Closed-shell Nuclei Research Articles

Stellar Thermonuclear Reaction Rates of Proton Radiative Capture by Closed Light Shell Isotopes

Light isotopes, especially closed shell nuclei, have significance in thermonuclear reactions of the Carbon-Nitrogen-Oxygen (CNO) cycle in stars. In this research, 12C(p, γ) 13N and 14N(p, γ) 15O reactions have been calculated by means of Matlab codes to find the reaction rate across a temperature range of 0.006 to 10 GK using non-resonant parts, as well as the astrophysical S- factor S(E) at low energies. It was concluded that the high binding energy of 12C and 14N nuclei make the reaction less probable thus enabling other competitive processes to develop, which enhances the probability of other competitive proton reactions in the CNO cycle.

Properties of charge-exchange giant spin-dipole resonances in medium-heavy closed-shell parent nuclei: A semimicroscopic description

Properties of charge-exchange giant spin-dipole resonances in medium-heavy closed-shell parent nuclei: A semimicroscopic description

Converging many-body perturbation theory for ab-initio nuclear structure: Brillouin-Wigner perturbation series for closed-shell nuclei

Convergence aspects of nuclear many-body perturbation theory for ground states of closed-shell nuclei are explored using a Brillouin-Wigner formulation with a new vertex function enabling high-order calculations. A general formalism for Hamiltonian partitioning and a convergence criterion for the perturbation series are proposed. Analytical derivations show that with optimal partitioning, the convergence criterion for ground states can always be satisfied. This feature attributes to the variational principle and does not depend on the choice of an internucleon interaction or a many-body basis. Numerical calculations of the ground state energies of He4 and O16 with Daejeon16 and a bare N3LO potential in both harmonic-oscillator and Hartree-Fock bases confirm this finding.

What can we learn from recent 2ν β β experiments?*

Abstract Recent measurements of the two neutrino double beta decay high precision electron spectra, combined with charge exchange or β-decay experimental data, have revealed severe constraints across current nuclear many body calculations. Our calculations show that the quasi-particle random phase approximation (QRPA) approach can adequately reproduce the measured spectra for the two open shell nuclei, Se and Mo. For the closed shell nucleus Xe, QRPA can also reproduce the spectra with proper treatments. Considering the high-lying state reduction, we also find that the nuclear shell model can also adequately reproduce the spectra and Gamow-Teller transition strength under a unique quenched axial-vector coupling constant . For Xe, we find that flipping the sign for the decay strength causes the spectra to go beyond the so-called high-lying state dominance hypothesis. These results call for future high precision measurements of charge-exchange reactions.

Semimicroscopic description of isoscalar giant multipole resonances in medium-mass closed-shell nuclei

Semimicroscopic description of isoscalar giant multipole resonances in medium-mass closed-shell nuclei

NuHamil : A numerical code to generate nuclear two- and three-body matrix elements from chiral effective field theory

The applicability of nuclear ab initio calculations has rapidly extended over the past decades. However, starting research projects is still challenging due to the required numerical expertise in the generation of underlying nuclear interaction matrix elements and many-body calculations. To ease the first issue, in this paper we introduce the numerical code NuHamil to generate the nucleon-nucleon (NN) and three-nucleon (3N) matrix elements expressed in a spherical harmonic-oscillator basis, inputs of many-body calculations. The ground-state energies for the selected doubly closed shell nuclei are calculated with the no-core shell-model (NCSM) and in-medium similarity renormalization group (IMSRG). The code is written in modern Fortran, and OpenMP+MPI hybrid parallelization is available for the 3N matrix-element calculations.

Can the PREX-2 and CREX results be understood by relativistic mean-field models with the astrophysical constraints?

We construct new effective interactions using the relativistic mean-field models with the isoscalar- and isovector-meson mixing, σ2δ2 and ωμωμρνρν. Taking into account the particle flow data in heavy-ion collisions, the observed mass of PSR J0740+6620, and the tidal deformability of a neutron star from the binary merger event, GW170817, we study the ground-state properties of finite, closed-shell nuclei, and try to explain the recent results from the PREX-2 and CREX experiments. It is found that the σ–δ mixing is very powerful to understand the terrestrial experiments and astrophysical observations of neutron stars self-consistently. We can predict the large neutron skin thickness of 208Pb, Rskin208=0.243 fm, using the slope parameter of nuclear symmetry energy, L=70 MeV, which is consistent with the PREX-2 result. However, to explain the CREX data, it is preferable to adopt the small value of L=20 MeV. It is very difficult to understand the PREX-2 and CREX results simultaneously within relativistic mean-field models.

Modewise Johnson–Lindenstrauss embeddings for nuclear many-body theory

In this work, we explore modewise Johnson-Lindenstrauss embeddings (JLEs) as a tool to reduce the computational cost and memory requirements of nuclear many-body methods. JLEs are randomized projections of high-dimensional data tensors onto low-dimensional subspaces that preserve key structural features. Such embeddings allow for the oblivious and incremental compression of large tensors, e.g., the nuclear Hamiltonian, into significantly smaller random sketches that still allow for the accurate calculation of ground-state energies and other observables. Their oblivious character makes it possible to compress a tensor without knowing in advance exactly what observables one might want to approximate at a later time. This opens the door for the use of tensors that are much too large to store in memory, e.g., complete two-plus three-nucleon Hamiltonians in large, symmetry-unrestricted bases. Such compressed Hamiltonians can be stored and used later on with relative ease. As a first step, we analyze the JLE's impact on the second-order Many-Body Perturbation Theory (MBPT) corrections for nuclear ground-state observables. Numerical experiments for a wide range of closed-shell nuclei, model spaces and state-of-the-art nuclear interactions demonstrate the validity and potential of the proposed approach: We can compress nuclear Hamiltonians hundred- to thousand-fold while only incurring mean relative errors of 1\% or less in ground-state observables. Importantly, we show that JLEs capture the relevant physical information contained in the highly structured Hamiltonian tensor despite their random characteristics. In addition to the significant storage savings, the achieved compressions imply multiple order-of magnitude reductions in computational effort when the compressed Hamiltonians are used in higher-order MBPT or nonperturbative many-body methods.

Magnetic quadrupole transitions in the relativistic energy density functional theory

Magnetic quadrupole (M2) excitation represents a fundamental feature in atomic nucleus associated to nuclear magnetism induced by spin and orbital transition operator. Since it has only been investigated within the non-relativistic theoretical approaches, and available experimental data are rather limited, it is interesting to study the properties of M2 transitions using the framework of relativistic nuclear energy density functional. In this work the nuclear ground state is calculated with relativistic Hartree-Bogoliubov model, while the M2 excitations are described using the relativistic quasiparticle random phase approximation with the residual interaction extended with the isovector-pseudovector term. The M2 transition strength distributions are described and analyzed for closed shell nuclei $$^{16}$$ O, $$^{48}$$ Ca, $$^{208}$$ Pb, open-shell $$^{18} \mathrm O$$ , $$^{42}$$ Ca, $$^{56}$$ Fe, and semi-magic $$^{90}$$ Zr. The evolution of M2 transition properties has been investigated within the $$^{36-64} \mathrm Ca$$ isotope chain. The main M2 transitions have rather rich underlying structure and detailed analysis shows that collectivity increases with the mass number due to larger number of contributing particle-hole configurations. Pairing correlations in open shell nuclei have strong effect, causing the reduction of M2 strength and shifts of the centroid energies to higher values. The analysis of M2 transition strengths indicate that considerable amount of experimental strength may be missing, mainly due to limitations to rather restricted energy ranges. The calculated M2 strengths for Ca isotopes, together with the future experimental data will allow constraining the quenching of the g factors in nuclear medium.

Spectroscopic quadrupole moments in Xe124

Background: The Xe isotopic chain with four valence protons above the Z=50 shell closure is an ideal laboratory for the study of the evolution of nuclear deformation. At the N=82 shell closure, Xe136 presents all characteristics of a doubly closed shell nucleus with a spherical shape. In the very neutron-deficient isotopes close to N=50, the α-decay chain of Xe was investigated to probe the radioactive decay properties near the drip-line and the magicity of Sn100. Additionally, the Xe isotopes present higher order symmetries in the nuclear deformation such as the octupole degree of freedom near N=60 and N=90 or O(6) symmetry in stable isotopes. Purpose: The relevance of the O(6) symmetry has been investigated by measuring the spectroscopic quadrupole moment of the first excited states in Xe124. In the O(6) symmetry limit, the spectroscopic quadrupole moment of collective states is expected to be null. Method: A stable Xe124 beam with energies of 4.03A MeV and 4.11A MeV was used to bombard a natW target at the GANIL facility. Excited states were populated via the safe Coulomb excitation reaction. The collision of the heavy ions with a large Z at low energy make this reaction sensitive to the diagonal E2 matrix element of the excited states. The recoils were detected in the VAMOS++ magnetic spectrometer and the γ rays in the AGATA tracking array. The least squares fitting code gosia was used for the analysis to extract both E2 and M1 transitional and E2 diagonal matrix elements. Results: The rotational ground state band was populated up to the 81+ state as well as the 22+ and 42+ states. Using high precision spectroscopic data to constrain the gosia fit, the spectroscopic quadrupole moments of the 21+, 41+, and 61+ states were determined for the first time. Conclusions: The spectroscopic quadrupole moments were found to be negative, large, and constant in the ground state band underlining the prolate axially deformed ground state band of Xe124. The present experimental data confirm that the O(6) symmetry is substantially broken in Xe124.1 MoreReceived 21 October 2022Accepted 23 January 2023DOI:https://doi.org/10.1103/PhysRevC.107.014324©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsElectromagnetic transitionsSpectroscopic factors & electromagnetic momentsProperties90 ≤ A ≤ 149Nuclear Physics

Ground-state properties of closed-shell neutron-rich nuclei

Ground-state properties of closed-shell neutron-rich nuclei

Study of the Nuclear Structure for Some Nuclei Using Self-Consistent RPA Calculations with Skyrme-Type Interaction

In the present research, some static and dynamic nuclear properties of the closed-shell nuclei; 58Ni, 90Zr, 116Sn, and 144Sm nuclei have been studied using the Random Phase Approximation (RPA) method framework and different Skyrme parameterizations, particularly SyO-, Sk255, SyO+, SLy4, BSk17, and SLy5. In particular, in studies of static properties such as nuclear densities for neutrons, protons, mass, and charge densities with their corresponding rms radii, the single-particle nuclear density distributions All the obtained results agreed well with the relevant experimental data. Concerning the dynamic properties, the excitation energy, transition density, and giant resonance modes for the excitation to the low-lying negative partite excited states 1–, 3–, 5–, and 7– have also been studied. The findings indicate that estimates of RPA with Skyrme-type interactions are a good way to describe the properties of the structure of even-even, closed-shell nuclei.

Self-Consistent RPA Calculations for the Excitation to the Negative Parity States in Closed-Shell Nuclei

Self-Consistent RPA Calculations for the Excitation to the Negative Parity States in Closed-Shell Nuclei

Reaction channel contributions to the proton +Pb208 optical potential at 40 MeV

Background: Reaction channel coupling substantially modifies the real and imaginary nucleon-nucleus interactions for nuclei of $Z=20$ or less in ways that cannot be represented as uniform renormalizations of folding model potentials. For such nuclei coupling to inelastic channels also contributes. This raises the question of the effect of these couplings for heavier target nuclei.Purpose: To establish and characterize the contribution to the proton-nucleus interaction generated by coupling to neutron pickup (outgoing deuteron) channels for 40 MeV protons on the heavy closed shell nucleus $^{208}\mathrm{Pb}$. To identify and evaluate the consequent dynamical non-locality.Methods: Coupled reaction channel (CRC) calculations provide the elastic channel $S$-matrix ${S}_{lj}$ due to the included processes. Inversion of ${S}_{lj}$ will produce the local potential that would yield, in a single channel calculation, the elastic scattering observables from the CRC calculation. Subtracting the bare potential of the CRC calculations gives a local and $l$-independent representation of the dynamical polarization potential (DPP). From the DPPs due to various combinations of channel couplings, the influence of dynamically generated nonlocality can be identified.Results: Coupling to deuteron channels generates a repulsive component for the real potential and an absorptive component for the imaginary term. The radial shapes of both terms were modified in ways that could not be represented by uniform renormalization; the rms radius of the real part was substantially altered. Evidence of the dynamical nonlocality of the DPP due to pickup is provided by the nonadditivity of contributions of different couplings and other effects. For the doubly closed shell $^{208}\mathrm{Pb}$ coupling to low-lying (nongiant) collective states has a very small effect on elastic scattering, making a negligible contribution compared with pickup, and was not included.Conclusions: The DPPs established here strongly challenge the notion that folding models, in particular local density models, provide a satisfactory description of elastic scattering of protons from heavy nuclei. Coupling to neutron pickup channels induces dynamical nonlocality in the proton optical model potential with implications for direct reactions.

Effect of Incompressibility and Symmetry Energy Density on Charge Distribution and Radii of Closed-Shell Nuclei

In this work, the effect of incompressibility modulus KNM and symmetry energy density J on charge distribution and root-mean-square radii of neutron Rn and proton Rp has been investigated for light, medium and heavy closed-shell nuclei 40, 48Ca, 90Zr, 116Sn, 144Sm and 208Pb within the framework of self-consistent Hartree-Fock (HF) with 20 types of Skyrme interactions having wide range of nuclear properties such as incompressibility modulus KNM and symmetry energy density J. The nuclear charge densities have been obtained and compared with the experiment data to give us a picture about the internal structure of the investigated nuclei. Also, the sensitivity of proton and neutron root-mean-square radii to nuclear matter properties has been examined by determining and discussion the statistical Pearson linear correlation coefficient.

Properties of Gamow-Teller and charge-exchange giant spin-monopole resonances in medium-heavy closed-shell parent nuclei: A semimicroscopic description

The basic version of the semimicroscopic particle-hole dispersive optical model is adopted and implemented to describe main properties of the Gamow-Teller and charge-exchange giant spin-monopole resonances in medium-heavy closed-shell parent nuclei. Calculation results obtained for $^{48}\mathrm{Ca}, ^{90}\mathrm{Zr}, ^{132}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ are compared with available experimental data.

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.

Calculations for nuclear matter and finite nuclei within and beyond energy-density-functional theories through interactions guided by effective field theory

We propose a novel idea to construct an effective interaction under energy-density-functional (EDF) theories which is adaptive to the enlargement of the model space. Guided by effective field theory principles, iterations of interactions as well as enlargements of the model space through particle-hole excitations are carried out for infinite nuclear matter and selected closed-shell nuclei ($^{4}\mathrm{He}, ^{16}\mathrm{O}, ^{40}\mathrm{Ca}, ^{56}\mathrm{Ni}$, and $^{100}\mathrm{Sn}$) up to next-to-leading order. Our approach provides a new way for handling the nuclear matter and finite nuclei within the same scheme, with advantages from both EDF and ab initio approaches.

To Shell Model, or Not to Shell Model, That Is the Question

The present review takes steps from the domain of the shell model into open shell nuclei. The question posed in the title is to dramatize how far shell model approaches, i.e., many nucleons occupying independent-particle configurations and interacting through two-body forces (a configuration interaction problem) can provide a description of nuclei as one explores the structure observed where neither proton nor neutron numbers match closed shells. Features of doubly closed and singly closed shell nuclei and adjacent nuclei are sketched, together with the roles played by seniority, shape coexistence, triaxial shapes and particle–core coupling in organizing data. An illuminating step is taken here to provide a detailed study the reduced transition rates, B(E2;21+→01+), in the singly closed shell nuclei with doubly closed shell plus or minus a pair of identical nucleons, and the confrontation between such data and state-of-the-art shell model calculations: this amounts to a review of the effective charge problem. The results raise many questions and point to the need for much further work. Some guidance on criteria for sharpening the division between the domain of the shell model and that of deformation-based descriptions of nuclei are provided. The paper is closed with a sketch of a promising direction in terms of the algebraic structure embodied in the symplectic shell model.

Emergence of an island of extreme nuclear isomerism at high excitation near 208Pb

Metastable states with T1/2 = 8(2) ms in 205Bi and T1/2 = 0.22(2) ms in 204Pb, with ≈ 8 MeV excitation energy and angular momentum ≥ 22 ħ, have been established. These represent, by up to two orders of magnitude, the longest-lived nuclear states above an excitation energy of 7 MeV, ever identified in the nuclear chart. Additionally, the half-life of the 10.17 MeV state in 206Bi has been determined to be 0.027(2) ms, the next highest value in this highly excited regime. These observations indicate the emergence of an island of extreme nuclear isomerism arising from core-excited configurations at high excitation in the vicinity of the doubly closed-shell nucleus 208Pb. These results are expected to provide discriminating tests of the effective interactions used in current large-scale shell-model calculations.