arXiv subjects

Dennis Bonatsos

Publications and source records attributed to Dennis Bonatsos.

At least 19 recordsLinked to original sources

arXiv2026

The Confined beta-Soft rotor model in rare-earth nuclei

Contemporary theoretical descriptions of nuclear structure rely mainly on microscopic, single-particle frameworks often in competition with collective degrees of freedom, especially when deformation plays a dominant role. Such phenomena are prominent in the rare-earth region, where rotational band structures and enhanced electric quadrupole transitions are systematically examined. The Confined beta-Soft (CBS) rotor model, introduced by N. Pietralla and O.M. Gorbachenko, bridges the gap between the X(5) critical point and the rigid-rotor limit in the region where the R_4/2 = E(4+)/E(2+) ratio lies between 2.904 and 3.333. In the present work, the CBS framework is employed to calculate ground-state band energies, associated B(E2) transition rates, and beta-band excitations of even-even nuclei in the rare-earth region. The theoretical results are systematically compared with available experimental data, and predictions are provided for nuclear observables that have not yet been measured, offering guidance for future experimental investigations.

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arXiv2026

Parameter-free deformation variables of the proxy-SU(3) symmetry in even-even actinide, superheavy and hyperheavy nuclei with Z=82-126, N=82-258

Superheavy and hyperheavy nuclei are one of the frontiers of nuclear structure nowadays, while also for many actinides rather limited experimental information exists. Therefore, theoretical methods providing parameter-independent predictions for these nuclei are of particular interest. Such a method is the proxy-SU(3) approximation to the shell model, which has been adequately tested against experimental data in medium-mass and heavy nuclei up to the rare earth region, and has been found to provide reliable, parameter-independent predictions for the collective deformation variables beta and gamma. Within the proxy-SU(3) approach, the SU(3) symmetry of the 3-dimensional harmonic oscillator, which is destroyed beyond the sd shell by the strong spin-orbit interaction, is restored through a unitary transformation. For each nucleus, the most symmetric irreducible representation (irrep) allowed by the Pauli principle and the short-range nature of the nucleon-nucleon interaction, called the highest-weight (hw ) irrep in mathematical language, is found to suffice, except in cases in which the hw irrep turns out to be completely symmetric, so that the next highest weight (nhw) irrep has also to be included. In this article we provide a full collection of the hw and nhw irreps, as well as of the corresponding parameter-free predictions for the deformation variables beta and gamma, for all atomic nuclei ranging from Z=82, N=82 to Z=126, N=258. Several cases exemplifying the use of the collected results for studying the prolate to oblate shape transition, mirror symmetries, as well as the evolution of the collective variables along the valley of stability are also considered.

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arXiv2026

Parameter-free deformation variables of the proxy-SU(3) symmetry in even-even atomic nuclei with Z=28-82, N=28-126

The proxy-SU(3) approximation to the shell model, which restores the SU(3) symmetry of the 3-dimensional harmonic oscillator beyond the sd shell, predicts the collective deformation variables beta and gamma of even-even atomic nuclei in a parameter-free way, based on the most symmetric irreducible representation (irrep) of SU(3) allowed by the Pauli principle and the short-range nature of the nucleon-nucleon interaction, which in group theoretical language is the highest weight (hw) irrep. In the few cases in which the hw irrep turns out to be completely symmetric, thus being able to accommodate only the ground state band, the next hw (nhw) irrep becomes indispensable. In the present article complete tables of the hw and nhw irreps are given for all atomic nuclei ranging from Z=28, N=28 to Z=82, N=126, along with the corresponding parameter-free predictions for the deformation variables beta and gamma. A few examples using the tabulated results for providing microscopic insight for specific effects in various regions of the nuclear chart are also given.

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arXiv2026

Islands of shape coexistence for Z=38-84 in a non-relativistic mean-field approach using Hartree-Fock-Bogoliubov theory

Based on the microscopic mechanism of the particle-hole (p-h) excitations in the proton and neutron single-particle energy levels relative to the Fermi energy, a search for islands of shape coexistence (SC) is performed over a wide range of even-even nuclei from Z=38 to 84 using non-relativistic self-consistent mean-field with the Hartree-Fock-Bogoliubov (HFB) theory using the Skyrme-SKI3 functional. The results of the present study show that neutron-induced islands of SC, corresponding to proton p-h excitations, are found around the magic numbers Z=82 and Z=50, centered at the relevant neutron midshells of N=104 and N=66 respectively, while proton-induced islands of SC, corresponding to neutron p-h excitations, are found around the neutron numbers N=90 and N=60, centered at the relevant proton midshells Z=66 and Z=38 respectively. In addition, islands of SC due to both neutron and proton particle-hole excitations are found around N=40, Z=40. The results of the present study are compared with the results of covariant density functional theory using the DDME2 functional, using the same p-h mechanism. The islands of SC that appeared in the CDFT work with the DDME2 functional are corroborated by the present study with the Skyrme-SKI3 functional, thus confirming the robustness of the particle-hole excitations mechanism in searching for islands of SC. In addition, the current study revealed new regions of SC, adjacent to the earlier islands and expanding their shores.

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arXiv2025

Triaxial shapes in even-even nuclei: A theoretical overview

Triaxial shapes in even-even nuclei have been considered since the early days of the nuclear collective model. Although many theoretical approaches have been used over the years for their description, no effort appears to have been made for grouping them together and identifying regions on the nuclear chart where the appearance of triaxiality might be favored. In addition, over the last few years, discussion has started on the appearance of small triaxiality in nuclei considered so far as purely axial rotors. In the present work we collect the predictions made by various theoretical approaches and show that pronounced triaxiality appears to be favored within specific stripes on the nuclear chart, with low triaxiality being present in the regions between these stripes, in agreement with parameter-free predictions made by the proxy-SU(3) approximation to the shell model, based on the Pauli principle and the short-range nature of the nucleon-nucleon interaction. The robustness of triaxiality within these stripes is supported by global calculations made in the framework of the Finite-Range Droplet Model (FRDM), which is based on completely different assumptions and possesses parameters fitted in order to reproduce fundamental nuclear properties.

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arXiv2024

Robustness of the proxy-SU(3) symmetry in atomic nuclei and the role of the next highest weight irreducible representation

The proxy-SU(3) symmetry predicts, in a parameter-free way, the collective deformation variables beta and gamma in even-even atomic nuclei away from closed shells based on the highest weight irreducible representations (irreps) of SU(3) in the relevant proton and neutron shells, which are the most symmetric irreps allowed by the Pauli principle and the short-range nature of the nucleon-nucleon interactions. The special cases in which the use of the next highest weight irrep of SU(3) becomes necessary are pointed out and numerical results are given for several regions of the nuclear chart, which can be used as input for irrep-mixing calculations.

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arXiv2024

Preponderance of triaxial shapes in atomic nuclei predicted by the proxy-SU(3) symmetry

The proxy-SU(3) symmetry predicts, in a parameter-free way, based only on the Pauli principle and the short-range nature of the nucleon-nucleon interaction, non-vanishing values of the collective variable gamma almost everywhere across the nuclear chart. Substantial triaxiality with gamma between 15 and 45 degrees is proved to be expected along horizontal and vertical stripes on the nuclear chart, covering the nucleon numbers 22-26, 34-48, 74-80, 116-124, 172-182. Empirical support for these stripes is found by collecting all even-even nuclei for which the first two excited 2+ states are known, along with the B(E2)s connecting them, as well as the second 2+ state to the ground state. The stripes are related to regions in which oblate SU(3) irreducible representations appear, bearing similarity to the appearance of triaxiality within the SU(3)* dynamical symmetry of the interacting boson model-2. Detailed comparisons of the proxy-SU(3) predictions to the data and to predictions by state-of-the-art Monte Carlo shell model calculations for deformed N=94, 96, 98 isotones in the rare earth region show good overall agreement, with the exception of Z=70 and N=94, which correspond to fully symmetric proxy-SU(3) irreps, suggesting that the latter are an artifact of the method which can be amended by considering the influence of the neighboring irreps.

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arXiv2024

Nuclear shape / phase transitions in the N = 40, 60, 90 regions

We investigate the isotopes of Se, Zr, Mo and Nd in the regions with N = 40, 60 and 90, where a first-order shape / phase transition, from spherical to deformed, can be observed. The signs of phase transitional behavior become evident by examining structure indicators, such as certain energy ratios and B(E2) transition rates and, in particular, how they evolve with neutron number. Microscopic mean-field calculations using the Skyrme-Hartree-Fock + Bardeen-Cooper-Schrieffer framework also reveal structural changes when considering the evolution of the resulting potential energy curves as functions of deformation. Finally, macroscopic calculations, using the Algebraic Collective Model, specifically for $^{74}$Se, $^{102}$Mo and $^{150}$Nd, after fitting its parameters to experimental spectra, result in potentials that resemble some of the potentials proposed in the framework of the Bohr Hamiltonian to describe shape transitions in nuclei.

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arXiv2024

Seven years of the proxy-SU(3) shell model symmetry

The proxy-SU(3) symmetry was first presented in HINPw4 in Ioannina in May2017, justified within the Nilsson model and applied to parameter-free predictions of the collective variables beta and gamma in medium-mass and heavy nuclei. Major steps forward, including the connection of the proxy-SU(3) symmetry to the shell model, the justification of the dominance of highest weight states in terms of the short range nature of the nucleon-nucleon interaction, as well as the first proposal of appearance of islands of shape coexistence on the nuclear chart, have been presented in HINPw6 in Athens in May 2021. The recently hot topic of the prevalence of triaxial shapes in heavy nuclei will also be briefly outlined in the proxy-SU(3) framework.

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arXiv2024

Mean-field derived IBM-1 Hamiltonian with intrinsic triaxial deformation

An interacting-boson-model-1 (IBM-1) Hamiltonian, derived from self-consistent mean-field calculations using a Skyrme energy density functional is employed for the study of energy spectra and $B(E2)$ transition strengths in the even-even $^{162-184}\mathrm{Hf}$ and $^{168-186}\mathrm{W}$. An intrinsic triaxial deformation, derived from fermionic proxy-SU(3) irreps, is incorporated into the IBM-1 potential energy curve, which is subsequently mapped to the fermionic one, in order to derive the parameters of the IBM-1 Hamiltonian. It is shown that the inclusion of the intrinsic triaxial deformation derived from the proxy-SU(3) irreps leads to a significantly improved agreement between the theoretical predictions and experimental data for the low-lying quadrupole bands in the examined isotopes, without the need of higher-order terms in the IBM-1 Hamiltonian. The calculated $B(E2)$ transition strengths are also improved, compared to the axially symmetric case. The recently suggested preponderance of triaxial deformation over extended regions of the nuclear chart is obtained as a by-product. Future potential improvements and extensions to this mapping approach are also discussed.

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arXiv2024

Prolate-oblate shape transitions and O(6) symmetry in even-even nuclei: A theoretical overview

Prolate to oblate shape transitions have been predicted in an analytic way in the framework of the Interacting Boson Model (IBM), determining O(6) as the symmetry at the critical point. Parameter-independent predictions for prolate to oblate transitions in various regions on the nuclear chart have been made in the framework of the proxy-SU(3) and pseudo-SU(3) symmetries, corroborated by recent non-relativistic and relativistic mean field calculations along series of nuclear isotopes, with parameters fixed throughout, as well as by shell model calculations taking advantage of the quasi-SU(3) symmetry. Experimental evidence for regions of prolate to oblate shape transitions is in agreement with regions in which nuclei bearing the O(6) dynamical symmetry of the IBM have been identified, lying below major shell closures. In addition, gradual oblate to prolate transitions are seen when crossing major nuclear shell closures, in analogy to experimental observations in alkali clusters.

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arXiv2023

Algebraic solutions for $o(12) {\leftrightarrow} u(2) \otimes u(10)$ quantum phase transitions in the proton-neutron interacting boson model

A simple systematic procedure to construct the proton-neutron unitary, $u_{\text{sd}}^{πν}{(12)}$, orthogonal, $o_{\text{sd}}^{πν}{(12)}$, and quasi-spin $\text{su}_{\text{sd}}^{πν}{(1,1)}$ algebras of the sd bosonic system is presented. New algebraic substructures of these algebras are discussed and the explicit formulae for their generators and Casimir operators are given in the spherical tensor form. The complementarity relationship of the Casimir operators of the $\text{su}_{\text{sd}}^{πν}{(1,1)}$ and $o_{\text{sd}}^{πν}{(12)}$ is derived. The exact algebraic solutions of the quantum phase transition Hamiltonian between the $o_{\text{sd}}^{πν}{(12)}$ and $u_s^{πν}{(2)} \otimes u_d^{πν}{(10)}$ limits has been considered, for the first time, in the framework of affine $\text{su}_{\text{sd}}^{πν}{(1,1)}$ Lie algebra. The low lying energy spectra of the $\, ^{70}\text{Ge},\, ^{76-78}\text{Se},\, ^{96-98}\text{Mo},\text{and}\, ^{100-102}\text{Ru}$ isotopes are calculated using the $o_{\text{sd}}^{πν} {(12)} {\leftrightarrow} u_s^{πν}{(2)} \otimes u_d^{πν}{(10)}$ transition Hamiltonian. The good agreement of our computation with empirical result in these isotopes emphasizes the importance of $u_s^{πν}{(2)} \otimes u_d^{πν}{(10)}$ limit. With this addition, symmetry can be extended to many nuclei.

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arXiv2023

Triaxial nuclei and analytical solutions of the conformable fractional Bohr Hamiltonian with some exponential-type potentials

New approximate analytical solutions have been obtained for the conformable fractional collective Bohr Hamiltonian suitable for triaxial nuclei, with the harmonic oscillator in γ-part of the collective potential and different exponential-type potentials (namely Morse, Tietz-Hua, and multi-parameter exponential-type potential) in \b{eta}-part. The conformable fractional Nikiforov-Uvarov approach is used to derive closed analytical formulas for energy spectra and wave functions. The relation between the conformable fractional spectra of the three potentials and the Z(5) spectrum has been studied. The evolution of the energy spectra as a function of the potential parameters has been investigated for the three potentials. The normalized B(E2) transition rates and spectra have been calculated and compared with the experimental data and theoretical predictions of Kratzer potential. The predictions can describe well the experimental results for 114,116Pd, 126,128Xe, and 192,194Pt isotopes.

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arXiv2023

Shape coexistence in even-even nuclei: A theoretical overview

The last decade has seen a rapid growth of our understanding of the microscopic origins of shape coexistence, assisted by the new data provided by the modern radioactive ion beam facilities built worldwide. Islands of the nuclear chart in which shape coexistence can occur have been identified, and the different microscopic particle-hole excitation mechanisms leading to neutron-induced or proton-induced shape coexistence have been clarified. The relation of shape coexistence to the islands of inversion, appearing in light nuclei, to the new spin-aligned phase appearing in N=Z nuclei, as well as to shape/phase transitions occurring in medium mass and heavy nuclei, has been understood. In the present review, these developments are considered within the shell model and mean field approaches, as well as by symmetry methods. In addition, based on systematics of data, as well as on symmetry considerations, quantitative rules are developed, predicting regions in which shape coexistence can appear, as a possible guide for further experimental efforts, which can help in improving our understanding of the details of the nucleon-nucleon interaction, as well as of its modifications occurring far from stability.

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arXiv2023

Signatures for shape coexistence and shape/phase transitions in even-even nuclei

Systematics of B(E2) transition rates connecting the first excited 0+ state to the first excited 2+ state of the ground state band in even-even nuclei indicates that shape coexistence of the ground state band and the first excited K=0 band should be expected in nuclei lying within the stripes of nucleon numbers 7-8, 17-20, 34-40, 59-70, 96-112 predicted by the dual shell mechanism of the proxy-SU(3) model, avoiding their junctions, within which high deformation is expected. Systematics of the excitation energies of the first excited 0+ states in even-even nuclei show that shape coexistence due to proton-induced neutron particle-hole excitations is related to a first-order shape/phase transition from spherical to deformed shapes, while shape coexistence due to neutron-induced proton particle-hole excitations is observed along major proton shell closures.

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arXiv2022

The proxy-SU(3) symmetry in atomic nuclei

The microscopic origins and the up-to-now predictions of the proxy-SU(3) symmetry model of atomic nuclei are reviewed. Starting from the experimental evidence for the special role played by nucleon pairs with maximal spatial overlap, the proxy-SU(3) approximation scheme is introduced and its validity is demonstrated through Nilsson model calculations, as well as through its connection to the spherical shell model. The major role played by highest weight irreducible representations of SU(3) in shaping up the nuclear properties is pointed out, resulting in parameter-free predictions of the collective variables beta and gamma for even-even nuclei, in the explanation of the dominance of prolate over oblate shapes in the ground states of even-even nuclei, in the prediction of a shape/phase transition from prolate to oblate shapes below closed shells, as well as in the prediction of specific islands on the nuclear chart in which shape coexistence is confined. Further developments within the proxy-SU(3) scheme are outlined.

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arXiv2022

Islands of shape coexistence: theoretical predictions and experimental evidence

Parameter-free theoretical predictions based on a dual shell mechanism within the proxy-SU(3) symmetry of atomic nuclei, as well as covariant density functional theory calculations using the DDME2 functional indicate that shape coexistence (SC) based on the particle-hole excitation mechanism cannot occur everywhere on the nuclear chart, but is restricted on islands lying within regions of 7-8, 17-20, 34-40, 59-70, 96-112, 146-168 protons or neutrons. Systematics of data for even-even nuclei possessing K=0 (beta) and K=2 (gamma) bands support the existence of these islands, on which shape coexistence appears whenever the K=0 bandhead 0_2^+ and the first excited state of the ground state band 2_1^+ lie close in energy, with nuclei characterized by 0_2^+ lying below the 2_1^+ found in the center of these islands. In addition a simple theoretical mechanism leading to multiple shape coexistence is briefly discussed.

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arXiv2022

Islands of shape coexistence from single-particle spectra in covariant density functional theory

Using covariant density functional theory with the DDME2 functional and labeling single-particle energy orbitals by Nilsson quantum numbers, a search for particle-hole (p-h) excitations connected to the appearance of shape coexistence is performed for Z=38 to 84. Islands of shape coexistence are found near the magic numbers Z=82 and Z=50, restricted in regions around the relevant neutron midshells N=104 and N=66 respectively, in accordance to the well accepted p-h interpretation of shape coexistence in these regions, which we call neutron-induced shape coexistence, since the neutrons act as elevators creating holes in the proton orbitals. Similar but smaller islands of shape coexistence are found near N=90 and N=60, restricted in regions around the relevant proton midshells Z=66 and Z=39 respectively, related to p-h excitations across the 3-dimensional isotropic harmonic oscillator (3D-HO) magic numbers N=112 and N=70, which correspond to the beginning of the participation of the opposite parity orbitals 1i13/2 and 1h11/2 respectively to the onset of deformation. We call this case proton-induced shape coexistence, since the protons act as elevators creating holes in the neutron orbitals, thus offering a possible microscopic mechanism for the appearance of shape coexistence in these regions. In the region around N=40, Z=40, an island is located on which both neutron p-h excitations and proton p-h excitations are present.

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