Shape Coexistence Research Articles

Magic numbers for shape coexistence

The increasing deformation in atomic nuclei leads to the change of the classical magic numbers (2,8,20,28,50,82…) which dictate the arrangement of nucleons in complete shells. The magic numbers of the three-dimensional harmonic oscillator (2,8,20,40,70,…) emerge at deformations around ε=0.6. At lower deformations the two sets of magic numbers antagonize, leading to shape coexistence. A quantitative investigation is performed using the usual Nilsson model wave functions and the recently introduced proxy–SU(3) scheme.

Synergy of nuclear data systematics and proxy-SU(3) in planning future experiments in the superheavies mass region

Spectroscopic information of hard–to–reach superheavy nuclei can be invaluable in understanding the dynamics of nuclear systems at large values of charge and volume. RIB factories of the next generation, such as FAIR, plan to provide heavy ion beams at high energies to facilitate experimental access to these mass regimes. In preparation of future experimental endeavours, a systematic survey of available nuclear data, mainly energies and reduced transition probabilities/lifetimes of short–lived 21+ states in even–even isotopes with Z=82,84,86 was undertaken. The principle motivation is to trace the competition between collective and single-particle degrees of freedom in the mass area just above Pb (Z=82), an area known to exhibit isomerism, octupole degrees of freedom and shape coexistence. Existing data were compared to the theoretical predictions using the analytical, parameter­­–free proxy–SU(3) scheme, for neutron numbers N=96–116. The model was further employed to predict currently unknown values for spectroscopic data in series of Pb, Po and Ra isotopes.

Nuclear magnetic moment studies of short–lived excited states at the edge of the island of inversion: the IS628 experiment

Nuclear gfactors are highly sensitive to the single–particle aspects of the wave function, revealing important information for the nuclear structure along the isotopic chart. The sdshell has been thoroughly studied, resulting in “universal” shell model Hamiltonians [1] and the development of an M1 operator [2]. However, there is still shortage of precise experimental gfactor data of excited states to consolidate the nuclear structure in this regime. Recently, the Time Differential Recoil in Vacuum (TDRIV) experimental technique was revamped to be applicable for radioactive beams. TDRIV has been tested successfully and produced high-precision results for the stable 24Mg nucleus [3]. However, the successful application of the technique relies heavily on calibrations of the de–orientation phenomenon. A recent experiment using the MINIBALL array at REX/ISOLDE (IS628) has focused on the application of the method with a radioactive 28Mg beam. The gfactor of the 28Mg first 2+excited state can act as an excellent probe of the N=16 shell gap and the νd3/2singleparticle energy, as well as the possible presence of spdfadmixtures. The particular measurement will be a next step towards a gfactor measurement on 32Mg in the center of the “island of inversion”, where the N=20 shell closure breaks down enhancing 1p–1h excitations and shape–coexistence. In this work, the analysis of the spectroscopic data recorded for a 22Ne beam, which was used for calibrating the experimental method before the actual run on 28Mg is reported. Preliminary data on the angular distributions for the 22Ne 21+→ 0+transition will be presented, an important prerequisite before a remeasurement of g(22Ne;21+).

Description of shape coexistence in Zr96 based on the quadrupole-collective Bohr Hamiltonian

Experimental data on $^{96}$Zr indicate coexisting spherical and deformed structures with small mixing amplitudes. We investigate the properties of the low-lying collective states of $^{96}$Zr based on the collective quadrupole Bohr Hamiltonian. The $\beta$-dependent collective potential having two minima -- spherical and deformed, is fixed so to describe experimental data in the best way.Good agreement with the experimental data on the excitation energies, $B(E2)$ and $B(M1)$ reduced transition probabilities is obtained. It is shown that the low-energy structure of $^{96}$Zr can be reproduced in a satisfactory way in the geometrical model with a potential function supporting shape coexistence. However, the excitation energy of the $2^+_2$ state can be reproduced only if the rotation inertia coefficient is taken five times smaller then the vibrational one in the region of the deformed well. It is shown also that shell effects are important for the description of the $B(M1;2^+_2 \rightarrow 2^+_1)$ value. An indication on the influence of the pairing vibrational mode on the $\rho^2 (0^+_2 \rightarrow 0^+_1)$ value is obtained.

Exotic structure and decay of medium mass nuclei near the drip lines

Properties of medium mass nuclei near the drip lines are not only relevant for nuclear structure, but are of high interest in nuclear astrophysics and in several applications, in particular nuclear technology. Shape coexistence effects play an essential role in the structure and dynamics of proton-rich A∼70 nuclei and neutron-rich A∼100 nuclei. Results concerning a self-consistent description of exotic phenomena including Gamow-Teller β-decay of proton-rich nuclei, triple shape coexistence and shape evolution in the N=58 Sr and Zr isotopes as well as Gamow-Teller β-decay strength distributions and structure properties of neutron- rich nuclei relevant for reactor decay heat obtained in the frame of the complex Excited Vampir model using realistic effective interactions in large model spaces will be presented.

Structure of Mg31 : Shape coexistence revealed by β−γ spectroscopy with spin-polarized Na31

The level structure of $^{31}\mathrm{Mg}$, which is located close to the region of the $N$ = 20 ``island of inversion'' in the nuclear chart, has been studied by $\ensuremath{\beta}\text{\ensuremath{-}}\ensuremath{\gamma}$ spectroscopy with spin-polarized $^{31}\mathrm{Na}$. In $^{31}\mathrm{Mg}$, shape coexistence is expected as a result of subtle competition between the spherical mean field and the nuclear correlation which favors deformed configurations. In the present work, our unique method utilizing the anisotropic $\ensuremath{\beta}$ decay of spin-polarized $^{31}\mathrm{Na}$ enables us to firmly assign the spins of all positive-parity excited levels in $^{31}\mathrm{Mg}$ below the neutron separation energy at 2.3 MeV. Furthermore, by constructing a very detailed decay scheme, including two newly found levels, the spins of negative-parity levels are restricted. The examination of the spectroscopic information shows that the deformed rotational bands with ${K}^{\ensuremath{\pi}}=1/{2}^{+}$ and $1/{2}^{\ensuremath{-}}$, which have very similar structures to those observed in a higher excitation energy region of $^{25}\mathrm{Mg}$, appear as the ground-state and low-lying bands, respectively, in $^{31}\mathrm{Mg}$. The experimental levels of $^{31}\mathrm{Mg}$ are compared, on the level-by-level basis, with two types of theoretical calculations. These are, first, the antisymmetrized molecular dynamics (AMD) plus generator coordinate method (GCM) and, second, the shell model with the EEdf1 interaction, which is microscopically derived from chiral effective field theory. It is understood that 8 levels among the experimental 11 levels are the members of four types of largely deformed rotational bands and 2 levels are of spherical nature. The $1/{2}^{+}$ 2.244-MeV level is successfully reproduced by the shell-model calculation with a dominant 4p4h configuration. The present work clearly demonstrates that various structures coexist in a low excitation energy region of $^{31}\mathrm{Mg}$.

Coexistence of chiral symmetry and pseudospin symmetry in one nucleus: triplet bands in 105Ag

The nearly degenerate triplet bands with the configuration in 105Ag are studied via the relativistic mean-field (RMF) theory and the multiparticle plus rotor model (MPRM). The configuration-fixed constrained triaxial RMF calculations exhibit pseudospin symmetry in single-particle spectra and triaxial shape coexistence. The experimental excitation energies and electromagnetic transition probabilities for the triplet bands are well reproduced by the MPRM calculations. The first and second lowest energy bands of the triplet bands are interpreted as pseudospin doublet bands, and the second and third bands are interpreted as chiral doublet bands. The chiral doublet bands show the same phase in the B(M1)/B(E2) staggering, while the pseudospin doublet bands hold the opposite phase. Such triplet bands in 105Ag provide the first example for the coexistence of chiral symmetry and pseudospin symmetry in one single nucleus.

Inelastic neutron scattering studies of Se76

The low-lying, low-spin levels of $^{76}\mathrm{Se}$ were studied with the $(n,{n}^{\ensuremath{'}}\ensuremath{\gamma})$ reaction. Gamma-ray excitation function measurements were performed at incident neutron energies from 2.0 to 3.5 MeV, and $\ensuremath{\gamma}$-ray angular distributions were measured at neutron energies of 2.4, 3.0, and 3.7 MeV. From these measurements, level spins, level lifetimes, branching ratios, and multipole mixing ratios were determined. We established the ${0}_{2}^{+}$ band, which supports the shape coexistence in $^{76}\mathrm{Se}$ predicted by large-scale shell model calculations and the interacting boson model.

Shape coexistence in 94Zr studied via Coulomb excitation

In recent years, a number of both theoretical and experimental investigations have been performed focusing on the zirconium isotopic chain. In particular, state-of-the-art Monte Carlo shell-model calculations predict shape coexistence in these isotopes. In this context, the 94Zr nucleus, which is believed to possess a nearly spherical ground state, is particularly interesting since the purported deformed structure is basedon the low-lying 02+ state, making it amenable for detailed study. In order to provide definitive conclusionson the shapes of the low-lying states, two complementary experiments to study 94Zr by means of low-energy Coulomb excitation were performed. This data will allow the quadrupole moments of the 21,2+ levels to be extracted as well as for the deformation parameters of the 01,2+ states to be determined and, thus, definitive conclusions to be drawn on the role of shape coexistence in this nucleus for the first time. The first experiment was performed at the INFN Legnaro National Laboratory with the GALILEO-SPIDER setup, which, for the first time, was coupled with 6 lanthanum bromide scintillators (LaBr3:Ce) in order to maximize the γ-ray detection effciency. The second experiment was performed at the Maier-Leibnitz Laboratory (MLL) in Munich and used a Q3D magnetic spectrograph to detect the scattered 12C ions following Coulomb excitation of 94Zr targets.

Study of neutron-deficient mercury isotopes Preliminary results on 189Hg

The mercury isotopic chain is depicted as one of the best fields to observe many phenomena related to collectivity evolution as, for instance, shape transition, shape coexistence or shape staggering. In this context, the 189Hg presents several interesting aspects and is still relatively unexplored. The nucleus has been studied at the Laboratori Nazionali di Legnaro using a fusion-evaporation reaction and the γ rays emitted have been detected by the GALILEO array, coupled with Neutron Wall and the GALILEO plunger. The presorting and the preliminary results are presented.

Shape Coexistence and Shape Isomerism in the Ni Isotopic Chain

Shape Coexistence and Shape Isomerism in the Ni Isotopic Chain

Coexistence and evolution of shapes: mean-field-based interacting boson model

A method of deriving the Hamiltonian of the interacting boson model, that is based on the microscopic framework of the nuclear energy density functional, is presented. The constrained self-consistent mean-field calculation with a given energy density functional provides potential energy surface within the relevant collective coordinates, which is subsequently mapped onto the expectation value of the interacting-boson Hamiltonian in the boson condensate state. This procedure completely determines the strength parameters of the IBM, and the diagonalization of the mapped Hamiltonian yields excitation spectra and transition rates for a given nucleus. Two recent applications of the method are discussed, that is, the descriptions of the intruder states in Cadmiumisotopes and the octupole correlations in neutron-rich odd-mass Barium isotopes.

Revealing microscopic origins of shape coexistence in the Ni isotopic chain

In a two–neutron transfer experiment, performed in Bucharest in July 2016 at sub–Coulomb barrier energy,a photon decay hindered – solely – by a nuclear shape change was identified in the 66Ni nucleus. Such a rare process, at spin zero, was clearly observed before only in actinide nuclei in the 1970’s,where fission isomers were found. The experimental findings on 66Ni have been well reproduced by the Monte Carlo Shell Model Calculations of the Tokyo group, which predict a multifaceted scenario of coexistence of spherical, oblate and prolate shapes in neutron–rich Ni isotopes. The results on 66Ni encouraged a comprehensive gamma–spectroscopy investigation of neutron–rich Ni isotopes, in particular 62Ni and 64–Ni, at IFIN–HH (Bucharest), IPN Orsay and ILL (Grenoble), employing different reaction mechanisms to pin down the wave function composition of selected excited states. The aim is to shed light on the microscopic origin of deformation in neutron–rich Ni nuclei, possibly locating other examples of “shape–isomer–like” structures inthis region.

Time–Frequency Warped Waveforms

The forthcoming communication systems are advancing toward improved flexibility in various aspects. Improved flexibility is crucial to cater diverse service requirements. This letter proposes a novel waveform design scheme that exploits axis warping to enable peaceful coexistence of different pulse shapes. A warping transform manipulates the lattice samples non-uniformly and provides flexibility to handle the time-frequency occupancy of a signal. The proposed approach enables the utilization of flexible pulse shapes in a quasi-orthogonal manner and increases the spectral efficiency. In addition, the rectangular resource block structure, which assists an efficient resource allocation, is preserved with the warped waveform design as well.

β− decay study of the Mn66−Fe66−Co66−Ni66 decay chain

Background: Shell evolution can impact the structure of the nuclei and lead to effects such as shape coexistence. The nuclei around $^{68}$Ni represent an excellent study case, however, spectroscopic information of the neutron-rich, $Z<28$ nuclei is limited. Purpose: The goal is to measure $\gamma$-ray transitions in $^{66}$Fe, $^{66}$Co and $^{66}$Ni populated in the $\beta^-$ decay of $^{66}$Mn, to determine absolute $\beta$-feedings and relative $\gamma$-decay probabilities and to compare the results with Monte Carlo Shell Model calculations in order to study the influence of the relevant single neutron and proton orbitals occupancies around $Z=28$ and $N=40$. Method: The low-energy structures of $^{65,66}$Fe, $^{66}$Co and $^{66}$Ni were studied in the $\beta^-$ decay of $^{66}$Mn produced at ISOLDE, CERN. The beam was purified by means of laser resonance ionization and mass separation. The $\beta$ and $\gamma$ events detected by three plastic scintillators and two MiniBall cluster germanium detectors, respectively, were correlated in time to build the low-energy excitation schemes and to determine the $\beta$-decay half-lives of the nuclei. Results: The relative small $\beta$-decay ground state feeding of $^{66}$Fe obtained in this work is at variant to the earlier studies. Spin and parity $1^+$ was assigned to the $^{66}$Co ground state based on the strong ground state feeding in the decay of $^{66}$Fe as well as in the decay of $^{66}$Co. Experimental log(ft) values, $\gamma$-ray deexcitation patterns and energies of excited states were compared to Monte Carlo Shell Model calculations. Based on this comparison, spin and parity assignments for the selected number of low-lying states in the $^{66}$Mn to $^{66}$Ni chain were proposed. Conclusions: The $\beta$-decay chain starting $^{66}$Mn towards $^{66}$Ni, crossing $N=40$, evolves from deformed nuclei to sphericity...

New insights into triaxiality and shape coexistence from odd-mass Rh109

Rapid shape evolutions near A = 100 are now the focus of much attention in nuclear science. Much of the recent work has been centered on isotopes with Z <= 40, where the shapes are observed to transition between near-spherical to highly deformed with only a single pair of neutrons added. At higher Z, the shape transitions become more gradual as triaxiality sets in, yet the coexistence of varying shapes continues to play an important role in the low-energy nuclear structure, particularly in the odd-Z isotopes. This work aims to characterize competing shapes in the triaxial region between Zr and Sn isotopes using ultrafast timing techniques to measure lifetimes of excited states in the neutron-rich nucleus Rh-109. The measurements confirm the persistence at higher Z of similarly large deformations observed near Z = 40. Moreover, we show that new self-consistent mean-field calculations, with proper treatment of the odd nucleon, are able to reproduce the coexisting triaxial and highly deformed configurations revealing, for the first time, the important contribution of the unpaired nucleon to these different shapes based on the blocking of specific single-particle orbitals.

Trait-based ecology of terrestrial arthropods.

ABSTRACTIn focusing on how organisms' generalizable functional properties (traits) interact mechanistically with environments across spatial scales and levels of biological organization, trait‐based approaches provide a powerful framework for attaining synthesis, generality and prediction. Trait‐based research has considerably improved understanding of the assembly, structure and functioning of plant communities. Further advances in ecology may be achieved by exploring the trait–environment relationships of non‐sessile, heterotrophic organisms such as terrestrial arthropods, which are geographically ubiquitous, ecologically diverse, and often important functional components of ecosystems. Trait‐based studies and trait databases have recently been compiled for groups such as ants, bees, beetles, butterflies, spiders and many others; however, the explicit justification, conceptual framework, and primary‐evidence base for the burgeoning field of ‘terrestrial arthropod trait‐based ecology’ have not been well established. Consequently, there is some confusion over the scope and relevance of this field, as well as a tendency for studies to overlook important assumptions of the trait‐based approach. Here we aim to provide a broad and accessible overview of the trait‐based ecology of terrestrial arthropods. We first define and illustrate foundational concepts in trait‐based ecology with respect to terrestrial arthropods, and justify the application of trait‐based approaches to the study of their ecology. Next, we review studies in community ecology where trait‐based approaches have been used to elucidate how assembly processes for terrestrial arthropod communities are influenced by niche filtering along environmental gradients (e.g. climatic, structural, and land‐use gradients) and by abiotic and biotic disturbances (e.g. fire, floods, and biological invasions). We also review studies in ecosystem ecology where trait‐based approaches have been used to investigate biodiversity–ecosystem function relationships: how the functional diversity of arthropod communities relates to a host of ecosystem functions and services that they mediate, such as decomposition, pollination and predation. We then suggest how future work can address fundamental assumptions and limitations by investigating trait functionality and the effects of intraspecific variation, assessing the potential for sampling methods to bias the traits and trait values observed, and enhancing the quality and consolidation of trait information in databases. A roadmap to guide observational trait‐based studies is also presented. Lastly, we highlight new areas where trait‐based studies on terrestrial arthropods are well positioned to advance ecological understanding and application. These include examining the roles of competitive, non‐competitive and (multi‐)trophic interactions in shaping coexistence, and macro‐scaling trait–environment relationships to explain and predict patterns in biodiversity and ecosystem functions across space and time. We hope this review will spur and guide future applications of the trait‐based framework to advance ecological insights from the most diverse eukaryotic organisms on Earth.

Empirical study of the shape evolution and shape coexistence in Zn, Ge and Se isotopes

The spectra of the isotopes of Zn, Ge and Se in the A=60–80 region of the nuclear landscape display interesting spectral variations with N and Z. At first we study these structures empirically. The state-wise deformation status of each isotope is deduced using the power index formula. The average value of the power index displays the variation with neutron number N. The linear plot of B(E2,01+→21+) versus [1/E(21+)] for a given Z gives further information on the spectral variation with N. The level energy spectra are used to study the role of the excited bands in the phase transitions and the possible shape co-existence. The common spectral features of the three isotopic chains and some unique features are pointed out from our study and the role of the Nilsson single particle orbits is discussed. A comparison with recent works for Ge and Se isotopes reveals the importance of our empirical studies vis-à-vis the high efficiency experiments and different theoretical interpretations of the shape changes with N and Z and spin.

Shape evolution and coexistence in neutron-deficient Nd and Sm nuclei

The evolution of shapes and low-energy shape coexistence is analyzed in neutron-deficient Nd and Sm nuclei, using a five-dimensional quadrupole collective Hamiltonian (5DCH). Deformation energy surfaces, calculated with the relativistic energy density functional PC-PK1 and a separable finite-range pairing interaction, exhibit a transition from spherical shapes near $N=80$, to $\gamma-$soft shapes, and to prolate deformed minima in lighter isotopes. The corresponding 5DCH model calculation, based on the self-consistent mean-field potentials, reproduces the empirical isotopic trend of characteristic collective observables, and predicts significantly different deformations for the first two $0^+$ states in the $N=74$ isotones $^{134}$Nd and $^{136}$Sm. In addition to bands based on the triaxial $\gamma-$soft ground state, in excellent agreement with data, the occurrence of a low-energy rotational band is predicted, built on the prolate deformed ($\beta\sim0.4$) excited state $0^+_2$.

Pseudospin Symmetry and Microscopic Origin of Shape Coexistence in the ^{78}Ni Region: A Hint from Lifetime Measurements.

Lifetime measurements of excited states of the light N=52 isotones ^{88}Kr, ^{86}Se, and ^{84}Ge have been performed, using the recoil distance Doppler shift method and VAMOS and AGATA spectrometers for particle identification and gamma spectroscopy, respectively. The reduced electric quadrupole transition probabilities B(E2;2^{+}→0^{+}) and B(E2;4^{+}→2^{+}) were obtained for the first time for the hard-to-reach ^{84}Ge. While the B(E2;2^{+}→0^{+}) values of ^{88}Kr, ^{86}Se saturate the maximum quadrupole collectivity offered by the natural valence (3s, 2d, 1g_{7/2}, 1h_{11/2}) space of an inert ^{78}Ni core, the value obtained for ^{84}Ge largely exceeds it, suggesting that shape coexistence phenomena, previously reported at N≲49, extend beyond N=50. The onset of collectivity at Z=32 is understood as due to a pseudo-SU(3) organization of the proton single-particle sequence reflecting a clear manifestation of pseudospin symmetry. It is realized that the latter provides actually reliable guidance for understanding the observed proton and neutron single particle structure in the whole medium-mass region, from Ni to Sn, pointing towards the important role of the isovector-vector ρ field in shell-structure evolution.