnetic transitions between the collective states of the ground state band and $K^π=0^{-}$ band are compared with experiment and some other collective models incorporating octupole and/or dipole degrees of freedom. The energy staggering which is a sensitive indicator of the octupole correlations in the even-even nuclei is also calculated and compared with experiment. The results obtained for the energy levels, energy staggering and transition strengths reveal the relevance of the used dynamical symmetry of the model for the simultaneous description of both positive and negative parity low-lying collective bands.

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arXiv2014

Axial asymmetry in the IVBM

The dynamical symmetry limit of the two-fluid Interacting Vector Boson Model (IVBM), defined through the chain $Sp(12,R) \supset U(3,3) \supset U_{p}(3) \otimes \overline{U_{n}(3)} \supset SU^{\ast}(3) \supset SO(3)$, is considered and applied for the description of nuclear collective spectra exhibiting axially asymmetric features. The effect of the introduction of a Majorana interaction to the $SU^{\ast}(3)$ model Hamiltonian on the $γ$-band energies is studied. The theoretical predictions are compared with the experimental data for $^{192}Os$, $^{190}Os$, and $^{112}Ru$ isotopes. It is shown that by taking into account the full symplectic structures in the considered dynamical symmetry of the IVBM, the proper description of the energy spectra and the $γ$-band energy staggering of the nuclei under considerations can be achieved. The obtained results show that the potential energy surfaces for the following two nuclei $^{192}Os$ and $^{112}Ru$, possess almost $γ$-flat potentials with very shallow triaxial minima, suggesting a more complex and intermediate situation between $γ$-rigid and $γ$-unstable structures. Additionally, the absolute $B(E2)$ intraband transition probabilities between the states of the ground state band and $γ$ band, as well as the $B(M1)$ interband transition probabilities between the states of the ground and $γ$ bands for the two nuclei $^{192}Os$ and $^{190}Os$ are calculated and compared with experiment and for the $B(E2)$ values with the predictions of some other collective models incorporating the $γ$-rigid or $γ$-unstable structures. The obtained results agree well with the experimental data and reveal the relevance of the used dynamical symmetry of IVBM in the description of nuclei exhibiting axially asymmetric features in their spectra.

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arXiv2014

Transition probabilities in the $U(3,3)$ limit of the symplectic IVBM

The tensor properties of the algebra generators are determined in respect to the reduction chain $Sp(12,R) \supset U(3,3) \supset U_{p}(3) \otimes \overline{U_{n}(3)}\supset U^{\ast}(3) \supset O(3)$, which defines one of the dynamical symmetry limits of the Interacting Vector Boson Model (IVBM). The symplectic basis according to the considered chain is thus constructed and the action of the $Sp(12,R)$ generators as transition operators between the basis states is illustrated. The matrix elements of the $U(3,3)$ ladder operators in the so obtained symmetry-adapted basis are given. The $U(3,3)$ limit of the model is further tested on the more complicated and complex problem of reproducing the $B(E2)$ transition probabilities between the collective states of the ground band in $^{104}Ru$, $^{192}Os$, $^{192}Pt$, and $^{194}Pt$ isotopes, considered by many authors to be axially asymmetric. Additionally, the excitation energies of the ground and $γ$ bands in $^{104}Ru$ are calculated. The theoretical predictions are compared with the experimental data and some other collective models which accommodate the $γ-$rigid or $γ-$soft structures. The obtained results reveal the applicability of the model for the description of the collective properties of nuclei, exhibiting axially asymmetric features.

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arXiv2011

Triaxial Shapes in the Interacting Vector Boson Model

A new dynamical symmetry limit of the two-fluid Interacting Vector Boson Model (IVBM), defined through the chain $Sp(12,R) \supset U(3,3) \supset U^{\ast}(3) \otimes SU(1,1) \supset SU^{\ast}(3) \supset SO(3)$, is introduced. The $SU^{\ast}(3)$ algebra considered in the present paper closely resembles many properties of the $SU^{\ast}(3)$ limit of IBM-2, which have been shown by many authors geometrically to correspond to the rigid triaxial model. The influence of different types of perturbations on the $SU^{\ast}(3)$ energy surface, in particular the addition of a Majorana interaction and an O(6) term to the model Hamiltonian, is studied. The effect of these perturbations results in the formation of a stable triaxial minimum in the energy surface of the IVBM Hamiltonian under consideration. Using a schematic Hamiltonian which possesses a perturbed $SU^{\ast}(3)$ dynamical symmetry, the theory is applied for the calculation of the low-lying energy spectrum of the nucleus $^{192}$Os. The theoretical results obtained agree reasonably with the experimental data and show a very shallow triaxial minimum in the energy surface for the ground state in $^{192}$Os, suggesting that the newly proposed dynamical symmetry might be appropriate for the description of the collective properties of different nuclei, exhibiting triaxial features.

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arXiv2011

Simultaneous Description of Even-Even, Odd-Mass and Odd-Odd Nuclear Spectra

The orthosymplectic extension of the Interacting Vector Boson Model (IVBM) is used for the simultaneous description of the spectra of different families of neighboring heavy nuclei. The structure of even-even nuclei is used as a core on which the collective excitations of the neighboring odd-mass and odd-odd nuclei are built on. Hence, the spectra of the odd-mass and odd-odd nuclei arise as a result of the consequent and self-consistent coupling of the fermion degrees of freedom of the odd particles, specified by the fermion sector $SO^{F}(2Ω)\subset OSp(2Ω/12,R)$, to the boson core which states belong to an $Sp^{B}(12,R)$ irreducible representation. The theoretical predictions for different low-lying collective bands with positive and negative parity for two sets of neighboring nuclei with distinct collective properties are compared with experiment and IBM/IBFM/IBFFM predictions. The obtained results reveal the applicability of the used dynamical symmetry of the model.

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arXiv2011

Structure of the doublet bands in doubly odd nuclei: The case of $^{128}Cs$

The structure of the $ΔJ = 1$ doublet bands in $^{128}Cs$ is investigated within the framework of the Interacting Vector Boson Fermion Model (IVBFM). A new, purely collective interpretation of these bands is given on the basis of the used boson-fermion dynamical symmetry of the model. The energy levels of the doublet bands as well as the absolute $B(E2)$ and $B(M1)$ transition probabilities between the states of both yrast and yrare bands are described quite well. The observed odd-even staggering of both $B(M1)$ and $B(E2)$ values is reproduced by the introduction of an appropriate interaction term of quadrupole type, which produces such a staggering effect in the transition strengths. The calculations show that the appearance of doublet bands in certain odd-odd nuclei could be a consequence of the realization of a larger dynamical symmetry based on the non-compact supersymmetry group $OSp(2Ω/12, R)$.

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arXiv2011

Phase Structure of the Interacting Vector Boson Model

The two-fluid Interacting Vector Boson Model (IVBM) with the U(6) as a dynamical group possesses a rich algebraic structure of physical interesting subgroups that define its distinct exactly solvable dynamical limits. The classical images corresponding to different dynamical symmetries are obtained by means of the coherent state method. The phase structure of the IVBM is investigated and the following basic phase shapes, connected to a specific geometric configurations of the ground state, are determined: spherical, $U_{p}(3)\otimes U_{n}(3)$, $γ-$unstable, O(6), and axially deformed shape, $SU(3)\otimes U_{T}(2)$. The ground state quantum phase transitions between different phase shapes, corresponding to the different dynamical symmetries and mixed symmetry case, are investigated.

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arXiv2009

New Description of the Doublet Bands in Doubly Odd Nuclei

The experimentally observed $ΔI = 1$ doublet bands in some odd-odd nuclei are analyzed within the orthosymplectic extension of the Interacting Vector Boson Model (IVBM). A new, purely collective interpretation of these bands is given on the basis of the obtained boson-fermion dynamical symmetry of the model. It is illustrated by its application to three odd-odd nuclei from the $A\sim 130$ region, namely $^{126}Pr$, $^{134}Pr$ and $^{132}La$. The theoretical predictions for the energy levels of the doublet bands as well as $E2$ and $M1$ transition probabilities between the states of the yrast band in the last two nuclei are compared with experiment and the results of other theoretical approaches. The obtained results reveal the applicability of the orthosymplectic extension of the IVBM.

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arXiv2008

Collective states of the odd-mass nuclei within the framework of the Interacting Vector Boson Model

A supersymmetric extension of the dynamical symmetry group $Sp^{B}(12,R)$ of the Interacting Vector Boson Model (IVBM), to the orthosymplectic group $OSp(2Ω/12,R)$ is developed in order to incorporate fermion degrees of freedom into the nuclear dynamics and to encompass the treatment of odd mass nuclei. The bosonic sector of the supergroup is used to describe the complex collective spectra of the neighboring even-even nuclei and is considered as a core structure of the odd nucleus. The fermionic sector is represented by the fermion spin group $SO^{F}(2Ω)\supset SU^{F}(2)$. The so obtained, new exactly solvable limiting case is applied for the description of the nuclear collective spectra of odd mass nuclei. The theoretical predictions for different collective bands in three odd mass nuclei, namely $^{157}Gd$, $^{173}Yb$ and $^{163}Dy$ from rare earth region are compared with the experiment. The $B(E2)$ transition probabilities for the $^{157}Gd$ and $^{163}Dy$ between the states of the ground band are also studied. The important role of the symplectic structure of the model for the proper reproduction of the $B(E2)$ behavior is revealed. The obtained results reveal the applicability of the models extension.

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arXiv2007

Transition probabilities in the U(6) limit of the Symplectic Interacting Vector Boson Model

The tensor properties of the algebra generators and the basis are determined in respect to the reduction chain $Sp(12,R) \supset U(6)% \supset U(3)\otimes U(2)\supset O(3)\otimes (U(1)\otimes U(1))$, which defines one of the dynamical symmetries of the Interacting Vector Boson Model. The action of the Sp(12,R) generators as transition operators between the basis states is presented. Analytical expressions for their matrix elements in the symmetry-adapted basis are obtained. As an example the matrix elements of the E2 transition operator between collective states of the ground band are determined and compared with the experimental data for the corresponding intraband transition probabilities of nuclei in the actinide and rare earth region. On the basis of this application the important role of the symplectic extension of the model is analyzed.

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arXiv2005

Six-dimensional Davidson potential as a dynamical symmetry of the symplectic Interacting Vector Boson Model

A six-dimensional Davidson potential, introduced within the framework of the Interacting Vector Boson Model (IVBM), is used to describe nuclei that exhibit transitional spectra between the purely rotational and vibrational limits of the theory. The results are shown to relate to a new dynamical symmetry that starts with the $Sp(12,R) \supset SU(1,1) \times SO(6)$ reduction. Exact solutions for the eigenstates of the model Hamiltonian in the basis defined by a convenient subgroup chain of SO(6) are obtained. A comparison of the theoretical results with experimental data for heavy nuclei with transitional spectra illustrates the applicability of the theory.

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