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Dennis Bonatsos

Publications and source records attributed to Dennis Bonatsos.

At least 37 records · Page 2Linked to original sources
arXiv2022

Islands of shape coexistence in proxy-SU(3) symmetry and in covariant density functional theory

Shape coexistence in even-even nuclei is observed when the ground state band of a nucleus is accompanied by another K=0 band at similar energy but with radically different structure. We attempt to predict regions of shape coexistence throughout the nuclear chart using the parameter-free proxy-SU(3) symmetry and standard covariant density functional theory. Within the proxy-SU(3) symmetry the interplay of shell model magic numbers, formed by the spin-orbit interaction, and the 3-dimensional isotropic harmonic oscillator magic numbers, leads to the prediction of specific horizontal and vertical stripes on the nuclear chart in which shape coexistence should be possible. Within covariant density functional theory, specific islands on the nuclear chart are found, in which particle-hole excitations leading to shape coexistence are observed. The role played by particle-hole excitations across magic numbers as well as the collapse of magic numbers as deformation sets in is clarified.

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arXiv2022

Microscopic origin of shape coexistence in the N=90, Z=64 region

A microscopic explanation of the nature of shape coexistence in the N=90, Z=64 region is suggested, based on calculations of single particle energies through standard covariant density functional theory. It is suggested that shape coexistence in the N=90 region is caused by the protons, which create neutron particle-hole (p-h) excitations across the N=112 3-dimensional isotropic harmonic oscillator (3D-HO) magic number, signaling the start of the occupation of the 1i13/2 intruder orbital, which triggers stronger proton-neutron interaction, causing the onset of the deformation and resulting in the shape/phase transition from spherical to deformed nuclei described by the X(5) critical point symmetry. A similar effect is seen in the N=60, Z=40 region, in which p-h excitations across the N=70 3D-HO magic number occur, signaling the start of the occupation of the 1h11/2 intruder orbital.

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arXiv2021

Unified picture of nucleon pairs playing leading roles in nuclear collectivity

Proxy-SU(3) symmetry is an approximation scheme extending the Elliott SU(3) algebra of the sd shell to heavier shells. When introduced in 2017, the approximation had been justified by calculations carried out within the Nilsson model, with nucleon pairs differing by $ΔK [ΔN Δn_z ΔΛ]=0[110]$ in the Nilsson quantum numbers playing a major role in the approximation. Recently our group managed to map the cartesian basis of the Elliott SU(3) model onto the spherical shell model basis, fully clarifying the approximations used within the proxy-SU(3) scheme and paving the way for using the proxy-SU(3) approximation in shell model calculations for heavy nuclei. As a by-product, the relation of the 0[110] Nilsson pairs used in proxy-SU(3) to the earlier used de Shalit-Goldhaber pairs $|Δn Δl Δj Δm_j\rangle = | 0110\rangle$ in spherical shell model notation is clarified, while the Federman-Pittel (FP) pairs known to play a major role at the onset of deformation are identified as $| 0010\rangle$ pairs, and the FP pairs further increasing the deformation after its onset are found to be $| 0110\rangle$ pairs, i.e. identical to the de-Shalit-Goldhaber pairs. The connection between the proxy-SU(3) scheme and the spherical shell model has also been worked out in the original framework of the Nilsson model, with identical results.

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arXiv2021

Connecting the proxy-SU(3) symmetry to the shell model

Proxy-SU(3) symmetry is an approximation scheme extending the Elliott SU(3) algebra of the sd shell to heavier shells. When introduced in 2017, the approximation had been justified by calculations carried out within the Nilsson model. Recently our group managed to map the cartesian basis of the Elliott SU(3) model onto the spherical shell model basis, proving that the proxy-SU(3) approximation corresponds to the replacement of the intruder orbitals by their de Shalit-Goldhaber partners, paving the way for using the proxy-SU(3) approximation in shell model calculations. The connection between the proxy-SU(3) scheme and the spherical shell model has also been worked out in the original framework of the Nilsson model, with identical results.

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arXiv2021

Highest weight irreducible representations favored by nuclear forces within SU(3)-symmetric fermionic systems

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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arXiv2021

Resolution of the spin paradox in the Nilsson model

In the well-known Nilsson diagrams, depicting the dependence of the nuclear single-particle energy levels on quadrupole deformation, a spin paradox appears {as the deformation sets in, leading from spherical shapes to prolate deformed shapes with cylindrical symmetry}. Bunches of levels corresponding to a spherical shell model orbital, sharing the same orbital angular momentum and the same total angular momentum, appear to correspond to Nilsson energy levels, labeled by asymptotic quantum numbers in cylindrical coordinates, some of which have spin up, while some others have spin down. Furthermore, for some orbitals the correspondence between spherical shell model quantum numbers and Nilsson asymptotic quantum numbers is not the same for protons and for neutrons. Introducing a new rule of correspondence between the two sets of quantum numbers, we show that the spin paradox is resolved and full agreement between the proton and neutron Nilsson diagrams is established. The form of the Nilsson diagrams as a function of the quadrupole deformation remains unchanged, the only difference between the new diagrams and the traditional ones being the mutual exchange of the Nilsson labels for certain pairs of single-particle energy levels.

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arXiv2021

The islands of shape coexistence within the Elliott and the proxy-SU(3) Models

A novel dual-shell mechanism for the phenomenon of shape coexistence in nuclei within the Elliott SU(3) and the proxy-SU(3) symmetry is proposed for all mass regions. It is supposed, that shape coexistence is activated by large quadrupole-quadrupole interaction and involves the interchange among the spin-orbit (SO) like shells within nucleon numbers 6-14, 14-28, 28-50, 50-82, 82-126, 126-184, which are being described by the proxy-SU(3) symmetry, and the harmonic oscillator (HO) shells within nucleon numbers 2-8, 8-20, 20-40, 40-70, 70-112, 112-168 of the Elliott SU(3) symmetry. The outcome is, that shape coexistence may occur in certain islands on the nuclear map. The dual-shell mechanism predicts without any free parameters, that nuclei with proton number (Z) or neutron number (N) between 7-8, 17-20, 34-40, 59-70, 96-112, 146-168 are possible candidates for shape coexistence. In the light nuclei the nucleons flip from the HO shell to the neighboring SO-like shell, which means, that particle excitations occur. For this mass region, the predicted islands of shape coexistence, coincide with the islands of inversion. But in medium mass and heavy nuclei, in which the nucleons inhabit the SO-like shells, shape coexistence is accompanied by a merging of the SO-like shell with the open HO shell. The shell merging can be accomplished by the outer product of the SU(3) irreps of the two shells and represents the unification of the HO shell with the SO-like shell.

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arXiv2021

Why nuclear forces favor the highest weight irreducible representations of the fermionic SU(3) symmetry

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 representation, 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.

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arXiv2020

Proxy-SU(3) symmetry in the shell model basis

The proxy-SU(3) symmetry has been proposed for spin-orbit like nuclear shells using the asymptotic deformed oscillator basis for the single particle orbitals, in which the restoration of the symmetry of the harmonic oscillator shells is achieved by a change of the number of quanta in the z-direction by one unit for the intruder parity orbitals. The same definition suffices within the cartesian basis of the Elliott SU(3) model. Through a mapping of the cartesian Elliott basis onto the spherical shell model basis, we translate the proxy-SU(3) approximation into spherical coordinates, proving, that in the spherical shell model basis the proxy-SU(3) approximation corresponds to the replacement of the intruder parity orbitals by their de Shalit--Goldhaber partners. Furthermore it is shown, that the proxy-SU(3) approximation in the cartesian Elliott basis is equivalent to a unitary transformation in the z-coordinate, leaving the x-y plane intact, a result which in the asymptotic deformed oscillator coordinates implies, that the z-projections of angular momenta and spin remain unchanged. The present work offers a microscopic justification of the proxy-SU(3) approximation and in addition paves the way, for taking advantage of the proxy-SU(3) symmetry in shell model calculations.

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arXiv2020

Shell model structure of proxy-SU(3) pairs of orbitals

The Nilsson orbitals used in the substitutions occurring in the proxy-SU(3) scheme, which are the orbitals bearing the maximum value of total angular momentum in each shell, have an extremely simple structure in the shell model basis |N l j Omega>, with each Nilsson orbital corresponding to a single shell model eigenvector. This simple structure is valid at all deformations for these orbitals, while in other orbitals it is valid only at small deformations. Nilsson 0[110] pairs are found to correspond to |1 1 1 0> pairs in the spherical shell model basis, paving the way for using the proxy-SU(3) approximation within the shell model.

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arXiv2020

Breaking SU(3) spectral degeneracies in heavy deformed nuclei

Symmetries are manifested in nature through degeneracies in the spectra of physical systems. In the case of heavy deformed nuclei, when described in the framework of the Interacting Boson Model, within which correlated proton (neutron) pairs are approximated as bosons, the ground state band has no symmetry partner, while the degeneracy between the first excited beta and gamma bands is broken through the use of three-body and/or four-body terms. In the framework of the proxy-SU(3) model, in which an approximate SU(3) symmetry of fermions is present, the same three-body and/or four-body operators are used for breaking the degeneracy between the ground state band and the first excited gamma band. Experimentally accessible quantities being independent of any free parameters are pointed out in the latter case.

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arXiv2020

Parameter-free predictions for the collective deformation variables beta and gamma within the pseudo-SU(3) scheme

The consequences of the short range nature of the nucleon-nucleon interaction, which forces the spatial part of the nuclear wave function to be as symmetric as possible, on the pseudo-SU(3) scheme are examined through a study of the collective deformation parameters beta and gamma in the rare earth region. It turns out that beyond the middle of each harmonic oscillator shell possessing an SU(3) subalgebra, the highest weight irreducible representation (the hw irrep) of SU(3) has to be used, instead of the irrep with the highest eigenvalue of the second order Casimir operator of SU(3) (the hC irrep), while in the first half of each shell the two choices are identical. The choice of the hw irrep predicts a transition from prolate to oblate shapes just below the upper end of the rare earth region, between the neutron numbers N=114 and 116 in the W, Os, and Pt series of isotopes, in agreement with available experimental information, while the choice of the hC irrep leads to a prolate to oblate transition in the middle of the shell, which is not seen experimentally. The prolate over oblate dominance in the ground states of even-even nuclei is obtained as a by-product.

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arXiv2019

Magic numbers of cylindrical symmetry

In nuclear physics a magic number is defined as the nucleon number, which is separated by a significantly large single-particle energy gap from the next nucleon. Magic numbers define the nuclear shells, which are considered to be active, only if they are partially occupied by nucleons. As a consequence the single particle interactions of the valence nucleons lead to the description of the collective properties of the whole nucleus in the shell model theory. But phenomena as the island of inversion, the shape coexistence and the break down of the N=20 magic number reveal that the above definition of a magic number is deficient. A complementary definition should rely on the selection rules of the single particle interactions. Specifically the selection rules of the quadrupole-quadrupole interaction lead to two sets of magic numbers, namely the harmonic oscillator magic numbers 2, 8 20, 40, 70, 112, ... and the spin-orbit SO-like magic numbers 2, 6, 14, 28, 50, 82, 126, ... The underlying symmetries are respectively the spherical symmetry of the 3D isotropic harmonic oscillator and the cylindrical symmetry of the 3D anisotropic harmonic oscillator with two frequencies equal. The above two sets of magic numbers along with the Elliott SU(3) symmetry framework predict long standing and puzzling phenomena in nuclear physics.

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arXiv2017

A symmetry for heavy nuclei: Proxy-SU(3)

The SU(3) symmetry realized by J. P. Elliott in the sd nuclear shell is destroyed in heavier shells by the strong spin-orbit interaction. However, the SU(3) symmetry has been used for the description of heavy nuclei in terms of bosons in the framework of the Interacting Boson Approximation, as well as in terms of fermions using the pseudo-SU(3) approximation. We introduce a new fermionic approximation, called the proxy-SU(3), and we comment on its similarities and differences with the other approaches.

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arXiv2017

Proxy-SU(3) symmetry in heavy nuclei: Foundations

An approximate SU(3) symmetry appears in heavy deformed even-even nuclei, by omitting the intruder Nilsson orbital of highest total angular momentum and replacing the rest of the intruder orbitals by the orbitals which have escaped to the next lower major shell. The approximation is based on the fact that there is a one-to-one correspondence between the orbitals of the two sets, based on pairs of orbitals having identical quantum numbers of orbital angular momentum, spin, and total angular momentum. The accuracy of the approximation is tested through calculations in the framework of the Nilsson model in the asymptotic limit of large deformations, focusing attention on the changes in selection rules and in avoided crossings caused by the opposite parity of the proxies with respect to the substituted orbitals.

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