Nuclear Structure Models Research Articles

Probabilistic seismic performance evaluation of nuclear containment structure subjected to far-fault ground motions

This study presents probabilistic seismic performance evaluation of nuclear containment structure subjected to far-fault ground motions. To achieve this objective, refined finite element model of nuclear containment structure is established and incremental dynamic analysis (IDA) is performed automatically using pre-processing and post-processing scripts. Cracking status, roof drift, damage dissipated energy and floor acceleration of the nuclear containment structure is discussed. Furthermore, probabilistic seismic safety margin of nuclear containment structure is quantitatively evaluated by median value method and confidence interval method. Finally, a closed-form solution for the annual frequency of exceedance for the roof drift of the nuclear containment structure is derived, and the effectiveness of the closed-form solution is verified by the classical direct numerical integration method. Annual frequency of exceedance for the roof drift of the nuclear containment structure corresponding to different performance levels is analyzed. Results indicated that the bottom of nuclear containment structure is the most vulnerable location. In general, nuclear containment structure subjected to far-fault ground motions is dominated by shearing cracks. When the ground motion intensity level is less than 0.4 g, damage dissipated energy of the nuclear containment structure is very small. In general, with the increase of elevation, acceleration amplification factor of the nuclear containment structure increases rapidly. Probabilistic seismic safety margin of the nuclear containment structure evaluated by median value method tends to be conservative. Analytical and classical numerical integration method provides almost the same prediction of the annual frequency of exceedance for the roof drift of the nuclear containment structure, which indicates the effectiveness of the proposed closed-form solution.

A Lightweight Among Heavyweights

Researchers have observed the lightest uranium isotope to date, offering insight into models of nuclear structure.

Equation of state of asymmetric nuclear matter and the tidal deformability of neutron star

Neutron star (NS) is a unique astronomical compact object where the four fundamental interactions have been revealed from the observation and studied in different ways. While the macroscopic properties of NS like mass and radius can be determined within the General Relativity using a realistic equation of state (EOS) of NS matter, such an EOS is usually generated by a nuclear structure model like, e.g., the nuclear mean-field approach to asymmetric nuclear matter. Given the radius of NS extended to above 10 km and its mass up to twice the solar mass, NS is expected to be tidally deformed when it is embedded in a strong tidal field. Such a tidal effect was confirmed unambiguously in the gravitation wave signals detected recently by the LIGO and Virgo laser interferometers from GW170817, the first ever direct observation of a binary NS merger. A nonrelativistic mean-field study is carried out in the present work within the Hartree-Fock formalism to construct the EOS of NS matter, which is then used to determine the tidal deformability, gravitational mass, and radius of NS. The mean-field results are compared with the constraints imposed for these quantities by the global analysis of the observed GW170817 data, and a strong impact by the incompressibility of nuclear matter on the hydrostatic configuration of NS is shown.

Free Molecule Studies by Perturbed γ-γ Angular Correlation: A New Path to Accurate Nuclear Quadrupole Moments.

Accurate nuclear quadrupole moment values are essential as benchmarks for nuclear structure models and for the interpretation of experimentally determined nuclear quadrupole interactions in terms of electronic and molecular structure. Here, we present a novel route to such data by combining perturbed γ-γ angular correlation measurements on free small linear molecules, realized for the first time within this work, with state-of-the-art abinitio electronic structure calculations of the electric field gradient at the probe site. This approach, also feasible for a series of other cases, is applied to Hg and Cd halides, resulting in Q(^{199}Hg,5/2^{-})=+0.674(17) b and Q(^{111}Cd,5/2^{+})=+0.664(7) b.

Nucleon-nucleus optical potential computed with the Gogny interaction

The ability of the Gogny forces of the D1 family to describe the nucleon-nucleus scattering is studied. To this end, we use an optical model (OM) potential built up using a semi-microscopic nuclear matter (NM) approach. The real and imaginary parts of the OM are provided by the first and second-order terms, respectively, of the Taylor expansion of the mass operator calculated within the Brueckner–Hartree–Fock (BHF) method using the reaction G-matrix built up with the effective Gogny force instead of a microscopic interaction. The optical potential in finite nuclei is obtained through the local density approximation (LDA) using the neutron and proton densities provided by a quasi-local Hartree–Fock (HF) calculation with the same Gogny force for the sake of consistency. A reasonable good agreement is found between the theoretical differential cross-sections and the analyzing powers (AP) of the elastic neutron and proton scattering along the periodic table from Ca to Pb calculated with the Gogny forces and the corresponding values predicted by the global phenomenological potential of Koning and Delaroche. To investigate the limits of the approximations used in this work, comparisons with the results of nucleon-nucleus elastic scattering in 40Ca and 48Ca obtained using the nuclear structure model (NSM) are also performed.

Th229m isomer from a nuclear model perspective

The physical conditions for the emergence of the extremely low-lying nuclear isomer $^{229m}$Th at approximately 8 eV are investigated in the framework of our recently proposed nuclear structure model. Our theoretical approach explains the $^{229m}$Th-isomer phenomenon as the result of a very fine interplay between collective quadrupole-octupole and single-particle dynamics in the nucleus. We find that the isomeric state can only appear in a rather limited model space of quadrupole-octupole deformations in the single-particle potential, with the octupole deformation being of a crucial importance for its formation. Within this deformation space the model-described quantities exhibit a rather smooth behaviour close to the line of isomer-ground state quasi-degeneracy determined by the crossing of the corresponding single-particle orbitals. Our comprehensive analysis confirms the previous model predictions for reduced transition probabilities and the isomer magnetic moment, while showing a possibility for limited variation in the ground-state magnetic moment theoretical value. These findings prove the reliability of the model and suggest that the same dynamical mechanism could manifest in other actinide nuclei giving a general prescription for the search and exploration of similar isomer phenomena.

Shape and electromagnetic properties of the229mTh isomer

We examine the physical conditions, and specifically the role of the quadrupole-octupole deformation, for the emergence of the 8 eV “clock” isomer229mTh. Our nuclear structure model suggests that such an extremely low-energy state can be the result of a very fine interplay between the shape and single-particle (s.p.) dynamics in the nucleus. We find that the isomer can only appear in a rather limited region of quadrupoleoctupole deformation space close to a line along which the ground-state and isomer s.p. orbitals 5/2[633] and 3/2[631], respectively, cross each other providing the isomer-formation quasi-degeneracy condition. The crucial role of the octupole deformation in the formation mechanism is pointed out. Our calculations within the outlined deformation region show a smooth behaviour of the229Th electromagnetic properties, including the isomer decay rate, allowing for their more precise theoretical determination

Neutrinoless double-electron capture

Double-beta processes play a key role in the exploration of neutrino and weak interaction properties, and in the searches for effects beyond the Standard Model. During the last half century many attempts were undertaken to search for double-beta decay with emission of two electrons, especially for its neutrinoless mode ($0\nu2\beta^-$), the latter being still not observed. Double-electron capture (2EC) was not in focus so far because of its in general lower transition probability. However, the rate of neutrinoless double-electron capture ($0\nu2$EC) can experience a resonance enhancement by many orders of magnitude in case the initial and final states are energetically degenerate. In the resonant case, the sensitivity of the $0\nu2$EC process can approach the sensitivity of the $0\nu2\beta^-$ decay in the search for the Majorana mass of neutrinos, right-handed currents, and other new physics. We present an overview of the main experimental and theoretical results obtained during the last decade in this field. The experimental part outlines search results of 2EC processes and measurements of the decay energies for possible resonant $0\nu$2EC transitions. An unprecedented precision in the determination of decay energies with Penning traps has allowed one to refine the values of the degeneracy parameter for all previously known near-resonant decays and has reduced the rather large uncertainties in the estimate of the $0\nu2$EC half-lives. The theoretical part contains an updated analysis of the electron shell effects and an overview of the nuclear structure models, in which the nuclear matrix elements of the $0\nu2$EC decays are calculated. One can conclude that the decay probability of $0\nu$2EC can experience a significant enhancement in several nuclides.

Statistical learnability of nuclear masses

After more than 80 years from the seminal work of Weizs\"acker and the liquid drop model of the atomic nucleus, deviations from experiments of mass models ($\sim$ MeV) are orders of magnitude larger than experimental errors ($\lesssim$ keV). Predicting the mass of atomic nuclei with precision is extremely challenging. This is due to the non--trivial many--body interplay of protons and neutrons in nuclei, and the complex nature of the nuclear strong force. Statistical theory of learning will be used to provide bounds to the prediction errors of model trained with a finite data set. These bounds are validated with neural network calculations, and compared with state of the art mass models. Therefore, it will be argued that the nuclear structure models investigating ground state properties explore a system on the limit of the knowledgeable, as defined by the statistical theory of learning.

SRC based model for the nuclear structure

The existence of SRCs inside nuclei has been verified by many experiments [1-3] and is considered to be underlying reason behind the EMC effect [4]. After discussion of various motivation for the new approach, a SRC based nuclear structure model is proposed. The model is shown to be equivalent to the liquid drop model for the consideration of the nuclear binding energy and its equivalence to the cluster model for specific applications is also highlighted. The proposed model provides many new insights about various nuclear observables and some of them are discussed qualitatively.

Recent advances in the description of reactions involving exotic nuclei

In this contribution to the proceedings of the International Nuclear Physics Conference 2019, I review recent developments made in reaction models used to analyse data measured at radioactive-ion beam facilities to study exotic nuclear structures. I focus in particular on reactions like elastic scattering and breakup, which are used to study halo nuclei. Although these peculiar nuclei challenge usual nuclear-structure models, some can now be computed ab initio. This brief review illustrates the progress made in nuclear-reaction theory in the last few years to improve the description of the projectile within reaction models. I dedicate this contribution to the memory of Mahir Hussein, who has significantly contributed to this field and who passed away in May this year.

Dynamical Symmetries in Shell and Collective Models of Nuclear Structure

The dynamical symmetries in the algebraic shell model and the collective Interacting Vector Boson Model (IVBM) realized in terms of fermion and boson creation and annihilation operators are investigated. The obtained analytic eigen-energies in both models are compared with the experimental ones and the strengths of the corresponding terms of the model Hamiltonians are evaluated in both cases. In the algebraic realization of the Pairing plus Quadrupole Shell Model the correlations and transition between the quadrupole and pairing phases—dynamical symmetries are investigated in application to nuclear systems in the first few light shells. In the symplectic extension of the IVBM the spectra of heavy even-even nuclei with transitional between rotational and vibrational character is well reproduced. The algebraic connections between dynamical symmetries of the nuclear collective spectra and the ordering of the low-lying states with fixed angular momentum permits a reasonable and experimentally proved prediction of the position of the 0+ band heads of the collective bands. The models based on dynamical symmetries give an elegant and simple way to describe the complex spectra of nuclei with different shapes.

High-resolution study of excited states in Gd158 with the (p, t) reaction

The excitation spectra in the deformed nucleus 158Gd have been studied with high energy resolution by means of the (p,t) reaction using the Q3D spectrograph facility at the Munich Tandem accelerator. The angular distributions of tritons were measured for more than 200 excited states seen in the triton spectra up to 4.3 MeV. A number of 36 excited 0+ states (five tentative), have been assigned by comparison of experimental angular distributions with the calculated ones using the CHUCK code. Assignments for levels with higher spins are the following: 95 for 2+ states, 64 for 4+ states, 14 for 6+ states and about 20 for negative parity states. Sequences of states which can be treated as rotational bands are selected. The analysis of the moments of inertia defined for these bands is carried out. This high number of excited states in a deformed nucleus, close to a complete level scheme, constitutes a very good ground to check models of nuclear structure. The large ensembles of states with the same spin-parity offer unique opportunities for statistical analysis. Such an analysis for the 0+, 2+ and 4+ states sequences, for all K-values and for well-determined projections K of the angular momentum is performed. The obtained data may indicate on a K symmetry breaking. Experimental data are compared with interacting boson model (IBM) calculations using the spdf version of the model. The energies of the low-lying levels, the transition probabilities in the first bands and the distribution in transfer intensity of the 0+ states are calculated and compared with experiment.

Nuclear structure model for double-charge-exchange processes

A new model, based on the BCS approach, is specially designed to describe nuclear phenomena $(A,Z)\rightarrow (A,Z\pm 2)$ of double-charge exchange (DCE). After being proposed, and applied in the particle-hole limit, by one of the authors (F. Krmpoti\'c [1]), so far it was never been applied within the BCS mean-field framework, nor has its ability to describe DCE processes been thoroughly explored. It is a natural extension of the pn-QRPA model, developed by Halbleib and Sorensen [2] to describe the single $\beta$-decays $(A,Z)\rightarrow (A,Z\pm 1)$, to the DCE processes. As such, it exhibits several advantages over the pn-QRPA model when is used in the evaluation of the double beta decay (DBD) rates. For instance, i) the extreme sensitivity of the nuclear matrix elements (NMEs) on the model parametrization does not occur, ii) it allows to study NMEs, not only for the fundamental state in daughter nuclei, as the pn-QRPA model does, but also for all final $0^+$ and $2^+$ states, accounting at the same time their excitation energies and the corresponding DBD Q-values, iii) together with the DBD-NMEs it provides also the energy spectra of Fermi and Gamow-Teller DCE transition strengths, as well as the locations of the corresponding resonances and their sum rules, iv) the latter are relevant for both the DBD and the DCE reactions, since the involved nuclear structure is the same; this correlation does not exist within the pn-QRPA model. As an example, detailed numerical calculations are presented for the $(A,Z)\rightarrow (A,Z+ 2)$ process in $^{48}$Ca $\rightarrow ^{48}$Ti and the $(A,Z)\rightarrow (A,Z- 2)$ process in $^{96}$Ru $\rightarrow ^{96}$Mo, involving all final $0^+$ states and $2^+$ states.

Experimental study of intruder components in light neutron-rich nuclei via single-nucleon transfer reaction

With the development of radioactive beam facilities, studies concerning the shell evolution of unstable nuclei have recently gained prominence. Intruder components, particularly s-wave intrusion, in the low-lying states of light neutron-rich nuclei near N=8 are of importance in the study of shell evolution. The use of single-nucleon transfer reactions in inverse kinematics has been a sensitive tool that can be used to quantitatively investigate the single-particle orbital component of selectively populated states. The spin-parity, spectroscopic factor (or single-particle strength), and effective single-particle energy can all be extracted from such reactions. These observables are often useful to explain the nature of shell evolution, and to constrain, check, and test the parameters used in nuclear structure models. In this article, the experimental studies of the intruder components in low-lying states of neutron-rich nuclei of He, Li, Be, B, and C isotopes using various single-nucleon transfer reactions are reviewed. The focus is laid on the precise determination of the intruder s-wave strength in low-lying states.

Research on Floor Response Spectrum of Shielded Building Structure under Seismic Loading

As a clean energy source, nuclear power has broad prospects for development. It is of great significance to study the seismic response of nuclear power plants. PLAXIS software is used to establish the whole finite element model of AP1000 nuclear power plant shielding plant structure. Considering the foundation embedding and soil-structure interaction, the seismic response analysis of nuclear power plants on different inclined soft rock sites was carried out under seismic loading. By analyzing and comparing the calculated results of the floor response spectrum amplification factor, the peak frequency of the floor response spectrum at the important position is smaller than the peak frequency of the design response spectrum, the inclination of the inclined site will affect the peak frequency and cause the amplification effect.

Stability of the heaviest elements: K isomer in No250

Decay spectroscopy of No250 has been performed using digital electronics and pulse-shape analysis of the fast nuclear decays for the first time. Previous studies of No250 reported two distinct fission decay lifetimes, related to the direct fission of the ground state and to the decay of an isomeric state but without the possibility to determine if the isomeric state decayed directly via fission or via internal electromagnetic transitions to the ground state. The data obtained in the current experiment allowed the puzzle to finally be resolved, attributing the shorter half-life of t1/2=3.8±0.3μs to the ground state and the longer half-life t1/2=34.9−3.2+3.9μs to the decay of an isomeric state. No250 becomes, thus, one of a very few examples of very heavy nuclei with an isomeric state living considerably longer than its ground state. This phenomenon has important consequences for the nuclear-structure models aiming to determine the borders of the island of stability of superheavy elements.

Group contractions and conformal maps in nuclear structure models

Group contraction is a procedure in which a symmetry group is reduced into a group of lower symmetry in a certain limiting case. Examples are provided in the large boson mumber limit of the Interacting Boson Approximation (IBA) model by a) the contraction of the SU(3) algebra into the [R5]SO(3) algebra of the rigid rotator, consisting of the angular momentum operators forming SO(3), plus 5 mutually commuting quantities, the quadrupole operators, b) the contraction of the O(6) algebra into the [R5]SO(5) algebra of the ∞-unstable rotator. We show how contrac- tions can be used for constructing symmetry lines in the interior of the symmetry triangle of the IBA model. In mathematics, a conformal map is a function which preserves angles. We show how this procedure can be used in the framework of the Bohr Hamiltonian, leading to a Hamiltonian in a curved space, in which the mass depends on the nuclear deformation Ø, while it remains independent of the collective variable ∞ and the three Euler angles. This Hamiltonian is proved to be equivalent to that obtained using techniques of Supersymmetric Quantum Mechanics.

Sensitivity of one-neutron knockout to the nuclear structure of halo nuclei

Background: Information about the structure of halo nuclei are often inferred from one-neutron knockout reactions. Typically the parallel-momentum distribution of the remaining core is measured after a high-energy collision of the exotic projectile with a light target. Purpose: We study how the structure of halo nuclei affects knockout observables considering an eikonal model of reaction. Method: To evaluate the sensitivity of both the diffractive and stripping parallel-momentum distributions to the structure of halo nuclei, we consider several descriptions of the projectile within a halo effective field theory. We consider the case of 11Be, the archetypical one-neutron halo nucleus, impinging on 12C at 68 MeV/nucleon, which are usual experimental conditions for such measurements. The low-energy constants of the description of 11Be are fitted to experimental data as well as to predictions of an ab initio nuclear-structure model. Results: One-neutron knockout reaction is confirmed to be purely peripheral, the parallel-momentum distribution of the remaining core is only sensitive to the asymptotics of the ground-state wavefunction and not to its norm. The presence of an excited state in the projectile spectrum reduces the amplitude of the breakup cross section; the corresponding probability flux is transferred to the inelastic-scattering channel. Although the presence of a resonance in the core-neutron continuum significantly affects the energy distribution, it has no impact on the parallel-momentum distribution. Conclusions: One-neutron knockout cross section can be used to infer information about the tail of the ground-state wavefunction, viz. its asymptotic normalization coefficient (ANC). The independence of the parallel-momentum distribution on the continuum description makes the extraction of the ANC from this observable very reliable.

Application of the collective model to determine some vibrational bands of 140La nucleus

140La is created from the thermal neutron capture reaction of 139La, which is the product of the fission reaction. It makes some effects into the components of the nuclear reactor core. Understanding the properties and structure of 140La is important in operating the nuclear reactor. Besides that, nuclear structure models are very effective in explaining the properties of nuclear structure. There are many nuclear structure models to solve those problems, such as Liquid Drop Model, Shell Model, Fermi Model, etc. Among them, the Collective Model has been very successful in describing the variety of nuclear properties, especially energy levels in deformed nuclei that the Shell Model and the Liquid Drop Model does not apply. This paper presents the application of the Collective Model to determine some vibrational bands of 140La nucleus. This experiment is performed at channel No.2 of Dalat Research Reactor (DRR), Prompt gamma neutron activation analysis method (PGNAA) is used. The result has found 8 vibrational bands of 140La nucleus. It’s quite relevant to the theoretical calculation. The deviations are less than 1.6 %.