Er Isotopes Research Articles

Photonuclear Reaction Rates of 157,159Ho and 163,165Tm and Their Impact in the γ-process

Reliable photonuclear reaction rates in stellar conditions are essential for understanding the origin of the heavy stable neutron-deficient isotopes between 74Se and 196Hg, i.e., p-nuclei. However, many reaction rates of relevance still have to rely on the Hauser–Feshbach (HF) model due to the rarity of experimental progress. One such case is in the mass range of 160 for Dy, Er, Ho, and Tm isotopes. In this work we attempt to constrain the HF model in the TALYS package by reproducing the available experimental data on 160Dy(p, γ)161Ho and 162Er(p, γ)163Tm in the A ∼ 160 mass region, and examine the effects of level density, gamma strength function, and the optical model potential. The constrained model then allows us to calculate the reaction rates of 157,159Ho(γ, p) and 163,165Tm(γ, p) for the γ-process nucleosynthesis in a carbon-deflagration model for Type Ia supernovae. Our recommended rates differ from the JINA REACLIB by more than one order of magnitude in the temperature range 2–3 GK. This results in changes in the final abundance of p-nuclei in the A ∼ 160 mass range by −5.5% to 3% from those with JINA, which means that the uncertainty of (γ, p) reactions is not predominant for the synthesis of these nuclei.

Structures of terminating bands in Er isotopes

The configurations of terminating bands in Er isotopes are investigated using the unpaired cranked Nilsson-Strutinsky (CNS), and the paired cranked Nilsson-Strutinsky-Bogoliubov (CNSB) models and also, new CNS(B) formalism. The calculated excitation energies of the bands have been compared with the experimental findings, and good agreements are observed. Our calculations show that the CNS(B) approach successfully is in agreement CNSB predictions and experimental results. Some systematics of terminating bands in erbium isotopes are also discussed.

The first and second crossings in low-lying rotational bands of Er isotopes: A systematic study

Essential understanding about the structure of rotating nuclei has come from the study on the band crossings which are often associated with the alignment of a pair of quasiparticles. In this work, the first and second discontinuities in the low-lying rotational bands of [Formula: see text]Er nuclei have been investigated systematically, for the first time, within the paired cranked Nilsson–Strutinsky–Bogoliubov (CNSB) framework. Our calculations show these irregularities are related to the high-j intruder [Formula: see text] neutron and [Formula: see text] proton alignment, which is consistent with the previous studies within the cranked shell model (CSM) approach. A comparison was made with the experimental data where available, and good agreement is observed.

Erbium-Doped LiYF4 as a Potential Solid-State Frequency Reference: Eligibility and Spectroscopic Assessment

Time and frequency metrology is a key enabler for both forefront science and innovation. At the moment, atomic frequency standards (AFSs) are based on atoms either in the vapor phase or trapped in magneto-optical lattices in a vacuum. Finding a solid-state material that contains atoms suitable to be used as a frequency reference would be an important step forward in the simplification of the setup of AFSs. Lanthanide-doped inorganic crystals, such as Er-doped LiYF4, have been studied for several decades, and their intrashell 4f transitions are usually identified as ultra-narrow. Nevertheless, a systematic characterization of these transitions and their linewidths with a correlation to the dopant’s concentration and isotopic purity at low temperatures is lacking. In this work, we studied Er-doped LiYF4 as a potential benchmark material for solid-state frequency references. We chose Er as it has a set of transitions in the telecom band. The influence of Er concentrations and isotope purity on the transition linewidth was systematically studied using high-resolution optical spectroscopy at 5 K. The results indicate that the material under study is an interesting potential candidate as a solid-state frequency reference, having transition linewidths as low as 250 MHz at ~1530 nm.

Enhanced Schiff and magnetic quadrupole moments in deformed nuclei and their connection to the search for axion dark matter

Deformed nuclei possess enhanced moments violating time reversal invariance ($T$) and parity ($P$). Collective magnetic quadrupole moments (MQM) appear in nuclei with a quadrupole deformation (which have ordinary $T$,$P$-conserving collective electric quadrupole moments). Nuclei with an octupole deformation have a collective electric octupole moment, electric dipole moment (EDM), Schiff moment and MQM in the intrinsic frame which rotates with the nucleus. In a state with definite angular momentum in the laboratory frame, these moments are forbidden by $T$ and $P$ conservation, meaning their expectation values vanish due to nuclear rotation. However, nuclei with an octupole deformation have doublets of close opposite parity rotational states with the same spin, which are mixed by $T$,$P$-violating nuclear forces. This mixing polarises the orientation of the nuclear axis along the nuclear spin, and all moments existing in the intrinsic frame appear in the laboratory frame (provided the nuclear spin $I$ is sufficiently large to allow such a moment). Such a mechanism produces enhanced $T$,$P$-violating nuclear moments. This enhancement also takes place in nuclei with a soft octupole vibration mode. In this paper we present updated estimates for the enhanced Schiff moment in isotopes of Eu, Sm, Gd, Dy, Er, Fr, Rn, Ac, Ra, Th, Pa, U, Np and Pu in terms of the CP-violating $\pi$-meson--nucleon interaction constants $\bar{g}_{0},\bar{g}_{1}$ and $\bar{g}_{2}$, the QCD parameter $\bar{\theta}$ and the quark chromo-EDMs. The implications of the enhanced $T$,$P$-violating moments to the search for axion dark matter in solid state experiments are also discussed, with potential alternative candidate compounds in which we may expect enhanced effects suggested.

The role of the orbitals to construct a terminating state of the A ∼ 160 mass region

In a terminating band, the nucleon number changes in a specific orbital not only lead to deformation changes of the band but also the type of the band termination is impressed. In this work, we consider the role of the orbitals near the Fermi surface in some of the nuclei with [Formula: see text]; such as Dy ([Formula: see text]), Ho ([Formula: see text]) and Er ([Formula: see text]) isotopes. Our results show that the contribution of the number of the proton holes in the core is very effective to energy cost at the end of the rotational bands and then, termination type. Change the number of the protons on high-[Formula: see text] orbitals ([Formula: see text]) in [Formula: see text] isotones and also, the neutrons on high-[Formula: see text] [Formula: see text] and low-[Formula: see text] [Formula: see text] neutron orbitals do not affect in the type of termination. They cause only to move up or down the terminating bands in energy.

Investigating the Nuclear Properties of 162-172 Er Isotopes using IBM-1, SEF, and NEE

The energy levels of the ground state band (GSB), , and γ-bands for 162-172Er isotopes are calculated in this work by adopting the Interacting Boson Model (IBM-1), the Semi-Empirical Formula (SEF) and the New Empirical Equation (NEE). The GSB, , and γ-bands results revealed that IBM-1, SEF, NEE, and the available experimental data are all in agreement with certain variations. The NEE is more compatible with the experimental data than the IBM-1 and SEF calculations. This study demonstrates that the SEF and NEE equations are able to describe the energy spectra of Er isotopes in comparison to IBM-1. The Er isotopes exhibit rotational SU(3) transition behavior.

Statistical correlations of nuclear quadrupole deformations and charge radii

Shape deformations and charge radii, basic properties of atomic nuclei, are influenced by both the global features of the nuclear force and the nucleonic shell structure. As functions of proton and neutron number, both quantities show regular patterns and, for nuclei away from magic numbers, they change very smoothly from nucleus to nucleus. In this paper, we explain how the local shell effects are impacting the statistical correlations between quadrupole deformations and charge radii in well-deformed even-even Er, Yb, and Hf isotopes. This implies, in turn, that sudden changes in correlations can be useful indicators of underlying shell effects. Our theoretical analysis is performed in the framework of self-consistent mean-field theory using quantified energy density functionals and density-dependent pairing forces. The statistical analysis is carried out by means of the linear least-square regression. The local variations of nuclear quadrupole deformations and charge radii, explained in terms of occupations individual deformed Hartree-Fock orbits, make and imprint on statistical correlations of computed observables. While the calculated deformations or charge radii are, in some cases, correlated with those of their even-even neighbors, the correlations seem to deteriorate rapidly with particle number. The statistical correlations between nuclear deformations and charge radii of different nuclei are affected by the underlying shell structure. Even for well deformed and superfluid nuclei for which these observables change smoothly, the correlation range usually does not exceed $\Delta N=4$ and $\Delta Z=4$, i.e., it is rather short. This result suggests that the frequently made assumption of reduced statistical errors for the differences between smoothly-varying observables cannot be generally justified.

Correction to: Study of Back Bending in 157,158Er Isotopes by Using Electromagnetic Reduced Transition Probabilities

Correction to: Study of Back Bending in 157,158Er Isotopes by Using Electromagnetic Reduced Transition Probabilities

Origin of the metamagnetic transitions in Y1−xErxFe2(H,D)4.2 compounds

The structural and magnetic properties of Y1−xErxFe2 intermetallic compounds and their hydrides and deuterides Y1−xErxFe2H(D)4.2 have been investigated using X-ray diffraction and magnetic measurements under static and pulsed magnetic field up to 60 T. The intermetallics crystallize in the C15 cubic structure (Fd-3m space group), whereas corresponding hydrides and deuterides crystallize in a monoclinic structure (Pc space group). All compounds display a linear decrease of the unit cell volume versus Er concentration; the hydrides have a 0.8% larger cell volume compared to the deuterides with same Er content. They are ferrimagnetic at low field and temperature with a compensation point at x = 0.33 for the intermetallics and x = 0.57 for the hydrides and deuterides. A sharp first order ferromagnetic-antiferromagnetic (FM-AFM) transition is observed upon heating at TFM−AFM for both hydrides and deuterides. These compounds show two different types of field induced transitions, which have different physical origin. At low temperature (T < 50 K), a forced ferri-ferromagnetic metamagnetic transition with Btrans1 ≈ 8 T, related to the change of the Er moments orientation from antiparallel to parallel Fe moment, is observed. Btrans1 is not sensitive to Er concentration, temperature and isotope effect. A second metamagnetic transition resulting from antiferromagnetic to ferrimagnetic state is also observed. The transition field Btrans2 increases linearly versus temperature and relates to the itinerant electron metamagnetic behavior of the Fe sublattice. An onset temperature TM0 is obtained by extrapolating TFM−AFM (B) at zero field. TM0 decreases linearly versus the Er content and is 45 ± 5 K higher for the hydrides compared to the corresponding deuteride. The evolution of TM0 versus cell volume shows that it cannot be attributed exclusively to a pure volume effect and that electronic effects should also be considered.

Rotational excitations in rare-earth nuclei: A comparative study within three cranking models with different mean fields and treatments of pairing correlations

High-spin rotational bands in rare-earth Er ($Z=68$), Tm ($Z=69$) and Yb ($Z=70$) isotopes are investigated by three different nuclear models. These are (i) the cranked relativistic Hartree-Bogoliubov (CRHB) approach with approximate particle number projection by means of the Lipkin-Nogami (LN) method, (ii) the cranking covariant density functional theory (CDFT) with pairing correlations treated by a shell-model-like approach (SLAP) or the so called particle-number conserving (PNC) method, and (iii) cranked shell model (CSM) based on the Nilsson potential with pairing correlations treated by the PNC method. A detailed comparison between these three models in the description of the ground state rotational bands of even-even Er and Yb isotopes is performed. The similarities and differences between these models in the description of the moments of inertia, the features of band crossings, equilibrium deformations and pairing energies of even-even nuclei under study are discussed. These quantities are considered as a function of rotational frequency and proton and neutron numbers. The changes in the properties of the first band crossings with increasing neutron number in this mass region are investigated. On average, a comparable accuracy of the description of available experimental data is achieved in these models. However, the differences between model predictions become larger above the first band crossings. Because of time-consuming nature of numerical calculations in the CDFT-based models, a systematic study of the rotational properties of both ground state and excited state bands in odd-mass Tm nuclei is carried out only by the PNC-SCM. With few exceptions, the rotational properties of experimental 1-quasiparticle and 3-quasiparticle bands in $^{165,167,169,171}$Tm are reproduced reasonably well.

Separation of Heavy Lanthanoids by Flash Column Chromatography for Precise Determination of Er and Yb Isotope Compositions in Rock Samples

We present a new column chemistry technique for the quantitative separation of heavy lanthanoids by an ultra‐fine‐grained LN resin (20–50 µm) with a specific emphasis on the purification of Er and Yb for their isotopic analysis. To achieve the quantitative separation of Er and Yb within a reasonable timescale, flash column chromatography was applied, where the column was attached to a newly designed vacuum box system, thus accelerating the elution speed by ten times compared with that of the normal column procedure operated by gravity flow. The recovery yields of Er and Yb were confirmed to be approximately 100%, which is important to suppress the effect of the mass‐independent fractionation of the Er and Yb isotopes during chromatography. Additionally, we have developed precise Er and Yb isotope measurements by thermal ionisation mass spectrometry (TIMS) using multistatic and/or dynamic methods. Moreover, in most cases, the Er and Yb isotope compositions of the measured four terrestrial rock samples were indistinguishable from those of the commercially available Er and Yb Alfa Aesar solutions. The new method presented in this work will be useful for future studies on heavy lanthanoids in various geological materials.

Study of Back Bending in 157,158Er Isotopes by Using Electromagnetic Reduced Transition Probabilities

Electromagnetic reduced transition probabilities B(E2) and B(M1) calculated by using the PSM (Projected Shell Model) code are used to study the back-bending phenomenon in 157,158Er isotopes. As a result, two great drops in the B(E2)/B(M1) ratio were observed in spins 12 ħ and (37/2) ħ for the 158Er and the 157Er isotopes, respectively, which coincident exactly with the inertia change versus rotational frequency in the usual back-bending plots for these isotopes.

Dy, Er, and Yb isotope compositions of meteorites and their components: Constraints on presolar carriers of the rare earth elements

One way to study the original building blocks of the Solar System is to investigate primitive meteorites and their components. Specifically, isolating these meteorites' individual components via sequential acid leaching can reveal isotopically diverse material present in the early Solar System, which can provide new insights into the mixing and transport processes that eventually led to planet formation. Such isotopic differences in the components are likely to be found in heavy rare earth elements, such as dysprosium (Dy), erbium (Er), and ytterbium (Yb), because their isotopes have different nucleosynthetic production pathways and the elements have significant differences in volatility; however, these specific elements have yet to be thoroughly investigated in the field of cosmochemistry. As such, we present the first combined Dy, Er, and Yb isotope compositions of sequential acid leachates from the Murchison meteorite, along with multiple bulk meteorites from different taxonomic classes. This work also presents a new method to separate, purify, and accurately measure Dy isotopes. Here we show that resolved Dy, Er, and Yb isotope variations in most bulk meteorites are due to neutron capture processes. However, Dy and Er isotopic compositions of bulk Murchison and Murchison leachates stem from the additions or depletions of a nucleosynthetic component formed by the s-process, most likely mainstream silicon carbide (SiC) grains. In contrast, the Yb isotope compositions of bulk Murchison and Murchison leachates display either unresolved or relatively small isotope anomalies. The disparate isotopic behavior between Dy-Er and Yb likely reflects their differing volatilities, with Dy and Er condensing/incorporating into the mainstream SiC grains, whereas the less refractory Yb remains in the gas phase during SiC formation. This work suggests that Yb is hosted in a non-SiC presolar carrier phase and, furthermore, that mainstream SiC grains may be the primary source of isotopic variation in bulk meteorites.

Ground-state shape evolution in Er and Yb isotopes

The ground-state shape (phase) evolution in Er and Yb isotopes is manifested in the axially deformed Nilsson mean-field plus extended pairing model. The energy ratio R02+/21+, the odd-even mass differences, the ground-state occupation probabilities of valence nucleon pairs with different angular momenta and the information entropy are calculated. It is shown from these quantities as functions of the quadrupole deformation parameter and the overall pairing interaction strength that the ground-state shape (phase) evolution is mainly driven by the pairing interaction and less affected by the quadrupole deformation, which thus provides a possible origin of the ground-state shape (phase) evolution of these isotopes.

Enhanced collectivity of $\gamma$ vibration in neutron-rich Dy isotopes with $N=108$–$110$

Background: The $\gamma$ vibrational mode of excitation is an acknowledged collective mode in deformed nuclei. The collectivity depends on the details of the shell structure around the Fermi levels, in particular the presence of the orbitals that have the enhanced transition matrix elements of the non-axial quadrupole excitation. Quite recently, a sudden decrease in the excitation energy of the $\gamma$ vibration was observed at RIKEN RIBF for the neutron-rich Dy isotopes at $N=106$. Purpose: In the present work, by studying systematically the microscopic structure of the $\gamma$ vibration in the neutron-rich Dy isotopes with $N=98-114$, we try to understand the mechanism of the observed softening. Methods: The low-frequency modes of excitation in the neutron-rich rare-earth nuclei are described based on nuclear density-functional theory. We employ the Skyrme energy-density functionals (EDF) in the Hartree-Fock-Bogoliubov calculation for the ground states and in the Quasiparticle Random-Phase Approximation (QRPA) for the excitations. Results: The lowering of the excitation energy around $N=106$ is reproduced well by employing the SkM* and SLy4 functionals. We find the similar isotopic dependence of the excitation energy in the neutron-rich Er and Yb isotopes as well. Conclusions: The microscopic framework of the Skyrme-EDF based QRPA describes well the isotopic dependence of the energy of the $\gamma$ vibration in the well-deformed neutron-rich rare-earth nuclei. The strong collectivity at $N=108-110$ is expected as the Fermi level of neutrons lies just among the orbitals that play an important role in generating the collectivity around $N=106$.

Shape vibration and quasiparticle excitations in the lowest0+excited state in erbium isotopes

The ground and first excited 0+ states of the {156-172}Er isotopes are analyzed in the framework of the generator coordinate method. The shape parameter beta is used to generate wave functions with different deformations which together with the two-quasiparticle states built on them provide a set of states. An angular momentum and particle number projection of the latter spawn the basis states of the generator coordinate method. With this ansatz and using the separable pairing plus quadrupole interaction we obtain a good agreement with the experimental spectra and E2 transition rates up to moderate spin values. The structure of the wave functions suggests that the first excited 0+ states in the soft Er isotopes are dominated by shape fluctuations, while in the well deformed Er isotopes the two-quasiparticle states are more relevant. In between both degrees of freedom are necessary .

Skyrme RPA description ofγ-vibrational states in rare-earth nuclei

The lowest γ -vibrational states with Kπ = 2+ γ in well-deformed Dy, Er and Yb isotopes are investigated within the self-consistent separable quasiparticle random-phase-approximation (QRPA) approach based on the Skyrme functional. The energies Eγ and reduced transition probabilities B(E2) γ of the states are calculated with the Skyrme force SV-mas10. We demonstrate the strong effect of the pairing blocking on the energies of γ -vibrational states. It is also shown that collectivity of γ -vibrational states is strictly determined by keeping the Nilsson selection rules in the corresponding lowest 2qp configurations.

Spectral statistics of rare-earth nuclei: Investigation of shell model configuration effect

The spectral statistics of even–even rare-earth nuclei are investigated by using all the available empirical data for Ba, Ce, Nd, Sm, Gd, Dy, Er, Yb and Hf isotopes. The Berry–Robnik distribution and Maximum Likelihood estimation technique are used for analyses. An obvious deviation from GOE is observed for considered nuclei and there are some suggestions about the effect due to mass, deformation parameter and shell model configurations.

Toward neutron-rich nuclei via transfer reactions with stable and radioactive beams

The possibilities of production of yet-undiscovered neutron-rich isotopes of Ca, Gd, Dy, Er, Yb, Hf, W, Os, Hg, Pb, and Th are explored in various multinucleon transfer reactions with stable and radioactive beams. The probable projectile-target combinations and bombarding energies to produce these neutron-rich isotopes are suggested for future experiments.