Shell Effects Research Articles

Alpha Decay Half-Lives Calculation of Even-Even Nuclei in the62≤Z≤100Region using Woods-Saxon Potential

Alpha decay properties of even-even nuclei in the 62 ≤ Z ≤ 100 region are investigated within the Unified Fission Model based on a Modified Woods-Saxon potential. The computed alpha decay half-lives are compared to experimental data and are found to be in good agreement with it. The acquired pattern of the variation of alpha decay half-lives as a function of neutron number are explained by the nuclear shell effect. The experimental alpha decay energy Q is found to have an inverse relation with the alpha decay half-lives. This work has shown that the Unified Fission Model based on a Modified Woods-Saxon potential is sufficient to obtain the values of alpha decay half-lives.

Fission-stability of high-K states in superheavy nuclei

Fission is the one of the primary radioactive decay modes for the heaviest nuclei and ultimately determines the existence of the heaviest elements on a macroscopic time scale, e.g., ge 10^{-14} s. The present experimental data on the decay properties of the heaviest nuclei with proton numbers 102–118 and/or of neutron numbers up to 177 show that fission occurs occasionally. This confirms that shell structure plays an essential role for their stability against fission. The shell effect on fission manifests in both collective and single-particle ways, which can experimentally be studied in decays of even–even, odd-A and odd–odd nuclei. At the same time, high-K states formed in couplings of quasiparticles are also known to be stable against fission. However, detailed knowledge and theoretical descriptions on a retardation effect/strength of high-K quantum number on fission are still scarce. In the present work, fission from high-K states are discussed and described within the semi-empirical approach. Fission half-lives are calculated for various high-K states, which have been theoretically predicted to exist in Fm-Rf (Z = 100–104) and Hs-Ds (Z = 108–112). The results are found to be in line with the available experimental findings, and also leading to different intriguing predictions, e.g., high-K states in superheavy nuclei tend to be more stable against fission compared to their ground states.

Quantitatively Revealing the Anomalous Enhancement in Shell-Isolated Nanoparticle-Enhanced Raman Spectroscopy Using Single-Nanoparticle Spectroscopy.

Surface-enhanced Raman spectroscopy (SERS) is an ultrasensitive spectroscopic technique that has been extensively applied in the studies of catalysis, electrochemistry, material science, etc.; however, it is substrate and material limited. The development of shell-isolated nanoparticle-enhanced Raman spectroscopy (SHINERS) effectively offsets this limitation that attracts enormous attention due to its potential to be applied to any surface. As the core of the SHINERS technique, the inert shell prevents the exposure of the active metal surface, however, also significantly enlarges the metallic gap where the light is trapped. Consequently, the shell is widely considered a side issue to debilitate the coupling efficiency and hinder the sensitivity of SHINERS without systematic studies. Herein, we investigate the shell and structural effect of SHINERS by performing the quantitative optical and structural characterization of single nanostructures. By a statistic of over two hundred nanostructures, we observe that the field enhancement loss due to the shell could be overcome by optimizing the coupling geometry of the shell-isolated nanoparticles (SHINs). An example of SHIN dimers shows even higher field enhancement than their bare Au nanoparticle counterparts as confirmed and explained by FDTD simulations. We demonstrate the signal enhancement of SHINERS saturates with the increasing number of hot spots but could be further optimized by altering the aggregation geometries of the nanoparticles. The sensitivity improvement of the SHINERS technique will boost its broader applications in material science.

Investigating the fission dynamics of the following neutron shell closed nuclei within a stochastic dynamical approach: 210Po, 212Rn, and 213Fr* *D.A. acknowledges the financial support from the University Grants Commission (UGC), Government of India, received in the form of a research fellowship (Ref. No. 19/06/2016/(i) EU-V, Sr. No. 2061651303)

The dissipative dynamics of nuclear fission is a well confirmed phenomenon that can be either described by a Kramers-modified statistical model or by a dynamical model employing the Langevin equation. Although dynamical models as well as statistical models incorporating fission delays have been found to explain the measured fission observables in several studies, they present conflicting results for shell closed nuclei in the mass region of 200. Notably, an analysis of the recent data on neutron shell closed nuclei in the excitation energy range of 4080 MeV failed to provide a satisfactory description of the data, which was attributed to a mismatch with shell effects and/or entrance channel effects, without reaching a definite conclusion. In the present study, we demonstrate that a well established stochastic dynamical code can simultaneously reproduce the available data for pre-scission neutron multiplicities and fission and evaporation residue excitation functions for the following neutron shell closed nuclei Po and Rn and their isotopes Po and Rn without the need for including any extra shell or entrance channel effects. The relevant calculations are performed by using a phenomenological universal friction form factor with no ad-hoc adjustment of the model parameters. However, we note a significant deviation, beyond experimental errors, for some Fr isotopes.

A Low-Concentration Electrolyte for High-Voltage Lithium-Metal Batteries: Fluorinated Solvation Shell and Low Salt Concentration Effect.

Concentration of electrolyte has significant effects on performances of rechargeable batteries. Previous studies mainly focused on concentrated electrolytes. So far, only several recipes on low-concentration electrolytes were studied, performing enhanced performance in advanced rechargeable batteries. Here, based on common electrolyte components, a low-concentration electrolyte composed of 0.2 M lithium hexafluorophosphate (LiPF6 ) solvated in fluoroethylene carbonate (FEC) and ethyl methyl carbonate (EMC) is employed for high-voltage Li metal battery. The synergistic working mechanisms of introducing fluorine-containing solvent in the solvated structure and low salt concentration effect are revealed, resulting in LiF-rich, uniform, and robust solid electrolyte interphase layer and fewer unfavorable decomposition products. As a result, this low-concentration electrolyte significantly enhances electrochemical performances of Li||Li symmetric cells and high-voltage LiCoO2 ||Li batteries.

Microscopic-macroscopic level densities for low excitation energies

Level density ρ(E,Q) is derived within the micro-macroscopic approximation (MMA) for a system of strongly interacting Fermi particles with the energy E and additional integrals of motion Q, in line with several topics of the universal and fruitful activity of A. S. Davydov. Within the extended Thomas Fermi and semiclassical periodic orbit theory beyond the Fermi-gas saddle-point method, we obtain ρ∝Iν(S)/Sν, where Iν (S) is the modified Bessel function of the entropy S. For small shell-structure contribution, one finds ν = κ/2 + 1, where κ is the number of additional integrals of motion. This integer number is a dimension of Q, Q = {N, Z, …} for the case of two-component atomic nuclei, where N and Z are the numbers of neutrons and protons, respectively. For much larger shell structure contributions, one obtains ν = κ /2 + 2. The MMA level density ρ reaches the well-known Fermi gas asymptote for large excitation energies and the finite micro-canonical combinatoric limit for low excitation energies. The additional integrals of motion can also be the projection of the angular momentum of a nuclear system for nuclear rotations of deformed nuclei, number of excitons for collective dynamics, and so on. Fitting the MMA total level density ρ(E, Q) for a set of the integrals of motion Q = {N, Z}, to experimental data on a long nuclear isotope chain for low excitation energies, one obtains the results for the inverse level-density parameter K, which differs significantly from those of neutron resonances due to shell, isotopic asymmetry, and pairing effects.

Microscopic investigations into fission dynamics beyond the saddle point

The real-space density-constrained time-dependent Hartree-Fock-Bogoliubov method is exploited to obtain the dynamic potential energy and several experimental variables of fission fragments. The resultant predictions of collective variables, especially the total kinetic energy and total excitation energy of the fission fragments, finely match the experimental data. It is demonstrated that scission dynamics including the shell effects and pairing correlations should be the focus of further studies.

Binding energies of proton-rich nuclei determined from their mirror pairs* *Supported by the National Natural Science Foundation of China (12075121 and 11605089), and by the Natural Science Foundation of Jiangsu Province (BK20190067 and BK20150762)

In addition to the Coulomb displacement energy, the residual differences between the binding energies of mirror nuclei (a pair of nuclei with the same mass number plus interchanged proton and neutron numbers) contribute to the shell effect via the valence scheme in this study. To this end, one linear combining type of valence nucleon number, namely, , is chosen to tackle this shell correction, in which and are the valence proton and neutron numbers with respect to the nearest shell closure, respectively. The mass differences of mirror nuclei, as the sum of the empirical Coulomb displacement energy and shell effect correction, are then used to obtain the binding energies of proton-rich nuclei through the available data of their mirror partners to explore the proton dripline of the nuclear chart.

Catalytic Synergies in Bimetallic RuPt Single–Atom Catalysts via Speciation Control

AbstractBimetallic single–atom catalysts (b–SACs) have recently gained prominence by virtue of the unique catalytic cooperative interactions they can exhibit, intertwining electronic and geometric effects. To date, research efforts have exclusively focused on direct mechanisms such as electron density transfer or sequential reactivity. Herein, the first study on indirect, coordination–induced catalytic synergies in carbon‐supported RuPt SACs is conducted. To this end, a holistic approach is developed, combining i) precision synthesis, ii) advanced characterization, iii) exploration of single–site adsorption properties via the hydrogen evolution reaction, and iv) modeling through density functional theory. Despite the lack of both intermetallic coordination in the first or second shell and charge redistribution effects, the RuPt SACs exhibit a H2 formation rate enhanced up to 15–fold compared with their monometallic counterparts. To unfold the origin of the intermetallic cooperativity, modifications of the structural and catalytic properties induced by the integration of a second metal species are investigated. Thus, Pt atoms are found to selectively occupy the most energeticallyfavorable cavities in the support, prompting Ru atoms to assume a distinct, more active, configuration. This contribution unveils a novel principle of bimetallic cooperativity, demonstrating the key role of integrative experimental and computational analyses in studying b–SACs.

Dependence of (n,γ)−(γ,n) equilibrium r -process abundances on nuclear physics properties

In most $r$-process expansions, the dominant nuclear evolution occurs in an $(n,\ensuremath{\gamma})\text{\ensuremath{-}}(\ensuremath{\gamma},n)$ equilibrium in which nuclei rapidly exchange neutrons but change charge much more slowly by beta decay. Freeze-out from this equilibrium shapes the final abundances but does not significantly alter the overall global abundance pattern; therefore, it is important to understand the details of $(n,\ensuremath{\gamma})\text{\ensuremath{-}}(\ensuremath{\gamma},n)$ equilibrium both because it is the main evolution phase that determines the final abundance pattern and because it is the starting point for the freeze-out. Through use of a simple but realistic phenomenological nuclear physics model, we show that isotopic abundances versus neutron number in $(n,\ensuremath{\gamma})\text{\ensuremath{-}}(\ensuremath{\gamma},n)$ equilibrium are well approximated as Gaussians. Nuclear pairing causes isotopic abundances to alternate between two Gaussians, and shell effects cause the isotopic abundances to shift from one Gaussian to another when the neutron number crosses a magic number. More complex neutron-separation energy curves versus mass number can be generated by adding a spike function to a linearly declining curve. In such a case, the equilibrium abundance curve jumps from one Gaussian to another for each added spike. Insights from our model can help shed light on how detailed theoretical or experimental nuclear data affect $r$-process nucleosynthesis during the $(n,\ensuremath{\gamma})\text{\ensuremath{-}}(\ensuremath{\gamma},n)$ equilibrium phase.

Production of neutron-rich heavy nuclei around $$N = 162$$ in multinucleon transfer reactions

Within the framework of the dinuclear system model, the production mechanism of neutron-rich heavy nuclei around \(N = 162\) has been investigated systematically. The isotopic yields in the multinucleon transfer reaction of \(^{238}\)U + \(^{248}\)Cm are analyzed and compared with the available experimental data at GSI. Systematics on the production of superheavy nuclei via the collisions of \(^{238}\)U on actinide nuclides \(^{252,254}\)Cf, \(^{254}\)Es and \(^{257}\)Fm is investigated thoroughly. It is found that the shell effect is of importance in the formation of neutron-rich nuclei around \(N~=~162\) owing to the enhancement of fission barrier and neutron separation energy. The fragments in the multinucleon transfer reactions manifest the broad isotopic distribution and are dependent on the beam energy. The polar angles of the fragments tend to the forward emission with increasing the beam energy. The production cross sections of new isotopes are estimated and the heavier targets are available for the neutron-rich superheavy nucleus formation. The optimal reaction system and beam energy are proposed for the future experimental measurements.

Neutron star crust properties: comparison between the compressible liquid-drop model and the extended Thomas-Fermi approach

We present a detailed analysis of three models predicting the properties of non-uniform matter in the crust of neutron stars: the compressible liquid-drop model, the fourth order Extended Thomas Fermi (ETF) method, and ETF plus Strutinsky integral (ETFSI) correction. The former treats the nuclear clusters as uniform hard spheres, the second takes into account the density distribution which can be different for neutrons and protons, and the last one includes the proton shell effects within the Strutinsky approach. The purpose of this work is to understand the importance of the improvements in the nuclear modeling and to analyze the quantities which are the most sensitive to them. We find that thermodynamic quantities such as pressure, energy and chemical potential, as well as the electron fraction, are in very good agreement among the three models. This confirms previous results where we have shown that the improvement in the finite-size description of the nuclear clusters has a small impact on these quantities, since they are mainly constrained by the bulk properties. The refinements in the finite-size modeling are shown to impact mostly the composition of the nuclear clusters (Z cl, N cl) in an ordering which ranks according to the leptodermous expansion. This analysis is performed considering both the r-cluster and the e-cluster representations. The proton shell effects are shown to stabilize Z cl, which consequently impacts the neutron number N cl as well.

Accreting neutron stars from the nuclear energy-density functional theory

Context. The accretion of matter onto the surface of a neutron star in a low-mass X-ray binary triggers X-ray bursts, whose ashes are buried and further processed thus altering the composition and the properties of the stellar crust. Aims. In this second paper of a series, the impact of accretion on the equation of state and on the global properties of neutron stars is studied in the framework of the nuclear energy-density functional theory. Methods. Considering ashes made of 56Fe, we calculated the equations of state using the same Brussels-Montreal nuclear energy-density functionals BSk19, BSk20, and BSk21, as those already employed for determining the crustal heating in our previous study for the same ashes. All regions of accreting neutron stars were treated in a unified and thermodynamically consistent way. With these equations of state, we determined the mass, radius, moment of inertia, and tidal deformability of accreted neutron stars and compared with catalyzed neutron stars for which unified equations of state based on the same functionals are available. Results. The equation of state of accreted neutron stars is found to be significantly stiffer than that of catalyzed matter, with an adiabatic index Γ ≈ 4/3 throughout the crust. For this reason, accreting neutron stars have larger radii. However, their crustal moment of inertia and their tidal deformability are hardly changed provided density discontinuities at the interface between adjacent crustal layers are properly taken into account. Conclusions. The enhancement of the stiffness of the equation of state of accreting neutron stars is mainly a consequence of nuclear shell effects, thus confirming the importance of a quantum treatment as stressed in our first study. With our previous calculations of crustal heating using the same functionals, we have thus obtained consistent microscopic inputs for simulations of accreting neutron stars.

Investigation of empirical heat capacity in hot-rotating A ∼ 200 nuclei

The empirical heat capacities of some hot-rotating A ∼ 200 nuclei (184Re, 200Tl, 211Po, and 212At) have been investigated by combining the angular-momentum dependent back-shifted Fermi gas (BSFG) model of nuclear level density (NLD) with the experimental NLD data extracted from the neutron-evaporation spectra at the average total angular momentum ⟨J⟩ = 12 ℏ. The parameters of the BSFG are obtained by fitting its NLD to the corresponding measured data using an advanced package of program modeling (CPM) provided by Python feature of IBM decision optimization CPLEX. The results obtained show that the shell correction plays an important role in the formation of empirical S-shaped heat capacity, which serves as a fingerprint for the pairing phase transition in finite nuclear systems. The 184Re nucleus, which is deformed and has small shell correction, exhibits a weaker S-shaped heat capacity than the remaining three spherical 200Tl, 211Po, and 212At nuclei that have large shell effects. This result contrasts with that recently predicted by the microscopic exact pairing plus independent-particle model at finite temperature (EP + IPM), in which the S-shaped heat capacity was predicted in 184Re only. This discrepancy between the heat capacities obtained within the BSFG and EP + IPM models suggests that an NLD model capable of well describing the experimental data while also having intrinsic and as complete as possible physical interpretations is still required in order to provide the exact description of nuclear thermodynamic quantities. In addition, more experimental NLD data in other mass and higher energy regions are also demanded.

Quantum mechanical approach to bifurcation point detection in Hamiltonian dynamical systems

Abstract The energy level statistics of a bounded quantum system whose classical dynamical system exhibits bifurcations is investigated using the two-point correlation function (TPCF), which at the bifurcation points exhibits periodic spike oscillations owing to the accumulation of levels called the shell effect. The spike oscillations of the TPCF are analyzed by the reduced chi-squared value, which exhibits abrupt increases at bifurcation points, thereby yielding a novel detection approach. Using this method, we attempt to numerically detect the bifurcation points of a lemon-shaped billiard.

Proton and neutron exchange as a prelude to fusion at near-barrier energies

Systematic examination of fusion for ${}^{39,41,45,47}\mathrm{K}+^{28}\mathrm{Si}$ and $^{36,44}\mathrm{Ar}+^{28}\mathrm{Si}$ provides insight into the impact of neutron and proton exchange on fusion for nuclei at and near the $N=20$ and $N=28$ shells. Comparison of the reduced excitation functions reveals a marked difference between the behavior of open-shell and closed-shell systems. While coupled channels calculations provide a good description for the closed-shell nuclei, they significantly underpredict the fusion cross section for open-shell nuclei. The observed trends are examined in the context of a potential energy surface, including shell effects, and multinucleon exchange with consideration of Pauli blocking.

Impact of tensor force on quantum shell effects in quasifission reactions

Quantum shell effects drive many aspects of many-body quantal systems and their interactions. Among these are the quasifission reactions that impede the formation of a compound nucleus in superheavy element (SHE) searches. Fragment production in quasifission is influenced by shell effects as a nontrivial manifestation of microscopic dynamics hindering the full equilibration of the composite system to form the compound nucleus. In this Letter, we use the microscopic time-dependent Hartree-Fock (TDHF) theory to study 48Ca+249Bk collisions to investigate the influence of the tensor component of the effective nucleon-nucleon interaction. The results show that the inclusion of the tensor force causes the spherical shell effect to become more prominent, particularly for the neutron number yield whose peak is exactly at magic number N=126. This suggests that the tensor force plays a compelling role in the evolution of dynamical shell effects in nuclear reactions, influencing the competition between spherical and deformed shell gaps.

Shell-shaped Bose-Einstein condensates based on dual-species mixtures

Ultracold quantum gases confined in three-dimensional bubble traps are promising tools for exploring many-body effects on curved manifolds. As an alternative to the conventional technique of radio-frequency dressing, we propose to create such shell-shaped Bose-Einstein condensates in microgravity based on dual-species atomic mixtures, and we analyze their properties as well as the feasibility of realizing symmetrically filled shells. Beyond similarities with the radio-frequency dressing method, as in the collective excitation spectrum, our approach has several natural advantages like the robustness of the created quantum bubbles and the possibility of magnifying shell effects through an interaction-driven expansion.

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.

Spectroscopy of super heavy elements with GABRIELA

The spectrum of states in very heavy and super heavy nuclei is the result of a delicate balance between the strong Coulomb repulsion between the numerous protons in the nucleus and the properties of the strong force acting between the many nucleons in the system. Fine-structure \(\alpha \) decay combined with \(\gamma \)-ray and internal-electron-conversion spectroscopy allows to identify the sequence and energies of low-lying nuclear states. This information can then be used to constrain the parameters that define the nuclear mean-field and thus improve the reliability of predictions in a region controlled critically by small shell effects. Detailed spectroscopy of transfermium nuclei is the prime motivation of the Franco-Russian GABRIELA (Gamma Alpha Beta Recoil Investigation with the ELectromagnetic Analyzer) project, launched more than 15 years ago. The current review aims at presenting the experimental developments that have been carried out over the years and discuss a selection of results that have been obtained.