Nuclear Structure Models Research Articles

Synthesis and photocatalytic activity of plasmon-enhanced core-shell upconversion luminescent photocatalytic Ag@SiO2@YF3:Ho3+@TiO2 nanocomposites

Examination of the local surface plasmon resonance (LSPR) effect of precious metals shows that combining noble metal nanomaterials and upconversion (UC) materials increases the luminescence quantum yield and luminescence stability of UC materials. Furthermore, this combination reduces the luminescence lifetime. In this study, a new type of UC luminescent material, Ag@SiO2@YF3:Ho3+, was synthesized. The SiO2 group was used to protect the YF3:Ho3+ group from Ag. In addition, Ag@SiO2 nuclear shell structure model was constructed using finite-difference time-domain (FDTD) simulation software. Ag particle size and SiO2 shell thickness, the parameters of the LSPR resonance peak that most improved the luminous intensity of the UC material, were calculated theoretically. Finally, the composite photocatalyst, Ag@SiO2@YF3:Ho3+@TiO2, was obtained by combining the LSPR-enhanced UC material with the photocatalyst TiO2. The FDTD simulation results showed that the conditions using a Ag particle radius of 75–125 nm and a SiO2 shell thickness of 20 nm most greatly enhanced the luminescence of the UC material YF3:Ho3+, which was deposited on top of the Ag@SiO2 shell structure. Ag@SiO2@YF3:Ho3+ prepared under these conditions possessed a core-shell structure in which the diameter of the Ag core was 150–250 nm and the composite shell, after loading TiO2, was divided into three layers. Furthermore, the results demonstrated the successful fabrication of the UC materials and composite materials. Finally, degradation experiments showed that a desirable photodegradation effect (76%) was obtained and the degradation rate of the dark reaction was 18%.

From homogeneous matter to finite nuclei: Role of the effective mass

Recent astronomical observations, nuclear-reaction experiments, and microscopic calculations have placed new constraints on the nuclear equation of state (EoS) and revealed that most nuclear structure models fail to satisfy those constraints upon extrapolation to infinite matter. A reverse procedure for imposing EoS constraints on nuclear structure has been elusive. Here we present for the first time a method to generate a microscopic energy density functional (EDF) for nuclei from a given immutable EoS. The method takes advantage of a natural Ansatz for homogeneous nuclear matter, the Kohn-Sham framework, and the Skyrme formalism. We apply it to the realistic nuclear EoS of Akmal-Pandharipande-Ravenhall and describe successfully closed-(sub)shell nuclei. In the process, we provide predictions for the neutron skin thickness of nuclei based directly on the given EoS. Crucially, bulk and static nuclear properties are found practically independent of the assumed effective mass value - a unique result in bridging EDF of finite and homogeneous systems in general.

Constraining spectroscopic factors near the r -process path using combined measurements: Kr86 (d, p)87Kr

Background: Modern nuclear structure models suggest that the shell structure near the valley of stability, with well-established shell closures at $N=50$, for example, changes in very neutron-rich nuclei far from stability. Single-particle properties of nuclei away from stability can be probed in single-neutron $(d,p)$ transfer reactions with beams of rare isotopes. The interpretation of these data requires reaction theories with various effective interactions. Often, approximations made to the final bound-state potential introduce a large uncertainty in the extracted single-particle properties, in particular the spectroscopic factor.Purpose: Mitigate this uncertainty using a combined measurement method to constrain the shape of the bound-state potential and to reliably extract the spectroscopic factor.Methods: The $^{2}\mathrm{H}(^{86}\mathrm{Kr},p)^{87}\mathrm{Kr}$ reaction was measured at 33 MeV/u at the National Superconducting Cyclotron Laboratory (NSCL) as a test of the combined method. The reaction protons were detected with the Oak Ridge Rutgers University Barrel Array (ORRUBA) of position sensitive silicon strip detectors, the first implementation of ORRUBA coupled to the S800 spectrograph with fast beams at NSCL.Results: These measurements at 33 MeV/u are combined with previous studies of the $^{86}\mathrm{Kr}(d,p)$ reaction at 5.5 MeV/u to demonstrate a successful case of the combined method to constrain the shape of the single-particle potential and deduce asymptotic normalization coefficients and spectroscopic factors. In particular, the single-particle asymptotic normalization coefficient for the ground state of $^{87}\mathrm{Kr}$ was constrained to ${b}_{d5/2}=6.{46}_{\ensuremath{-}0.57}^{+1.12}\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1/2}$, and therefore the deduced spectroscopic factor is $S=0.{44}_{\ensuremath{-}0.13}^{+0.09}$ with uncertainties dominated by experimental statistics.Conclusions: By combining measurements at two very different beam energies, single-particle asymptotic normalization coefficients, at least for low angular momentum transfers, can be constrained. Therefore, spectroscopic factors can be deduced with uncertainties dominated by experimental uncertainties, rather than limited knowledge of bound-state potential parameters.

One-proton and one-neutron knockout reactions from N=Z=28Ni56 to the A=55 mirror pair Co55 and Ni55

We present a high-resolution in-beam $\gamma$-ray spectroscopy study of excited states in the mirror nuclei $^{55}$Co and $^{55}$Ni following one-nucleon knockout from a projectile beam of $^{56}$Ni. The newly determined partial cross sections and the $\gamma$-decay properties of excited states provide a test of state-of-the-art nuclear structure models and probe mirror symmetry in unique ways. A mirror asymmetry for the partial cross sections leading to the two lowest $3/2^-$ states in the $A = 55$ mirror pair was identified as well as a significant difference in the $E1$ decays from the $1/2^+_1$ state to the same two $3/2^-$ states. The mirror asymmetry in the partial cross sections cannot be reconciled with the present shell-model picture or small mixing introduced in a two-state model. The observed mirror asymmetry in the $E1$ decay pattern, however, points at stronger mixing between the two lowest $3/2^-$ states in $^{55}$Co than in its mirror $^{55}$Ni.

Observation of two-neutrino double electron capture in 124Xe with XENON1T

Two-neutrino double electron capture (2νECEC) is a second-order weak-interaction process with a predicted half-life that surpasses the age of the Universe by many orders of magnitude1. Until now, indications of 2νECEC decays have only been seen for two isotopes2-5, 78Kr and 130Ba, and instruments with very low background levels are needed to detect them directly with high statistical significance6,7. The 2νECEC half-life is an important observable for nuclear structure models8-14 and its measurement represents a meaningful step in the search for neutrinoless double electron capture-the detection of which would establish the Majorana nature of the neutrino and would give access to the absolute neutrino mass15-17. Here we report the direct observation of 2νECEC in 124Xe with the XENON1T dark-matter detector. The significance of the signal is 4.4 standard deviations and the corresponding half-life of 1.8×1022years(statistical uncertainty, 0.5×1022years; systematic uncertainty, 0.1×1022years) is the longest measured directly so far. This study demonstrates that the low background and large target mass of xenon-based dark-matter detectors make them well suited for measuring rare processes and highlights the broad physics reach of larger next-generation experiments18-20.

Mag2Pol: a program for the analysis of spherical neutron polarimetry, flipping ratio and integrated intensity data

Mag2Pol is a graphical user interface program which is devoted to the treatment of data from polarized neutron diffractometers with spherical polarization analysis. Nuclear and magnetic structure models can be introduced using space-group symbols and individual symmetry operators, respectively, and viewed in an OpenGL widget. The program calculates nuclear/magnetic structure factors, flipping ratios and polarization matrices for magnetic Bragg reflections, taking into account structural twins and magnetic domains. Spherical neutron polarimetry data can be analyzed by refining a magnetic structure model including magnetic domain populations in a least-squares fit and can also be correlated with an integrated intensity data set in a joint refinement. Further features are the simultaneous refinement of nuclear and magnetic structures with integrated intensity data and the analysis of flipping ratios either with tabulated magnetic form factors or using a multipole expansion of the magnetization density.

Application of the collective model to determine some rotational bands of 239U nucleus

238U material is component in fuels of nuclear reactor core. Understanding properties and structure of 238U nucleus is necessary before simulating and designing nuclear reactor. Besides that, the study of nuclear reaction is necessary to identify the specific characteristics of nucleus, it is the most effective experimental method up to now. However, in order to explain the properties of nuclear structure, in addition to study of the nuclear reaction, nuclear structure models and its theory must be used. There are many nuclear structure models to solve those properties of nucleus. This paper presents application of the Collective Model to determine some rotational bands of 239U nucleus, using Prompt gamma neutron activation analysis method (PGNAA). Experiment is performed at channel No.2 of Dalat Research Reactor (DRR), using Filtered Thermal Neutron Beam and Compton Suppression Spectroscopy with High – Purity Germanium detector (HPGe). The results have found 11 rotational bands of 239U nucleus. This work is very necessary for the research of nuclear structure which controls material technology by itself.

Interpolating formula for the 0νββ -decay half-life in the case of light and heavy neutrino mass mechanisms

We revisit the "interpolating formula" proposed in our previous publication. It allows one to calculate the neutrinoless double beta decay ($0\nu\beta\beta$-decay) half-life for arbitrary neutrino mass without involvement of the complicated results for nuclear matrix elements (NME) obtained within specific nuclear structure models. The formula derives from the finding that the value of a properly normalized ratio of the NMEs for the light and heavy neutrino mass mechanisms weakly depends on isotope. From this fact it follows, in particular, that the light and heavy neutrino mass mechanisms can hardly be distinguished in a model independent way searching for $0\nu\beta\beta$-decay of different nuclei. Here we show that this formula holds for all the known nuclear structure approaches. We give a mathematical justification of our results examining analytical properties of the NMEs. We also consider several simplified benchmark scenarios within left-right symmetric models and analyze the conditions for the dominance of the light or heavy neutrino mass mechanisms in $0\nu\beta\beta$-decay.

Excitation energy shift and size difference of low-energy levels in p -shell Λ hypernuclei

We investigated structures of low-lying $0s$-orbit $\Lambda$ states in $p$-shell $\Lambda$ hypernuclei ($^A_\Lambda Z$) by applying microscopic cluster models for nuclear structure and a single-channel folding potential model for a $\Lambda$ particle. For $A>10$ systems, the size reduction of core nuclei is small, and the core polarization effect is regarded as a higher-order perturbation in the $\Lambda$ binding. The present calculation qualitatively describes the systematic trend of experimental data for excitation energy change from $^{A-1} Z$ to $^A_\Lambda Z$, in $A>10$ systems. The energy change shows a clear correlation with the nuclear size difference between the ground and excited states. In $^7_\Lambda \textrm{Li}$ and $^9_\Lambda \textrm{Be}$, the significant shrinkage of cluster structures occurs consistently with the prediction of other calculations.

2nd-order optical model of the isotopic dependence of heavy ion absorption cross sections for radiation transport studies

Abstract Heavy ion absorption cross sections play an important role in radiation transport codes used in risk assessment and for shielding studies of galactic cosmic ray (GCR) exposures. Due to the GCR primary nuclei composition and nuclear fragmentation leading to secondary nuclei heavy ions of charge number, Z with 3 ≤ Z ≥ 28 and mass numbers, A with 6 ≤ A ≥ 60 representing about 190 isotopes occur in GCR transport calculations. In this report we describe methods for developing a data-base of isotopic dependent heavy ion absorption cross sections for interactions. Calculations of a 2nd-order optical model solution to coupled-channel solutions to the Eikonal form of the nucleus-nucleus scattering amplitude are compared to 1st-order optical model solutions. The 2nd-order model takes into account two-body correlations in the projectile and target ground-states, which are ignored in the 1st-order optical model. Parameter free predictions are described using one-body and two-body ground state form factors for the isotopes considered and the free nucleon-nucleon scattering amplitude. Root mean square (RMS) matter radii for protons and neutrons are taken from electron and muon scattering data and nuclear structure models. We report on extensive comparisons to experimental data for energy-dependent absorption cross sections for over 100 isotopes of elements from Li to Fe interacting with carbon and aluminum targets. Agreement between model and experiments are generally within 10% for the 1st-order optical model and improved to less than 5% in the 2nd-order optical model in the majority of comparisons. Overall the 2nd-order optical model leads to a reduction in absorption compared to the 1st-order optical model for heavy ion interactions, which influences estimates of nuclear matter radii.

Langevin model of low-energy fission

Background: Since the earliest days of fission, stochastic models have been used to describe and model the process. For a quarter century, numerical solutions of Langevin equations have been used to model fission of highly excited nuclei, where microscopic potential-energy effects have been neglected.Purpose: In this paper I present a Langevin model for the fission of nuclei with low to medium excitation energies, for which microscopic effects in the potential energy cannot be ignored.Method: I solve Langevin equations in a five-dimensional space of nuclear deformations. The macroscopic-microscopic potential energy from a global nuclear structure model well benchmarked to nuclear masses is tabulated on a mesh of approximately ${10}^{7}$ points in this deformation space. The potential is defined continuously inside the mesh boundaries by use of a moving five-dimensional cubic spline approximation. Because of reflection symmetry, the effective mesh is nearly twice this size. For the inertia, I use a (possibly scaled) approximation to the inertia tensor defined by irrotational flow. A phenomenological dissipation tensor related to one-body dissipation is used. A normal-mode analysis of the dynamical system at the saddle point and the assumption of quasiequilibrium provide distributions of initial conditions appropriate to low excitation energies, and are extended to model spontaneous fission. A dynamical model of postscission fragment motion including dynamical deformations and separation allows the calculation of final mass and kinetic-energy distributions, along with other interesting quantities.Results: The model makes quantitative predictions for fragment mass and kinetic-energy yields, some of which are very close to measured ones. Varying the energy of the incident neutron for induced fission allows the prediction of energy dependencies of fragment yields and average kinetic energies. With a simple approximation for spontaneous fission starting conditions, quantitative predictions are made for some observables which are close to measurements.Conclusions: This model is able to reproduce several mass and energy yield observables with a small number of physical parameters, some of which do not need to be varied after benchmarking to $^{235}\mathrm{U}(n,f)$ to predict results for other fissioning isotopes.

Global Correlations for Low-Lying Collective 2+ States

By using the triaxial rotor model and the anharmonic vibrator model with phonon mixing, we derive a global correlation between the quadrupole moments of the two lowest 2+ states in collective nuclei that had previously been observed in experimental data across the periodic table. We then derive other electromagnetic properties for these two models of nuclear structure and compare them globally with experimental data. We find that both models are able to robustly describe the experimental data across the region of nuclei for which the models are applicable, including a large number that they have in common. We then show that there seems to exists a robust orthogonal transformation between these two models for realistic nuclear systems, suggesting that these two seemingly diverse descriptions of quadrupole collective phenomena seem to act in a similar model space and may therefore have a common origin.

Study of similarity and dissimilarity between10Be and9Li nuclei with microscopic structure and reaction models

We apply the microscopic nuclear structure and reaction models to the elastic scattering of the10Be and9Li nuclei. The states of the10Be and9Li nuclei are described as an α + α(t) + n + n four-body system based on the cluster wave function, respectively. The elastic scattering cross section is obtained by the microscopic coupled channel (MCC) calculation with the MPa interaction, which is the latest version of the complex G-matrix interaction derived from the ESC NN interaction model. We compare the channel coupling (CC) effect of the10Be nucleus with that of the9Li nucleus in the elastic scattering cross sections calculated with the same incident energy per nucleon. At the backward angles, the CC effect on the elastic scattering cross section for the incident10Be nucleus is clearly larger than that for the incident9Li nucleus. We investigate the dissimilarity for the CC effect through the dynamical polarization potential.

Reduced Transition Probabilities for the Gamma Decay of the 7.8eV Isomer in ^{229}Th.

The reduced magnetic dipole and electric quadrupole transition probabilities for the radiative decay of the ^{229}Th 7.8 eV isomer to the ground state are predicted within a detailed nuclear-structure model approach. We show that the presence and decay of this isomer can only be accounted for by the Coriolis mixing emerging from a remarkably fine interplay between the coherent quadrupole-octupole motion of the nuclear core and the single-nucleon motion within a reflection-asymmetric deformed potential. We find that the magnetic dipole transition probability which determines the radiative lifetime of the isomer is considerably smaller than presently estimated. The so-far disregarded electric quadrupole component may have non-negligible contributions to the internal conversion channel. These findings support new directions in the experimental search of the ^{229}Th transition frequency for the development of a future nuclear frequency standard.

“Sloppy” nuclear energy density functionals. II. Finite nuclei

A study of parameter sensitivity of nuclear energy density functionals, initiated in the first part of this work \cite{NV.16}, is extended by the inclusion of data on ground-state properties of finite nuclei in the application of the manifold boundary approximation method (MBAM). Density functionals used in self-consistent mean-field calculations, and nuclear structure models based on them, are generally "sloppy" and exhibit an exponential range of sensitivity to parameter variations. Concepts of information geometry are used to identify the presence of effective functionals of lower dimension in parameter space associated with parameter combinations that can be tightly constrained by data. The MBAM is used in an iterative procedure that systematically reduces the complexity and the dimension of parameter space of a sloppy functional, with properties of nuclear matter and data on finite nuclei determining not only the values of model parameters, but also the optimal functional form of the density dependence.

Particle decay of proton-unbound levels in N12

Background: Transfer reactions are a useful tool for studying nuclear structure, particularly in the regime of low level densities and strong single-particle strengths. In addition, transfer reactions can populate levels above particle decay thresholds, allowing for the possibility of studying the subsequent decays and furthering our understanding of the nuclei being probed. In particular, the decay of loosely bound nuclei such as $^{12}\mathrm{N}$ can help inform and improve structure models.Purpose: To learn about the decay of excited states in $^{12}\mathrm{N}$, to more generally inform nuclear structure models, particularly in the case of particle-unbound levels in low-mass systems which are within the reach of state-of-the-art ab initio calculations.Method: In this follow-up analysis of previously published data [Chipps et al. (JENSA Collaboration), Phys. Rev. C 92, 034325 (2015)], decay particles from excited states populated in $^{12}\mathrm{N}$ have been detected in coincidence with tritons from the $^{14}\mathrm{N}(p,t)^{12}\mathrm{N}$ transfer reaction. Specifically, decay protons from proton-unbound levels above $\ensuremath{\sim}2$ MeV excitation energy were observed by utilizing the Jet Experiments in Nuclear Structure and Astrophysics (JENSA) gas jet target.Results: Isotropic proton branching ratios for the $p0$ and $p1$ decay channels are calculated and decay particle spectra for the populated levels from $p0$, $p1$, and $p2$ decay are given.Conclusions: The current data from $^{14}\mathrm{N}(p,t)^{12}\mathrm{N}$ will help provide nuclear structure and decay information input to models in this mass region.

The Dynamic Response Analysis of Pseudo Three Dimensional of Nuclear Island Plant Structure under Non-lithology Foundation Condition

Building nuclear power plant structure on lithology ground or soft ground has become an inevitable and popular trend in the development of nuclear island plant structure. It leads the seismic analysis of non-lithology foundation to be the key technical issues to choose the nuclear power plant site. In order to solve the engineering practicality issues of seismic analysis of non-lithology foundation and the issues of simplifying the complex nuclear power plant structure, the three- dimensional (3D) finite element model of the AP1000 nuclear power plant structure has been simplified to two-dimensional model in this paper based on ANSYS software. The principle of the simplification is that the mass and stiffness of models should be equivalent. Then establish the pseudo 3D model in SuperFLUSH software to explore the mechanism of the earthquake loads and seismic response characteristics of nuclear power plant structure. Finally, compare the frequency characteristics and compare the true three-dimensional results of SASSI software with the results of SuperFLUSH software to verify the rationality and effectiveness of the simplification.

Seismically induced uplift effects on nuclear power plants. Part 1: Containment building rocking spectra

Current nuclear regulatory codes specify design considerations for extreme seismic scenarios, focusing primarily on the response of the containment structure of a nuclear power plant. However, in current state-of-practice and in most seismic regulations worldwide, the consideration of soil-structure interaction and potential development of geometrically nonlinear effects, such as rocking and sliding with uplift, is not taken into consideration. To explore this issue, a refined 3D finite element model of a typical nuclear power plant containment structure is developed, comprising solid elements for the soil and foundation, plus shell elements for the structure. The aim is identification of foundation-soil separation phenomena under a suite of ground motions with distinct frequency content. At first, harmonic excitations are used, for both cases of stiff sand and rock subsoil profiles, leading to rocking spectra that depict the displacement demand in connection with nonlinear separation. Clear influence zones can be distinguished, especially in the low frequency bands for the stiff sand case. Next, three subsets of 30 ground motion records are carefully selected and grouped in ensembles according to their frequency content, normalized to a PGA of 0.36g, which corresponds to the highest design acceleration in Europe. Ground motions with low mean frequency content are observed to lead to the onset of geometrically nonlinear phenomena, along with a higher displacement demand. The interplay between ground motion characteristics, dynamic properties of the containment structure and stiffness of the soil is also highlighted. More specifically, it is shown that stiff containment structures on soft soils are more prone to foundation uplift. This possibility is often neglected in design codes and the consequence is that under certain circumstances, damage may be caused to the internal power generation equipment.

Macroscopic-microscopic model of nuclear potential energy

To improve the evaluation of nuclear observables, refined models are to be used more and more as underlying analysis tools. Fission is a complex process and is the less accurately described with current models. Standard evaluation models rely on the Hill-Wheeler formalism for the fission transmission coefficient, which in turns is based on phenomenological parameters “reflecting” the fission barrier heights and widths. To reduce the weight of phenomenology in the evaluation process, nuclear structure models are expected to embed more and more microscopic descriptions. As models are rarely exact, evaluators are often compelled to “tune” model parameters so that observables can be properly reproduced. Related computation time can thus be a major hindrance to the use of advanced models in evaluation as final adjustments are expected to remain necessary. For this reason, a macroscopic-microscopic model has been selected to replace the current phenomenological description of fission barriers. The Finite-Range Liquid-Drop Model (FRLDM) has been implemented in the CONRAD evaluation code and its present implementation shows remarkable consistency with experimental and published benchmark data. The CONRAD code can be used to provide expectation values but also related uncertainties and covariance data. Sensitivity of FRLDM parameters and the correlation matrix between these parameters have been obtained so that further uncertainty propagation on barrier heights can be carried out in the near future.

Commissioning of the BRIKEN beta-delayed neutron detector for the study of exotic neutron-rich nuclei

Beta-delayed neutron emission (Beta-n) is a form of radioactive decay in which an electron, an anti-neutrino and one or more neutrons are emitted. This process arises if the energy window of the decay Q_Beta is greater than the neutron separation energy S n of the daughter. The probability in each decay of emitting neutrons is called the Pn value. This form of decay plays a key role in the synthesis of chemical elements in the Universe via the rapid neutron capture process, or r-process. The r-process proceeds far from the valley of nuclear stability, and leads to very neutron-rich nuclei that then decay to the line of stability. Most of these nuclei are sn emitters. The initial abundance distribution is shaped by the decay half-life T1/2, but the neutron emission affects the final abundances in two ways: on the one hand it shifts the decay path to lower masses and on the other hand it provides a source of neutrons for late captures that will shift it in the opposite way. Thus, a good knowledge of Pn and T1/2 values of the nuclei between the line of stability and the r-process path is needed for a correct understanding of the observed abundances. Besides the astrophysical interest, the measurement of new Pn values and half-lives is also useful for refining nuclear structure models, constraining parameters of the models and testing s-strength functions [3]. Our current understanding of the process of s-delayed multiple neutron emission, as well as the competition between different open channels (gamma, one-neutron, two-neutron, etc), is incomplete because of the scarcity of experimental data. With these ideas in mind, the BRIKEN (Beta-delayed-neutron-measurements at RIKEN) collaboration was established, with the aim of greatly improving the quantity and quality of data the decays of very neutron-rich nuclei close to the r-process path.