Odd-even Staggering Research Articles

Nuclear charge radii of germanium isotopes around N = 40

Collinear laser spectroscopy measurements were performed on 68−74Ge isotopes (Z=32) at ISOLDE-CERN, by probing the 4s24p2P13→4s24p5sP1o3 atomic transition (269 nm) of germanium. Nuclear charge radii are determined via the measured isotope shifts, revealing a larger local variation than the neighboring isotopic chains. Nuclear density functional theory with the Fayans functionals Fy(Δr,HFB) and Fy(IVP), and the SV-min Skyrme describes the experimental data for the differential charge radii δ〈r2〉 and charge radii Rc within the theoretical uncertainties. The observed large variation in the charge radii of germanium isotopes is better accounted for by theoretical models incorporating ground state quadrupole correlations. This suggests that the polarization effects due to pairing and deformation contribute to the observed large odd-even staggering in the charge radii of the Ge isotopic chain.

Proton-neutron symplectic model description of 106Cd

In this study, a microscopic shell-model description of the low-lying collective states in the weakly deformed nucleus Cd within the recently proposed microscopic version of the Bohr-Mottelson model is provided. A good description of the excitation energies of the lowest ground, γ, and β quasibands is obtained without the adjustable kinetic energy term. Furthermore, γ degrees of freedom are shown to play a crucial role in the description of spectroscopy of this nucleus. A modified preserving high-order interaction is used to produce a γ-unstable type of odd-even staggering, observed experimentally between the states of the quasi-γ band. The current approach enables the characterization of observed intraband and interband quadrupole collectivity. The findings of this study propose an alternative interpretation of the fundamental question regarding the nature of low-energy vibrations, as well as the emergence of deformation and collectivity in weakly deformed atomic nuclei.

Odd-even shape staggering and kink structure of charge radii of Hg isotopes by the deformed relativistic Hartree–Bogoliubov theory in continuum

We examined the shape staggering of relative charge radii in 180−186Hg isotopes, which was first measured in 1977 and recently confirmed using advanced spectroscopy techniques. To understand the nuclear structure underlying this phenomenon, we employed the deformed relativistic Hartree–Bogoliubov theory in continuum (DRHBc). Our analysis revealed that the shape staggering can be attributed to nuclear shape transition in the Hg isotopes. Specifically, we demonstrated that prolate shapes of 181,183,185Hg lead to an increase in the charge radii compared to oblate shapes of 180,182,184,186Hg isotopes. We explained the nuclear shape staggering in terms of the evolution of occupation probability (OP) of ν1i13/2, ν1h9/2, π1h9/2, and π3s1/2 states. Additionally, we clarified the kink structure of the charge radii in the Hg isotopes near N=126 magic shell does not come from the change of the OP of π1h9/2 state, but mainly by the increase of the OPs of ν1i11/2 and ν2g9/2 states.

The optimized point-coupling interaction for the relativistic energy density functional of Hartree-Bogoliubov approach quantifying the nuclear bulk properties

We propose a newly optimized nonlinear point-coupling parameterized interaction, PC-L3R, for the relativistic Hartree-Bogoliubov framework with a further optimized separable pairing force by fitting to observables, i.e., the binding energies of 91 spherical nuclei, charge radii of 63 nuclei, and 12 sets of mean pairing gaps consisting of 54 nuclei in total. The separable pairing force strengths of proton and neutron are optimized together with the point-coupling constants, and are justified in satisfactory reproducing the empirical pairing gaps. The comparison of experimental binding energies compiled in AME2020 for 91 nuclei with the ones generated from the present and other commonly used point-coupling interactions indicates that the implementation of PC-L3R in relativistic Hartree-Bogoliubov yields the lowest root-mean-square deviation. The charge radii satisfactory agree with experiment. Meanwhile, PC-L3R is capable of estimating the saturation properties of the symmetric nuclear matter and of appropriately predicting the isospin and mass dependence of binding energy. The experimental odd-even staggering of single nucleon separation energies is well reproduced. The comparison of the estimated binding energies for 7,373 nuclei based on the PC-L3R and other point-coupling interactions is also presented.

Charge distribution of light mass fission products in the thermal neutron induced fission of 233U, 235U and 239Pu

Fractional cumulative yields (FCY) of various light mass fission products in the 233U(nth, f), 235U(nth, f) and 239Pu(nth, f) reactions were measured by using an off-line γ-ray spectrometric technique. The values of most probable charge (ZP) were obtained by using the width of isobaric charge distribution (σZ) of nearby fissioning systems with proper apportion. From the ZP values, the experimental charge polarization (ΔΖEXPT) as a function of fragment mass were also deduced. The ΔΖEXPT values for the light mass chains from the present work and for the heavy mass chains from earlier work show an oscillating nature in the interval of five mass units due to even-odd staggering. A local effect around the shell region and a systematic decreasing trend with the approach of symmetric split was also observed. The ΔΖMPE values based on minimum potential energy surface were theoretically calculated, which shows no oscillation but only a systematic decreasing trend with the approach of symmetric split due to the assumption of liquid drop behaviour of the fissioning nucleus.

New measurement of the elemental fragmentation cross sections of 218 MeV/nucleon Si28 on a carbon target

Elemental fragmentation cross sections (EFCSs) of stable and unstable nuclides have been investigated with various projectile-target combinations at a wide range of incident energies. These data are critical to constrain and develop the theoretical reaction models and to study the propagation of galactic cosmic rays (GCR). In this work, we present a new EFCS measurement for $^{28}$Si on carbon at 218~MeV/nucleon performed at the Heavy Ion Research Facility (HIRFL-CSR) complex in Lanzhou. The impact of the target thickness has been well corrected to derive an accurate EFCS. Our present results with charge changes $\Delta Z$ = 1-6 are compared to the previous measurements and to the predictions from the models modified EPAX2, EPAX3, FRACS, ABRABLA07, NUCFRG2, and IQMD coupled with GEMINI (IQMD+GEMINI). All the models fail to describe the odd-even staggering strength in the elemental distribution, with the exception of the IQMD+GEMINI model, which can reproduce the EFCSs with an accuracy of better than 3.5\% for $\Delta Z\leq5$. The IQMD+GEMINI analysis shows that the odd-even staggering in EFCSs occurs in the sequential statistical decay stage rather than in the initial dynamical collision stage. This offers a reasonable approach to understand the underlying mechanism of fragmentation reactions.

Examining the impact of α -decay energies on the odd-even staggering in half-lives: α -decay spectroscopy of Ac207–209

The α decays of Ac207–209, located near the proton drip-line, were reinvestigated by means of α-decay spectroscopy. They were produced in the fusion reaction Ar36+Hf176 and separated in flight using the gas-filled recoil separator SHANS. A new α-decay line at 7483(15) keV was observed and assigned as the decay from the ground state of Ac208 to the excited (2+) or (4+) state in Fr204. In addition, the previously known α-decay properties of Ac207–209 were measured with improved precision. The half-lives obtained, together with the existing decay data of other N≤126 actinium isotopes, were compared with the values calculated with the Wentzel-Kramers-Brillouin approximation and without considering the α-preformation factors. It is shown that the calculated half-lives exhibit a distinct odd-even staggering (OES) following the same trend as the experimental data, whereas the amplitudes of the exhibited OES are 30–60 % of the real ones. This implies that apart from the α-preformation factors, the α-decay energies also contribute significantly to the OES of α-decay half-lives.Received 20 September 2022Accepted 10 November 2022DOI:https://doi.org/10.1103/PhysRevC.106.064311©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNuclear structure & decaysProperties190 ≤ A ≤ 219Nuclear Physics

A new relation for nuclear masses based on the nuclide chain with the same number of neutrons

There are many studies in Odd–Even staggering (OES) of nuclear masses, but the research on nuclear masses by using the systematicness of OES is indeed very few. In this work, we analyze the relationship among the four neighboring nuclei based on the OES of nuclide chain with the same number of neutrons in atomic mass evaluation database (AME2016 database). Our purpose in this paper is to describe an empirical formula with one constant for OES of nuclear masses that can be useful in describing and predicting nuclear masses with mass number [Formula: see text]. With the empirical formula and AME2016 database, the root-mean-square deviation (RMSD) of the nuclei that we have successfully obtained 172[Formula: see text]keV for [Formula: see text] (the RMSD is 140[Formula: see text]keV for [Formula: see text]). This paper also uses Levenberg–Marquart (L-M) neural network approach to study the OES of nuclear masses ([Formula: see text], RMSD [Formula: see text][Formula: see text]keV; [Formula: see text], RMSD [Formula: see text][Formula: see text]keV). The results show that the RMSD of nuclear masses for [Formula: see text] based on neural network approach 30[Formula: see text]keV decreases than that based on empirical formula (the accuracy is increased by about 17%). In addition, the predicted values based on the empirical formula and L-M neural network approach are consistent with the values in AME2020 database, and the difference between our predicted values based on AME2016 database and experimental values measured in recent years is small. These results show that the new relation for nuclear masses has good simplicity, accuracy and reliability. Accurate nuclear mass is helpful to the research of nuclear physics, nuclear technology and astrophysics.

β-Delayed One and Two Neutron Emission Probabilities Southeast of ^{132}Sn and the Odd-Even Systematics in r-Process Nuclide Abundances.

The β-delayed one- and two-neutron emission probabilities (P_{1n} and P_{2n}) of 20 neutron-rich nuclei with N≥82 have been measured at the RIBF facility of the RIKEN Nishina Center. P_{1n} of ^{130,131}Ag, ^{133,134}Cd, ^{135,136}In, and ^{138,139}Sn were determined for the first time, and stringent upper limits were placed on P_{2n} for nearly all cases. β-delayed two-neutron emission (β2n) was unambiguously identified in ^{133}Cd and ^{135,136}In, and their P_{2n} were measured. Weak β2n was also detected from ^{137,138}Sn. Our results highlight the effect of the N=82 and Z=50 shell closures on β-delayed neutron emission probability and provide stringent benchmarks for newly developed macroscopic-microscopic and self-consistent global models with the inclusion of a statistical treatment of neutron and γ emission. The impact of our measurements on r-process nucleosynthesis was studied in a neutron star merger scenario. Our P_{1n} and P_{2n} have a direct impact on the odd-even staggering of the final abundance, improving the agreement between calculated and observed Solar System abundances. The odd isotope fraction of Ba in r-process-enhanced (r-II) stars is also better reproduced using our new data.

New experimental evidence for universal odd-even staggering in fragmentation cross sections

About 100 isotopes with $(N\ensuremath{-}Z)$ from 1--9 produced by 300 MeV/nucleon $^{78}\mathrm{Kr}$ projectiles impinging on an ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ target have been separated and identified at the RIBLL2 separator of HIRFL, where their production yields have been measured. The odd-even staggering (OES) in these experimental yields is quantitatively studied by employing a third-order difference formula. Measured data are used to validate the universality of this OES by comparing with other experimental data produced by fragmentation of different krypton projectiles on various targets as well as the OES evaluated from thousands of accurate cross sections measured in many different reactions. These comparisons between experimental data from a large variety of fragmentation reactions provide strong evidence that the OES magnitude almost does not depend on the projectile-target combinations and thus the OES is universal for different reaction systems. The OES magnitudes in these experimental data are also applied to examine the OES predicted by the abrasion-ablation model. There are large discrepancies between the OES magnitudes in predicted and measured cross sections.

Evolution of nuclear charge radii in copper and indium isotopes * *Supported by the Reform and Development Project of Beijing Academy of Science and Technology (13001-2110); Supported in part by the National Natural Science Foundation of China (12135004, 11635003, 11961141004, 12047513). X. J. is grateful for the support of the National Natural Science Foundation of China (11705118). L.-G. C. is

Systematic trends in nuclear charge radii are of great interest due to universal shell effects and odd-even staggering (OES). The modified root mean square (rms) charge radius formula, which phenomenologically accounts for the formation of neutron-proton (np) correlations, is here applied for the first time to the study of odd-Z copper and indium isotopes. Theoretical results obtained by the relativistic mean field (RMF) model with NL3, PK1 and NL3* parameter sets are compared with experimental data. Our results show that both OES and the abrupt changes across and 82 shell closures are clearly reproduced in nuclear charge radii. The inverted parabolic-like behaviors of rms charge radii can also be described remarkably well between two neutron magic numbers, namely to 50 for copper isotopes and to 82 for indium isotopes. This implies that the np-correlations play an indispensable role in quantitatively determining the fine structures of nuclear charge radii along odd-Z isotopic chains. Also, our conclusions have almost no dependence on the effective forces.

Impact of Nuclear Deformation and Pairing on the Charge Radii of Palladium Isotopes.

The impact of nuclear deformation can been seen in the systematics of nuclear charge radii, with radii generally expanding with increasing deformation. In this Letter, we present a detailed analysis of the precise relationship between nuclear quadrupole deformation and the nuclear size. Our approach combines the first measurements of the changes in the mean-square charge radii of well-deformed palladium isotopes between A=98 and A=118 with nuclear density functional calculations using Fayans functionals, specifically Fy(std) and Fy(Δr,HFB), and the UNEDF2 functional. The changes in mean-square charge radii are extracted from collinear laser spectroscopy measurements on the 4d^{9}5s ^{3}D_{3}→4d^{9}5p ^{3}P_{2} atomic transition. The analysis of the Fayans functional calculations reveals a clear link between a good reproduction of the charge radii for the neutron-rich Pd isotopes and the overestimated odd-even staggering: Both aspects can be attributed to the strength of the pairing correlations in the particular functional which we employ.

Charge radii of potassium isotopes in the RMF (BCS)* approach * *This work is partly Supported by the National Natural Science Foundation of China (11735003, 11975041, 11775014, 11961141004), the fundamental Research Funds for the Central Universities; Supported by the National Natural Science Foundation of China (12135004, 11635003, 11961141004, 12047513), and the Reform and Development Project of Beijing Academy of Science

We apply the recently proposed RMF (BCS)* ansatz to study the charge radii of the potassium isotopic chain up to 52K. It is shown that the experimental data can be reproduced rather well, qualitatively similar to the Fayans nuclear density functional theory, but with a slightly better description of the odd–even staggerings (OES). Nonetheless, both methods fail for 50K and to a lesser extent for 48,52K. It is shown that if these nuclei are deformed with a , then one can obtain results consistent with experiments for both charge radii and spin-parities. We argue that beyond-mean-field studies are needed to properly describe the charge radii of these three nuclei, particularly for 50K.

Odd-even staggering and shell effects of charge radii for nuclei with even Z from 36 to 38 and from 52 to 62

A unified theoretical model reproducing charge radii of known atomic nuclei plays an essential role in making extrapolations for unknown nuclei. Recently developed new ansatz which phenomenologically takes into account the neutron-proton short-range correlations ($np$-SRCs) can describe the discontinuity properties and odd-even staggering (OES) effect of charge radii along isotopic chains remarkably well. In this work, we further review the modified root-mean-square (rms) charge radii formula in the framework of relativistic mean field (RMF) theory. The charge radii are calculated along various isotopic chains that include the nuclei featuring the $N=50$ and 82 magic shells. Our results suggest that RMF with and without considering a correction term give an almost similar trend of nuclear size for some isotopic chains with open proton shell, especially the abrupt increases across the strong neutron closed shells and the OES behaviors. This reflects that the $np$-SRCs have almost no influence for some nuclei due to the strong coupling between different levels around Fermi surface. The weakening OES behavior of nuclear charge radii is observed generally at completely filled neutron shells and this may be proposed as a signature of magic indicator.

Theoretical description of fission yields: Toward a fast and efficient global model

Background: A quantitative microscopic understanding of the fission-fragment yield distributions represents a major challenge for nuclear theory as it involves the intricate competition between large-amplitude nuclear collective motion and single-particle nucleonic motion. Purpose: A recently proposed approach to global modeling of fission fragment distributions is extended to account for odd-even staggering in charge yields and for neutron evaporation. Method: Fission trajectories are obtained within the density functional theory framework, allowing for a microscopic determination of the most probable fission prefragment configurations. Mass and charge yields distributions are constructed by means of a statistical approach rooted in a microcanonical ensemble. Result: We show that the proposed hybrid model can reproduce experimental mass and charge fragment yields, including the odd-even staggering, for a wide range of fissioning nuclei. Experimental isotopic yields can be described within a simple neutron evaporation scheme. We also explore fission fragment distributions of exotic neutron-rich and superheavy systems, and compare our predictions with other state-of-the art global calculations. Conclusion: Our study suggests that the microscopic rearrangement of nucleons into fission fragments occurs well before the scission, and that the subsequent dynamics is mainly driven by the thermal excitations and bulk features of the nuclear binding. The proposed simple hybrid approach is well suited for large-scale calculations involving hundreds of fissioning nuclei.

Triaxial projected shell model study of γ-bands in even even 104−122Cd nuclei

A systematic study of the nuclear observables related to the triaxial nature of the even-even 104−122Cd isotopes is presented microscopically using multi-quasiparticle triaxial projected shell model (TPSM) approach. In the present work, we have performed a detailed study of γ-bands in cadmium isotopes in addition to the yrast band. The present calculations are found to reproduce the observed systematics of the R42=[E(41+)/E(21+)], E-GOS plots and B(E2) values for 104−122Cd isotopic mass chain. The E-GOS plots along with the R42 ratios predict the quasi-deformed structure for these bands. Besides this, odd-even staggering in γ bands, inter band and intra band reduced transition probabilities and g-factors have also been discussed in the present work and it is shown that TPSM approach provides a reasonable description of the measured properties.

Novel Bayesian neural network based approach for nuclear charge radii

Charge radius is one of the most fundamental properties of a nucleus. However, a precise description of the evolution of charge radii along an isotopic chain is highly nontrivial, as reinforced by recent experimental measurements. In this paper, we propose a novel approach which combines a three-parameter formula and a Bayesian neural network. We find that the novel approach can describe the charge radii of all $A\ge40$ and $Z\ge20$ nuclei with a root-mean-square deviation about 0.015 fm. In particular, the charge radii of the calcium isotopic chain are reproduced very well, including the parabolic behavior and strong odd-even staggerings. We further test the approach for the potassium isotopes and show that it can describe well the experimental data within uncertainties.

Global Performance of Covariant Density Functional Theory in Description of Charge Radii and Related Indicators

A short review of existing efforts to understand charge radii and related indicators on a global scale within the covariant density functional theory (CDFT) is presented. Using major classes of covariant energy density functionals (CEDFs), the global accuracy of the description of experimental absolute and differential charge radii within the CDFT framework has been established. This assessment is supplemented by an evaluation of theoretical statistical and systematic uncertainties in the description of charge radii. New results on the accuracy of the description of differential charge radii in deformed actinides and light superheavy nuclei are presented and the role of octupole deformation in their reproduction is evaluated. Novel mechanisms leading to odd-even staggering in charge radii are discussed. Finally, we analyze the role of self-consistency effects in an accurate description of differential charge radii.

Charge radii in covariant density functional theory: A global view

The authors provide a systematic global study of differential charge radii of nuclei within covariant density functional theory. They present results for chains of isotopes as they cross major closed neutron shell numbers, where there is usually a change of slope (kink) in the charge radii. The odd-even staggering of charge radii is also investigated, and particle-vibration coupling in odd-mass nuclei is suggested to play a significant role in addition to pairing. This detailed study lays a solid foundation to assess how various forms of interactions within the nuclear many-body system affect fundamental nuclear properties such as nuclear radii and how they evolve with nucleon number.

Charge radii, moments, and masses of mercury isotopes across the N=126 shell closure

Combining laser spectroscopy in a Versatile Arc Discharge and Laser Ion Source (VADLIS) with Penning-trap mass spectrometry at the CERN-ISOLDE facility, this work reports on mean-square charge radii of neutron-rich mercury isotopes across the N=126 shell closure, the electromagnetic moments of Hg207, and more precise mass values of Hg206–208. The odd-even staggering (OES) of the mean square charge radii and the kink at N=126 are analyzed within the framework of covariant density functional theory (CDFT), with comparisons between different functionals to investigate the dependence of the results on the underlying single-particle structure. The observed features are defined predominantly in the particle-hole channel in CDFT, since both are present in the calculations without pairing. However, the magnitude of the kink is still affected by the occupation of the ν1i11/2 and ν2g9/2 orbitals with a dependence on the relative energies as well as pairing.5 MoreReceived 4 August 2021Accepted 20 October 2021DOI:https://doi.org/10.1103/PhysRevC.104.054322Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBinding energy & massesNuclear structure & decaysRare & new isotopesSpectroscopic factors & electromagnetic momentsProperties190 ≤ A ≤ 219Electric momentMagnetic momentNuclear bindingTechniquesMass spectrometryNuclear density functional theoryPhotoionizationRadioactive beamsAccelerators & BeamsAtomic, Molecular & OpticalNuclear Physics