Dy Nuclei Research Articles

An Investigation into Properties for (_66^156)Dy Isotope Using IBM-1 and IVBM Model

Abstract: The (_66^156)Dy isotopes in the O (6) region were investigated. The positive ground-state band of (_66^156)Dy nuclei was calculated using the interacting boson model ‎(IBM-1) and the interacting vector boson model (IVBM). The negative parity band energies of the above isotope were calculated using (IVBM) only. We plotted the ratios ((E(I+2))/(〖E(2〗_1^+)), (E(I+2))/(E(I)),r(((I+2))/I)) and the E-GOS curve as a function of the spin (I) to investigate the properties of the yrast band. Accordingly, the best-fit values of the parameters were used to construct the Hamiltonian, and the electromagnetic transition probability B(E2) of this nucleus was determined. Theoretical energy levels of dysprosium-156 isotope with a neutron number N = 90 and spin parity up to 〖30〗_1^+ were obtained using the MATLAB-20 simulation program. A comparison of these calculated energy levels with the corresponding experimentally measured ones shows a good agreement. The results also ‎draw our attention to the fact that the nucleus of interest deforms and exhibits gamma-instability ‎properties. Keywords: Dysprosium Isotopes, Even-even nuclei, Interacting Boson Model-1, Interacting Vector Boson Model, Negative parity, Yrast band. Abbreviations and Acronyms, IBM: Interacting Boson Model, IVBM: Interacting Vector Boson Model, U(5): Spherical limit, SU(3): Axially deformed shape limit O(6): γ-unstable limit, SP(12; R): the non-compact symplectic group.

Description of intruder levels in the 162,164,166Dy nuclei by two different algebraic approaches

In this paper, we tried to describe both normal and intruder levels of the ground and first excited beta and gamma rotational bands of 162,164,166Dy deformed nuclei in the framework of the interacting boson model. A normal Hamiltonian of SU(3) dynamical symmetry limit is extended by adding a 2p-2 h excitation term. Also, the results are compared with the predictions of the partial dynamical symmetry for these levels of considered nuclei. The results show that, this extension removes the degeneracy suggested by the pure SU(3) symmetry and makes satisfactory agreement with the experimental counterparts for the energy levels, too. Also, a comparison between the results of this extended formalism and partial dynamical symmetry shows the advantages of the first one in the description of intruder levels, whereas the latter, makes exact results for the normal energy levels of beta and gamma energy bands. The predictions of pure SU(3), partial dynamical symmetry SU(3) and mixed formalism for different quadrupole transition rates between normal and intruder levels of this nucleus are compared with the predictions of pseudo-SU(3) model and the advantages of each model have explained in detail.

Photon strength functions, level densities, and isomeric ratio in Er168 from the radiative neutron capture measured at the DANCE facility

Background: The statistical approach is usually applied for the description of electromagnetic decay of the nucleus with the exception of the lowest excitation energies as well as for the calculation of the interaction of photons with nuclei, in particular the reaction cross sections. This concept employs nuclear level density (NLD) and photon strength functions (PSFs).Purpose: While PSFs and NLD of some well-deformed rare-earth nuclei were measured by several methods, sometimes with conflicting results, the PSFs of $^{168}\mathrm{Er}$ were addressed only by $(\ensuremath{\gamma},{\ensuremath{\gamma}}^{\ensuremath{'}})$ experiments. On the other hand, the low-lying levels of $^{168}\mathrm{Er}$ are well studied, including the isomeric state at 1094 keV, which enables various tests of the statistical approach.Methods: The $\ensuremath{\gamma}$ rays following radiative neutron capture on a $^{167}\mathrm{Er}$ sample were measured with the highly segmented $\ensuremath{\gamma}$-ray calorimeter Detector for Advanced Neutron Capture Experiments at the Los Alamos Neutron Science Center. The $\ensuremath{\gamma}$-ray energy spectra for different multiplicities (multistep cascade, or MSC, spectra) were gathered for many $s$-wave resonances of both possible spins. Moreover, we were able to detect the decay of the short-lived isomer and deduce the isomeric ratio for a few resonances.Results: Analysis of the MSC spectra within the statistical model enabled us to draw conclusions about dipole PSFs, in particular on the properties of the scissors mode, and NLD. The spectra can be well reproduced with phenomenological PSFs models but not with any of several models based on quasiparticle random-phase approximation (QRPA) calculations with different interactions. We showed that nonstatistical effects in feeding of the isomeric state play a role up to excitation energies of at least about 2 MeV.Conclusions: Deduced parameters of the scissors mode were found to be similar to those of neighbor well-deformed even-even Gd and Dy nuclei. Models like that of Kadmenskij, Markushev, and Furman (KMF) or like the modified generalized Lorentzian (MGLO) model provide a good description of experimental spectra. In contrast to several previous analyses of well-deformed rare-earth isotopes, we were able to match the experimental isomeric ratio with statistical model simulations.

Updated heat capacities of \(^{161-164}\)Dy nuclei

This work presents the updated heat capacities of \(^{161-164}\)Dy nuclei in the nuclear temperature region from 0 to 1 MeV. The updated heat capacities are obtained within the canonical ensemble method making use of the most recent and recommended experimental nuclear level density (NLD) data together with those calculated within the back-shifted Fermi gas (BSFG) model with energy-dependent parameters. By comparing the updated heat capacities with the un-updated ones, which are obtained by using the old experimental NLD data and the BSFG with energy-independent parameters, we found that the updated and un-updated heat capacities are almost identical at low temperature, but differ from each others at high temperature. This discrepancy can be interpreted by the damping of nuclear shell structure with increasing the excitation energy. Besides, we observe that the S-shape in the updated heat capacities is much more pronounced in even-even Dy isotopes than in even-odd ones, whereas the un-updated heat capacities do not clearly exhibit this S-shape. Therefore, the updated heat capacities should provide a more convincing evidence for the signature of pairing phase transition in nuclear systems.

Spectroscopic and Electrochemical Analyses for Dysprosium Complexes In Potassium Bis(trifluoromethylsulfonyl)amide Melts

The coordination states of multivalent dysprosium complexes of potassium bis(trifluoromethylsulfonyl) amide (K[NTf2]) were investigated by Raman spectroscopy. The concentration dependence of the deconvoluted Raman spectra was investigated for 0.23−0.45 mol kg−1 Dy(III), and a mixed sample of Dy(II)/Dy(III) (molar ratio 1/3), in K[NTf2]. Using conventional analysis, the solvation number, n, of the dysprosium complexes was determined to be 4.12 for Dy(II) and 5.09 for Dy(III). The electrochemical behavior of [DyIII(NTf2)5]2– in K[NTf2] melts was also investigated in this study. It is speculated that the first reduction peak at approximately +2.24 V probably corresponds to the formation of [DyII(NTf2)4]2–. Electrochemical analysis revealed that the reduction peak of [DyIII(NTf2)5]2– at approximately +0.81 V at 483 K is based on an electrodeposition reaction from [DyIII(NTf2)5]2– to Dy(0). The diffusion coefficient and activation energy of [DyIII(NTf2)5]2– in K[NTf2] melts were measured in the range 473–493 K by semi-integral and semi-differential analyses. Furthermore, the nucleation behavior of [DyIII(NTf2)5]2– was evaluated using chronoamperometry. The results indicated that the nucleation mechanism of Dy nuclei changed from instantaneous to progressive nucleation when the overpotential became more negative than the deposition potential of Dy(0). The electrodeposits were identified as mostly the metallic state by X-ray photoelectron spectroscopy.

On the symmetry energy and deformed magic number at N = 100 in rare earth nuclei

The exotic nuclei are a fertile source of new features of nuclear structure. The evolution of new shell gaps accompanied by quenching of classical magic numbers is one of the marked features in these nuclei. These studies aimed to search and explore such behavior and find major significance on both the experimental and theoretical fronts. Here, we present an inclusive study and significant evidence of the existence of deformed shell closure at the neutron number N = 100 in rare earth Nd, Sm, Gd and Dy nuclei, obtained from the persistence of a peak in the analysis of symmetry energy and its bulk and surface components, over the isotopic chains of these nuclei, within the coherent density fluctuation model (CDFM). The relativistic mean field densities, employing the NL3 and recently developed IOPB-I parameter sets, have been used as an input within CDFM. This result is in excellent agreement with our earlier prediction of deformed magic shell closure at N = 100 in rare earth nuclei [Satpathy et al (2004 J. Phys. G 30 771); Ghouri et al (2012 Phys. Rev. C 85 064327)] and further reinforced by the experimental confirmation of deformed magicity at N = 100 in 162Sm and 164Gd nuclei [Patel et al (2014 Phys. Rev. Lett. 113 262502)]. An important consequence of the work is that N = 100 isotopes of these nuclei can serve as a waiting point in r-process nucleosynthesis and influence the heavy nuclei formation in astrophysical entities.

Effect of temperature on the volume and surface contributions in the symmetry energy of rare earth nuclei

The effect of temperature on the volume and surface contributions in the nuclear symmetry energy and their ratio in the isotopic chains of rare earth Nd, Sm, Gd, and Dy nuclei with N = 82-126 is analyzed in the framework of coherent density fluctuation model (CDFM). The weight function of nuclei, within CDFM, are calculated by using the densities from the temperature-dependent relativistic mean-field (RMF) model. Firstly, we discuss the temperature-dependence of bulk properties of nuclei, within RMF model, such as binding energy, deformation parameter, charge radius and isotopic shift along with comparison with the available experimental data at temperature T=0 MeV. Further, we discuss the thermal evolution of symmetry energy and its volume and surface components. At T=0 MeV, the persistence of a peak in the symmetry energy and components at neutron number N=100 shows the manifestation of deformed shell closure in consonance with an earlier study by one of us [L. Satpathy, S.K. Patra, J. Phys. G 30 (2004) 771; S.K. Ghorui, et al., Phys. Rev. C 85 (2012) 064327]. However, the scenario changes with rise in temperature and the magnitude of peak decreases at higher temperatures. At T=3 MeV, the peak disappears which may be due to shape change in addition to quenching of shell effects since the quadrupole deformation parameter β2 decreases with an increase in temperature and nuclei become spherical at T=3 MeV. It indicates that behavior of symmetry energy is closely related to the deformation/shape of the nuclei. We have also discussed the values of volume symmetry energy, surface symmetry energy and their ratio which are in consonance with available experimental data.

Critical Point of the 152Sm, 154Gd, and 156Dy Isotones

The even—even rare-earth nuclei in U(5)—SU(3) region at neutron number (N) = 90, have been systematically studied using the Bohr—Mottelson Model (BM), Interacting Vector Boson Model (IVBM), and Interacting Boson Model (IBM). The positive ground-state band (GSB) of 152Sm, 154Gd, and 156Dy nuclei has been calculated by using BM, IVBM, and IBM, while the negative-parity band (NPB) of those nuclei are calculated by BM and IVBM only. To determine the intermediate structure, the ratio (r(I + 2)/I) and E-GOS curve (E-Gamma Over Spin) as a function of the spin (I) have been drawn. In the IBM, the calculated reduced B(E2) transition probabilities of the GSB in the 152Sm, 154Gd, and 156Dy nuclei are analyzed and compared to the prediction of vibrational U(5) and rotational SU(3) limits. In the Sm—Dy nuclei with N = 90, the U(5)—SU(3) IBM potential energy surfaces (PES’s) are analyzed and evolve from spherical to deformed shapes with increasing the boson number. The critical phase transition points are identified in the space of model parameters and 152Sm,154Gd, and 156Dy nuclei have been found to be close to critical points.

Systematic study of high-K isomers in the midshell Gd and Dy nuclei

High-K isomers are well known in the rare-earth region and provide unique access to the high spin structures of the nuclei. With the current interest in the study of neutron-rich rare-earth nuclei at Radioactive Ion Beam (RIB) facilities, we present here theoretical results of the band structures of neutron-rich Gd and Dy nuclei, including the high K-isomers. Apart from the already known K-isomers, we predict some more K-isomers and these are suggested for future studies at RIB facilities. Self-consistent Deformed Hartree-Fock and Angular Momentum Projection theories are used to get the intrinsic structures, band-spectra and electromagnetic transitions probabilities of the ground band as well as bands based on isomers.

Description of the Ba–Dy(N = 92) nuclei in the interacting boson model

Interacting Boson Model (IBM -1) has been used to study the energy levels and [Formula: see text] transition rates in Ba–Dy ([Formula: see text]) isotones. A simplified Hamiltonian is used which is written in the creation and annihilation form and for each nucleus, by fitting the selected experimental energy levels and [Formula: see text] transition rates with the calculated ones to get the best model parameters. Using the (IBM) Hamiltonian with an intrinsic state formalism, the potential energy surfaces (PES) for even–even Ba–Dy nuclei have been obtained and the contour plot of PES show that the shape phase transitions from spherical [Formula: see text] to deformed shape [Formula: see text] has been determined for the [Formula: see text], while [Formula: see text]Ce, [Formula: see text]Nd, [Formula: see text]Sm, [Formula: see text]Gd and [Formula: see text]Dy nuclei are deformed and have rotational-like characters. The behavior of energy and [Formula: see text] ratios in the ground state band are examined.

Role of neutrons and protons in entropy, spin cut off parameters, and moments of inertia

The nuclear level densities, spin cut off parameters, and entropies have been extracted in ${}^{116\ensuremath{-}119}$Sn and ${}^{162,163}$Dy nuclei using superconducting theory, which includes nuclear pairing interaction. The results agree well with the recent data obtained from experimental level densities by the Oslo group for these nuclei. Also, the entropy excess ratio proposed by Razavi et al. [R. Razavi, A.N. Behkami, S. Mohammadi, and M. Gholami, Phys. Rev. C 86, 047303 (2012)] for a proton and neutron as a function of nuclear temperature have been evaluated and are compared with the spin cut off excess ratio. The role of the neutron (proton) system is well determined by the entropy excess ratio as well as the spin cut off excess ratio. The moment of inertia for even-odd and even-even nuclei are also compared. The moment of inertia carried by a single hole is smaller than the single particle moment of inertia.

CHARACTERIZATION OF BACKBENDING IN EVEN–EVEN ISOTOPES OF 164–174Hf AND 154–164Dy NUCLEI BY A MODIFIED PHENOMENOLOGICAL MODEL

A modified phenomenological model is used to calculate nuclear energy levels and describe successfully the backbending of the moment of inertia for the ground state bands in even–even isotopes of Hf and Dy nuclei. The model is a combination of the Myers and Swiatecki model with variable moment inertia (VMI) model. Since the Myers and Swiatecki model has a deviation from experimental energies in which it takes into account pairing effect with constant moment of inertia, in the rotation of nuclei, the Coriolis force acts to de-pair the nucleons pair and align their angular momentum with nuclei total angular momentum, thus Coriolis force increasing and decrease the rotational energy. So, the moment of inertia varies with the angular momentum. Therefore, we modified this model by adding a term to make the moment of inertia vary with angular momentum in the same manner of the VMI model which has a term added to the rotational energy equation. The modified model fits remarkably with the experimental observation and other models in many cases with the use of few parameters especially in rotational nuclei regions similar to Hf and Dy nuclei.

Microscopic explanation of the shape-phase transition atN=88–90and theZ=64subshell effect for Ba–Dy

Background: The shape-phase transition at $N$ $=$ 88--90, and the role of $Z$ $=$ 64 subshell effect therein has been a subject of study on empirical basis and in the context of the ${N}_{p}$N${}_{n}$ scheme, but a microscopic view of the same has been lacking.Purpose: A microscopic view of the $N$ $=$ 88--90 shape-phase transition is developed. The $Z$ $=$ 64 subshell effect is viewed in terms of the Nilsson single-particle orbitals in this region.Method: The dynamic pairing plus quadrupole model is employed to predict the occupation probabilities of the neutron and proton deformed, single-particle orbitals. The nuclear structure of Ba--Dy ($N$ > 82) nuclei is studied and the shape equilibrium parameters derived.Results: The filling of neutron orbitals at $N$ $=$ 86, 88, and 90 plays an important role in the shape-phase transition. The filling of the proton Nilsson orbitals of varying slopes leads to the variation of nuclear structure with varying $Z$, which leads to the $Z$ $=$ 64 subshell effect, which disappears at $N=90$.Conclusions: The effect of the $n$-$p$ interaction of the \ensuremath{\pi}${h}_{11/2}$ and \ensuremath{\nu}${h}_{9/2}$ orbitals, along with the contribution of the \ensuremath{\nu}${i}_{13/2}$ orbital leads to the shape-phase transition at $N=88\ensuremath{-}90$. The slopes of proton Nilsson orbitals explain the $Z$ $=$ 64 subshell effect.

Level density and thermodynamic properties of dysprosium isotopes

${}^{163,164}$Dy nuclei have been measured by use of the Oslo method on data from pick-up ${(}^{3}\mathrm{He},\ensuremath{\alpha})$ and inelastic scattering ${(}^{3}\mathrm{He}{,}^{3}\phantom{\rule{-0.16em}{0ex}}{\mathrm{He}}^{\ensuremath{'}})$ reactions, respectively. The level densities for these dysprosium isotopes together with previously measured ${}^{160--162}$Dy are extracted in the region below the neutron binding energy. Thermodynamic properties are deduced within both micro-canonical and canonical ensemble theories. A phase transition from the pair-correlated state at low energies to a less correlated or uncorrelated state is studied in both ensembles. It is investigated whether the temperature of the nucleus is constant or a varying function of excitation energy. It is found that above an excitation energy of 3 MeV the temperature of all five dysprosium nuclei have a constant value within the experimental uncertainties. The impact of a constant-temperature level density versus a Fermi gas level density is discussed with respect to the canonical heat capacity.

Determination of (n,γ) cross sections in the rare-earth region using the surrogate ratio method

The surrogate ratio method was used to convert experimentally determined relative {gamma}-decay probabilities for excited {sup 171}Yb and {sup 161}Dy nuclei, populated using ({sup 3}He, {sup 3}He{sup '}) and ({sup 3}He, {alpha}) reactions, into neutron-induced {gamma}-decay cross sections in an equivalent neutron energy range of 165-465 keV. The relative {gamma}-decay probabilities were measured using the CACTUS array at the Oslo Cyclotron Laboratory and were found to agree with the ratio of neutron-induced {gamma}-decay cross sections for the same compound nuclei over the range of excitation energies measured. No significant entrance-channel effects on the extracted (n,{gamma}) cross sections were observed. The cross sections obtained using the surrogate ratio method were compared to directly measured neutron-capture cross sections and found to agree within the total estimated uncertainty over the range of equivalent neutron energies measured.

Publisher's Note: Negative-parity states and β decays in odd Ho and Dy nuclei withA=151,153[Phys. Rev. C 77, 034303 (2008)

Publisher's Note: Negative-parity states and β decays in odd Ho and Dy nuclei with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mn>151</mml:mn><mml:mo>,</mml:mo><mml:mn>153</mml:mn></mml:mrow></mml:math>[Phys. Rev. C 77, 034303 (2008)

The desynaptic (dy) and desynaptic1 (dsy1) mutations in maize (Zea mays L) cause distinct telomere-misplacement phenotypes during meiotic prophase.

During meiotic prophase, telomeres actively attach themselves to the nuclear envelope and cluster in an arrangement called the bouquet. The bouquet is unique to meiosis, highly conserved, and thought to facilitate homologous chromosome synapsis. Analy sis of three-dimensional fluorescence in situ hybridization (3-D FISH) image data has been employed to characterize the bouquet in fixed pollen mother cells of maize (Zea mays L.). In order to examine the function of the bouquet further, several meiotic mutants were screened for telomeric defects using 3-D FISH as an assay. Two mutants, desynaptic (dy) and desynaptic1 (dsy1), were found to exhibit novel telomere-misplacement phenotypes. In both cases, the telomere-associated mutant phenotypes occurred prior to what was previously reported as the earliest affected stage. Three alleles of the desynaptic1 mutation (dsy1-1, dsy1-9101, and dsy1-9307) resulted in a partial bouquet phenotype at the zygotene stage of meiotic prophase. By contrast, dy nuclei contained apparently normal bouquets, but then resulted in a premature intranuclear localization of telomeres at the pachytene stage, when telomeres normally disperse but remain attached to the nuclear envelope. The dsy1 mutation is known to impair the fidelity and progression of homologous synapsis, whereas the dy mutation is known to reduce recombination rates. If the telomere misplacements are primary defects of these mutants, then these data would be consistent with the hypothesis that meiotic telomeres have at least two separable functions, one involving proper homologous chromosome synapsis at the bouquet stage and another involving post-bouquet cross-over control.

Spin dependence of the shape of even-even nuclei within the Davydov-Chaban model

Within a model of a nonaxial even-even nucleus soft in β vibrations, the shape parameters of the 154Gd, 156,158,160Dy, 164,168Er, 168Yb, 176Hf, and 180W nuclei are calculated in the quadrupole approximation as functions of the excited-state spin.

Alpha energy distribution as a probe for the feeding of ND and SD bands in 151,152Dy nuclei

The study of the α-particle energy distributions associated with ND and SD states in 151,152Dy has been carried out. The Dy isotopes were produced in the reaction 37Cl +123Sb at 191 MeV via the (α5n) and (α4n) channels, respectively. In 151Dy the α-particle energy distributions associated to ND and SD are very different from each other, both at the low and high energy sides inducing a difference of 3 MeV in the α-particle mean energy. In 152Dy the situation is different; the α-particle spectral shapes are similar and a difference in the α-particle mean energy of only 0.7 MeV is deduced. A description in terms of energy localization of entry states is given.

Investigation of the backbending region of heavy Dy isotopes via incomplete fusion

The interpretation of the first backbending point in deformed rare earth nuclei as a crossing of the ground state band with a rotational band built on an aligned i 13 2 neutron pair is rather well established. However, in terms of such a two-band mixing model one cannot understand the exclusive population of yrast states in and above the backbending point observed in Coulomb excitation experiments of neutron-rich, stable rare earth nuclei. To investigate this problem in more detail for the heavy Dy nuclei 160, 162Dy, an Incomplete Fusion experiment has been performed at the MPI für Kernphysik in Heidelberg in order to investigate its suitability for studying these n-rich nuclei. A cross section of σ ≈ 150 mbarn for producing the nuclei with a spin distribution covering the first backbending region could be established.