Microscopic Nuclear Structure Research Articles

Predicting nucleon-nucleus scattering observables using nuclear structure theory

Developing a predictive capability for inelastic scattering will find applications in multiple areas. Experimental data for neutron-nucleus inelastic scattering is limited and thus one needs a robust theoretical framework to complement it. Charged-particle inelastic scattering can be used as a surrogate for (n, γ) reactions to predict capture cross sections for unstable nuclei. Our work uses microscopic nuclear structure calculations for spherical nuclei to obtain nucleon-nucleus scattering potentials and calculate cross sections for these processes. We implement the Jeukenne, Lejeune, Mahaux (JLM) semi-microscopic folding approach, where the medium effects on nuclear interaction are parameterized in nuclear matter to obtain the nucleon-nucleon (NN) interaction in a medium at positive energies. We solve for the nuclear ground state using the Hartree-Fock-Bogliubov (HFB) many-body method, assuming the nucleons within the nucleus interact via the Gogny-D1M potential. The vibrational excited states of the target nucleus are calculated using the quasi-particle random phase approximation (QRPA). We demonstrate our approach for spherical nuclei in the medium-mass region, showing scattering results for the 90Zr nucleus.

The NUMEN project: probing nuclear response to weak interaction by nuclear reactions

Different reactions channels induced by the 18O + 40Ca collisions at 275 MeV incident energy are simultaneously measured and analysed consistently within the same reaction and structure frameworks within the NUMEN project. The project aims to provide data-driven information for the determination of the nuclear matrix elements involved in the neutrinoless double beta decay. In particular, the elastic and inelastic scattering, one- and two-proton transfer, one-neutron transfer, and single charge exchange reactions are explored. The full quantum-mechanical calculations, performed by including microscopic nuclear structure inputs, describe well all the experimental data, giving support to a multi-channel strategy for the analysis of heavy-ion induced direct reactions.

Finite-nuclear-size effect in hydrogenlike ions with relativistic nuclear structure

The finite-nuclear-size (FNS) effect has a large contribution to atomic spectral properties, especially for heavy nuclei. By adopting the microscopic nuclear charge-density distributions obtained from the relativistic continuum Hartree-Bogoliubov (RCHB) theory, we systematically investigate the FNS corrections to atomic energy levels and bound-electron $g$ factors of hydrogenlike ions with nuclear charge up to 118. The comparison of the present numerical calculations with the predictions from empirical nuclear charge models, the nonrelativistic Skyrme-Hartree-Fock calculations, and the results based on experimental charge densities indicate that both the nuclear charge radius and the detailed shape of the charge-density distribution play important roles in determining the FNS corrections. The variation of FNS corrections to energy levels and $g$ factors with respect to the nuclear charge are investigated for the several lowest bound states of hydrogenlike ions. It is shown that they both increase by orders of magnitude with increasing nuclear charge, while the ratio between them has a relatively weak dependence on the nuclear charge. The FNS corrections to the ${s}_{1/2}$ and ${p}_{1/2}$ bound-state energies from the RCHB calculations are generally in good agreement with the analytical estimations by Shabaev [V. M. Shabaev, J. Phys. B 26, 1103 (1993)] based on the homogeneously charged sphere nuclear model, with the discrepancy indicating the distinct contribution of microscopic nuclear structure to the FNS effects.

Local position-space two-nucleon potentials from leading to fourth order of chiral effective field theory

We present local, position-space chiral NN potentials through four orders of chiral effective field theory ranging from leading order (LO) to next-to-next-to-next-to-leading order (N3LO, fourth order) of the Delta-less version of the theory. The long-range parts of these potentials are fixed by the very accurate pi-N LECs as determined in the Roy-Steiner equations analysis. At the highest order (N3LO), the NN data below 190 MeV laboratory energy are reproduced with the respectable chi^2/datum of 1.45. A comparison of the N3LO potential with the phenomenological Argonne v_18 (AV18) potential reveals substantial agreement between the two potentials in the intermediate range ruled by chiral symmetry, thus, providing a chiral underpinning for the phenomenological AV18 potential. Our chiral NN potentials may serve as a solid basis for systematic ab initio calculations of nuclear structure and reactions that allow for a comprehensive error analysis. In particular, the order by order development of the potentials will make possible a reliable determination of the truncation error at each order. Our new family of local position-space potentials differs from existing potentials of this kind by a weaker tensor force as reflected in relatively low D-state probabilities of the deuteron (P_D less or equal 4.0% for our N3LO potentials) and predictions for the triton binding energy above 8.00 MeV (from two-body forces alone). As a consequence, our potentials may lead to different predictions when applied to light and intermediate-mass nuclei in ab initio calculations and, potentially, help solve some of the outstanding problems in microscopic nuclear structure.

Mirror nucleon removal reactions in p -shell nuclei

Nucleon removal reactions have been shown to be an effective tool for studying the single particle structure of nuclei. This work continues efforts to experimentally probe and benchmark the reaction and structure models used to calculate the removal reaction cross sections when using microscopic nuclear structure inputs. Three different single nucleon removal reactions were performed, from p-shell nuclei with masses A=7, 9, and 10. The residual nuclei from the reactions were detected in coincidence with γ rays to determine partial cross sections to individual final states. The eikonal direct-reaction model is combined with overlap functions and residual nucleus densities from microscopic, variational Monte Carlo calculations to provide consistent nuclear structure input to the partial cross section calculations. Comparisons of measured and calculated cross sections, including for mirror reactions, are presented. The analysis of the partial cross sections leading to the ground states shows a similar behavior to the one observed from analyses of inclusive cross sections using shell model nuclear structure input: the theoretical description of the removal process is in better agreement with the data when removing weakly bound nucleons, than when removing well-bound ones. The two mirror reaction pairs presented here show consistent results between the respective members of the pairs. The results obtained for the population of the excited states, however, show a systematically different trend that appears connected to the structure part of the calculation. Additional cases are needed to better understand the respective roles of structure and dynamical effects in the deviations.1 MoreReceived 24 November 2021Accepted 18 February 2022DOI:https://doi.org/10.1103/PhysRevC.105.034314©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDirect reactionsProperties6 ≤ A ≤ 19TechniquesNuclear reactionsNuclear structure & decaysQuantum Monte CarloSpectrometers & spectroscopic techniquesNuclear Physics

Nuclear reaction network unveils novel reaction patterns based on stellar energies

Despite the advances in discovering new nuclei, modeling microscopic nuclear structure, nuclear reactors, and stellar nucleosynthesis, we still lack a systemic tool, such as a network approach, to understand the structure and dynamics of over 70 thousands reactions compiled in JINA REACLIB. To this end, we develop an analysis framework, under which it is simple to know which reactions generally are possible and which are not, by counting neutrons and protons incoming to and outgoing from any target nucleus. Specifically, we assemble here a nuclear reaction network in which a node represents a nuclide, and a link represents a direct reaction between nuclides. Interestingly, the degree distribution of nuclear network exhibits a bimodal distribution that significantly deviates from the common power-law distribution of scale-free networks and Poisson distribution of random networks. Based on the dynamics from the cross section parameterizations in REACLIB, we surprisingly find that the distribution is universal for reactions with a rate below the threshold, , where T is the temperature and γ ≈ 1.05. Moreover, we discover three rules that govern the structure pattern of nuclear reaction network: (i) reaction-type is determined by linking choices, (ii) network distances between the reacting nuclides on 2D grid of Z vs N of nuclides are short, and (iii) each node in- and out-degrees are close to each other. By incorporating these three rules, our model universally unveils the underlying nuclear reaction patterns hidden in a large and dense nuclear reaction network regardless of nuclide chart expansions. It enables us to predict missing links that represent possible new nuclear reactions not yet discovered.

A Constrained Analysis of the 40Ca(18O,18F)40K Direct Charge Exchange Reaction Mechanism at 275 MeV

The40Ca(18O,18F)40K single charge exchange (SCE) reaction is explored at an incident energy of 275 MeV and analyzed consistently by collecting the elastic scattering and inelastic scattering data under the same experimental conditions. Full quantum-mechanical SCE calculations of the direct mechanism are performed by including microscopic nuclear structure inputs and adopting either a bare optical potential or a coupled channel equivalent polarization potential (CCEP) constrained by the elastic and inelastic data. The direct SCE mechanism describes the magnitude and shape of the angular distributions rather well, thus suggesting the suppression of sequential multi-nucleon transfer processes.

Analytic formula for estimating the α -particle preformation factor

In the present work, we build a bridge between the $\ensuremath{\alpha}$ decay energy and the $\ensuremath{\alpha}$-particle preformation factor, and put forward an analytic formula for estimating the $\ensuremath{\alpha}$-particle preformation factor. With the help of this formula, experimental $\ensuremath{\alpha}$ decay half-lives of 535 nuclei varying from $6.90\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ to $6.34\ifmmode\times\else\texttimes\fi{}{10}^{26}$ s are reproduced within a factor of 1.81. Noticeably, for superheavy nuclei, calculated $\ensuremath{\alpha}$ decay half-lives can well reproduce experimental data and reduce the deviations significantly. This formula can be applied to estimate the $\ensuremath{\alpha}$-particle preformation factors and predict the $\ensuremath{\alpha}$ decay half-lives for unsynthesized superheavy nuclei, which would be useful for future experiments in synthesizing new superheavy elements and isotopes. This formula can shed light on microscopic nuclear structure information such as shell and odd-even staggering effects, and provide a positive signal for the existence of an island of stability for superheavy nuclei.

Systematic study of Coulomb displacement energy based on the Coulomb energy empirical formula and mass model

In this study, starting from the nuclear binding energy, we studied the empirical formula of the Coulomb energy systematically. Beginning with the simplest empirical formula, we added the Coulomb exchange term, pairing correlation, and shell correction, to calculate the Coulomb energy more precisely. In addition, we investigated the Coulomb displacement energy of widely used mass models. The discrepancies between the calculation results and experimental data might be caused by the missing of the isospin breaking terms of strong interactions in theory. By investigating these discrepancies, we found that the results obtained by microscopic theories presented a distinctive systematical behavior. Thus, these theories can be improved by including isospin breaking terms. However, in the results obtained by phenomenological models, the systematical behavior is unclear. This occurs because it is difficult for the information of the microscopic nuclear structure to be absorbed into the parameters of phenomenological models.

Nucleon-Nucleon Scattering Up to N5LO in Chiral Effective Field Theory

During the past few decades a large effort has been made towards describing the NN interaction in the framework of chiral Effective Field Theory (EFT). The main idea is to exploit the symmetries of QCD to obtain an effective theory for low energy nuclear systems. In 2003, the first accurate charge-dependent $NN$ potential in this scheme was developed and it has been applied to many ab-initio calculations, opening the possibility to study nuclear systems in a systematic and accurate way. It was shown that the fourth order (N3LO) was necessary and sufficient to describe the NN scattering data with a $\chi^2/$d.o.f of the order of one. However the systematics of chiral EFT also allow to relate two- and many-body interactions in a well-defined way. Since many-body forces make their first appearance at higher order, they are substantially smaller then their two-body counterparts, but may never-the-less be crucial for some processes. Thus, there are observables where they can have a big impact and they are expected to solve problems like the long standing Ay puzzle of N-d scattering. The last few years, have also seen substantial progress towards higher orders of chiral EFT which was motivated by the fact that only three-body forces of rather high order may solve some outstanding issues in microscopic nuclear structure and reactions. In this chapter we will review the chiral EFT based potentials that have been developed up to N4LO as well as first calculations conducted for NN scattering at N5LO.

Phenomenological level density model with hybrid parameterization of deformed and spherical state densities

ABSTRACT A phenomenological level density model that has different level density parameter sets for the state densities of the deformed and the spherical states and the optimization of the parameters using experimental data of the average s-wave neutron resonance spacing are presented. The transition to the spherical state from the deformed one is described using the parameters derived from a microscopic nuclear structure calculation. The nuclear reaction calculation has been performed by the statistical model using the present level density. Resulting cross sections for various reactions with the spherical, deformed, and transitional target nuclei show a good agreement with the experimental data, which indicates the effectiveness of the present model. The role of the rotational collective enhancement in the calculations of those cross sections is also discussed.

The High-Density Symmetry Energy in Heavy-Ion Collisions and Compact Stars

High-density nuclear symmetry energy is of crucial importance in astrophysics. Information on such energy has been obtained from mass–radius determinations of neutron stars (NSs), and in the future NS mergers will increasingly contribute. In the laboratory, the symmetry energy can be studied in heavy-ion collisions (HICs) at different incident energies over a large range, from very low to several times higher saturation density. Transport theory is necessary to extract the symmetry energy from the typically non-equilibrated nuclear collisions. In this contribution, we first review the transport approaches, their differences, and recent studies of their reliability. We then discuss several prominent observables, which have been used to determine the symmetry energy at high density: collective flow, light cluster emission, and particle production. It is finally argued that the results of the symmetry energy from microscopic many-body calculations, nuclear structure, nuclear reactions, and astrophysics begin to converge but still need considerable improvements in terms of accuracy.

Mass Ratios and Proton Pairing for Isotones with N = 20, 50, and 82

Different estimates of the even–odd effect for the nuclear mass surface are discussed. The proton-number dependence of the energy gap is derived from the measured masses of the N = 20, 50, and 82 isotones with closed neutron shells. Its interrelation with the properties of external proton shells is demonstrated, and the effects of proton pairing are considered along with the microscopic nuclear structure.

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.

Evolving theoretical descriptions of heavy-ion fusion: from phenomenological to microscopic approaches

We overview the current status of theoretical approaches for heavy-ion fusion reactions at subbarrier energies. We particularly discuss theoretical challenges in the coupled-channels approach, that include i) a description of deep subbarrier hindrance of fusion cross sections, ii) the role of nuclear dissipation, iii) fusion of unstable nuclei, and iv) an interplay between fusion and multi-nucleon transfer processes. We also present results of a semi-microscopic approach to heavy-ion fusion reactions, that combines the coupled-channels approach with state-of-the-art microscopic nuclear structure calculations.

Neutron- γ competition for β -delayed neutron emission

We present a coupled Quasi-particle Random Phase Approximation and Hauser-Feshbach (QRPA+HF) model for calculating delayed particle emission. This approach uses microscopic nuclear structure information which starts with Gamow-Teller strength distributions in the daughter nucleus, and then follows the statistical decay until the initial available excitation energy is exhausted. Explicitly included at each particle emission stage is $\gamma$-ray competition. We explore this model in the context of neutron emission of neutron-rich nuclei and find that neutron-gamma competition can lead to both increases and decreases in neutron emission probabilities, depending on the system considered. A second consequence of this formalism is a prediction of more neutrons on average being emitted after $\beta$-decay for nuclei near the neutron dripline compared to models that do not consider the statistical decay.

Probes of shape transitions from mass and charge radii of nuclear ground states

The masses and sizes of nuclear ground states constitute two of the most precise and extensive arrays of experimental information. These data make a model-independent view of microscopic nuclear structure possible. Relevant differential observables of nuclear mass and charge radius can be highly sensitive to nuclear shape transitions. In this contribution, we examine the correlation of these two bulk properties to nuclear shape transitions. By combining different observables, it is even possible to isolate shape transitions from nuclear shell closures.

Pygmy resonances and radiative nucleon captures for stellar nucleosynthesis

The impact of low-energy multipole excitations and pygmy resonances on radiative neutron and proton-capture cross sections in nuclei close to the $\ensuremath{\beta}$-stability line is investigated. For this purpose, a microscopic theoretical approach based on self-consistent density functional theory and quasiparticle-random-phase-approximation formalism extended with multiphonon degrees of freedom is implemented in a statistical reaction model. The advantage of the method is the microscopic nuclear structure input for unified description of low-energy multiphonon excitations and pygmy and giant resonances. This is found to be important for the understanding of the fine structure and dynamics of the nuclear response function at low energies, which strongly influences nuclear reaction rates of astrophysical relevance. Calculations of the radiative capture cross sections of the reactions $^{85}\mathrm{Kr}(n,\ensuremath{\gamma})^{86}\mathrm{Kr}, ^{87}\mathrm{Sr}(n,\ensuremath{\gamma})^{88}\mathrm{Sr}$, and $^{89}\mathrm{Y}(p,\ensuremath{\gamma})^{90}\mathrm{Zr}$ are discussed in comparison with experimental data. For the reactions $^{89}\mathrm{Zr}(n,\ensuremath{\gamma})^{90}\mathrm{Zr}$ and $^{91}\mathrm{Mo}(n,\ensuremath{\gamma})^{92}\mathrm{Mo}$ theoretical predictions of the reaction cross sections are made.

Effect of first-forbidden decays on the shape of neutrino spectra

We examine the effect of First Forbidden (FF) decays on $\beta$-decay neutrino spectra by performing microscopic nuclear structure calculations. By analyzing the FF decay branches of even-even nuclei we conclude that FF decays may be responsible for part of the missing neutrinos in the so called "Reactor Neutrino Anomaly". Further calculations and more experimental data are needed for a firm conclusion.

Systematics of intermediate-energy single-nucleon removal cross sections

There is now a large and increasing body of experimental data and theoretical analyses for reactions that remove a single nucleon from an intermediate-energy beam of neutron- or proton-rich nuclei. In each such measurement, one obtains the inclusive cross section for the population of all bound final states of the mass A-1 reaction residue. These data, from different regions of the nuclear chart, and that involve weakly- and strongly-bound nucleons, are compared with theoretical expectations. These calculations include an approximate treatment of the reaction dynamics and shell-model descriptions of the projectile initial state, the bound final states of the residues, and the single-particle strengths computed from their overlap functions. The results are discussed in the light of recent data, more exclusive tests of the eikonal dynamical description, and calculations that take input from more microscopic nuclear structure models.