P-shell Nuclei Research Articles

Nuclear structure studies within the realistic shell model

The role of three-nucleon forces on structure properties of nuclei is discussed within the realistic shell model. Calculations are performed by employing effective shell-model Hamiltonians derived by way of many-perturbation theory from chiral potentials including the nucleon-nucleon and three-nucleon components. A sketch of the formalism in treating the three-nucleon force is given and some selected results for f p- and p-shell nuclei are shown. Particular attention is devoted to the effects of the three-nucleon force on the monopole component of the effective shell-model interaction by showing how relevant they are in correcting the monopole interaction derived from the nucleon-nucleon force only and correctly describing the formation of shell structure as well as the enhancement in the spin-orbit splitting. A decomposition scheme based on the rank of irreducible tensors forming the three-nucleon force at the next-to-next-to-leading order is also presented to recognize their impact on the spin-orbit enhancement.

Description of elastic scattering for 7Li-induced reactions on 1p-shell nuclei* *Supported by the National Natural Science Foundation of China (11405099, 11575291, 12065003), the Natural Science Foundation of Shanxi Province, China (202103021224309, 201901D111317). This work is also a part of IAEA Coordinated Research Projects (CRPs) on Recommended Input Parameter Library (RIPL) for Fission Cross Section Calculations (20464)

The experimental data of elastic scattering angular distributions for 9Be, 10B, 11B, 12C, 13C, 15N, and 16O targets from 4.5 to 131.8 MeV and 7Li target from 8.0 to 42.0 MeV are fitted to realize the global phenomenological optical potentials (GPOPs) for the 7Li-induced reactions on 1p-shell nuclei. Thus, the 7Li elastic scattering from the 1p-shell nuclei can be systematically described using the established GPOPs. The elastic scattering angular distributions are also reanalyzed using a microscopic method within the framework of the new version of double folding São Paulo potential (SPP2). To better describe the elastic scattering at backward angles, the contribution of elastic transfer is further estimated by the distorted wave Born approximation (DWBA) method. Based on the obtained GPOPs, the inelastic scattering angular distributions are also obtained through the coupled channels (CC) method for the different excited states.

Determination of Photonuclear Reaction Cross-Sections on Stable P-shell Nuclei by Using Deep Neural Networks

Determination of Photonuclear Reaction Cross-Sections on Stable P-shell Nuclei by Using Deep Neural Networks

Uncertainties in ab initio nuclear structure calculations with chiral interactions

We present theoretical ground state energies and their uncertainties for p-shell nuclei obtained from chiral effective field theory internucleon interactions as a function of chiral order, fitted to two- and three-body data only. We apply a Similary Renormalization Group transformation to improve the numerical convergence of the many-body calculations, and discuss both the numerical uncertainties arising from basis truncations and those from omitted induced many-body forces, as well as chiral truncation uncertainties. With complete Next-to-Next-to-Leading (N2LO) order two- and three-body interactions, we find significant overbinding for the ground states in the upper p-shell, but using higher-order two-body potentials, in combination with N2LO three-body forces, our predictions agree with experiment throughout the p-shell to within our combined estimated uncertainties. The uncertainties due to chiral order truncation are noticeably larger than the numerical uncertainties, but they are expected to become comparable to the numerical uncertainties at complete N3LO.

Optical potential for the elastic scattering of 6Li projectile on 1p-shell nuclei

A set of global optical potential parameters describing the elastic scattering of 6Li projectile on 1p-shell nuclei is obtained by fitting the experimental data of elastic scattering angular distributions for 9Be, [Formula: see text]B, [Formula: see text]B, [Formula: see text]C, [Formula: see text]C, [Formula: see text]C, [Formula: see text]N, [Formula: see text]O and [Formula: see text]O targets with incident energies from 4.0,MeV to 210.0,MeV and with 6Li and 7Li targets from 2.0,MeV to 156.0,MeV. The comparison is performed between the results calculated using the derived optical potential and the existing experimental data. The calculations agree well with the experimental data in the whole energy region except from 20,MeV to 50,MeV at backward angles, where there is an upward trend for the experimental data of angular distributions. Besides, the inelastic scattering contributions of the first excited states are deduced by the present global optical potential. The results are also in good agreement with the experimental data. In order to improve the description of elastic scattering, the inelastic scattering contributions of the first excited states are considered in the calculations between 20 and 50,MeV. A satisfactory fit is obtained between them.

Robust ab initio prediction of nuclear electric quadrupole observables by scaling to the charge radius

Meaningful predictions for electric quadrupole (E2) observables from ab initio nuclear theory are necessary, if the ab initio description of collective correlations is to be confronted with experiment, as well as to provide predictive power for unknown E2 observables. However, converged results for E2 observables are notoriously challenging to obtain in ab initio no-core configuration interaction (NCCI) approaches. Matrix elements of the E2 operator are sensitive to the large-distance tails of the nuclear wave function, which converge slowly in an oscillator basis expansion. Similar convergence challenges beset ab initio prediction of the nuclear charge radius. We demonstrate that the convergence patterns of the E2 and radius observables are strongly correlated, and that meaningful predictions for the absolute scale of E2 observables may be made by calibrating to the experimentally-known ground-state charge radius. We illustrate by providing robust ab initio predictions for several E2 transition strengths and quadrupole moments in p-shell nuclei, in cases where experimental results are available for comparison.

Nonlocal optical model for deuteron elastic scattering

Deuteron elastic scattering off light, intermediate, and heavy nuclei from 10Be to 120Sn corresponding to incident energies in the range 10–70 MeV is considered using the nonlocal model of Perey and Buck, which explicitly includes a Gaussian nonlocality (Perey and Buck. Nucl. Phys. A, 32, 353 (1962). doi:10.1016/0029-5582(62)90345-0). We obtain two sets of global nonlocal parameters, one for light 1p-shell nuclei and the other for intermediate and heavy ones. The geometrical parameters of each set are fixed, while the imaginary volume and imaginary surface depths vary linearly with both energy and the neutron–proton asymmetry of the target. Our best angular distribution fits are in very good agreement with the measured data. To test the model, we used our global parameters to predict the angular distributions for nuclei and energies that have not been included in the fitting procedure. The resulting χ2 values are as good as the values calculated using global local potentials in the literature or better, despite the fact that 12 out of the 15 parameters of the nonlocal potential are fixed. For the deuteron–nucleus scattering, we determined a nonlocality parameter of 0.45 fm, which compares well with the values obtained in previous works.

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

Exploring the relationship between nuclear matter and finite nuclei with chiral two- and three-nucleon forces

We address the connection between the saturating behavior of infinite nuclear matter and the description of finite nuclei based on state-of-the-art chiral two- and three-nucleon forces. We observe that chiral two- and three-nucleon interactions (at N2LO and at N3LO) which have been found to predict realistic binding energies and radii for a wide range of finite nuclei (from p-shell nuclei up to nickel isotopes) are unable to saturate infinite nuclear matter. On the other hand, it has been shown that, when the fits of the cD and cE couplings of the chiral three-nucleon interactions include the constraint of nuclear matter saturation in addition to, as is typically the case, the triton binding energy, medium-mass nuclei are underbound and their radii are sytematically too large. We discuss this apparent inconsistency and perform test calculations for various scenarios to shed light on the issue.

Modification of tensor force in 0p-shell model effective interaction

In many shell model interactions, the tensor force monopole matrix elements often retain systematic trends originating in the bare tensor force. However, in this work, we find that Isospin [Formula: see text] tensor force monopole matrix elements of widely used p-shell effective interaction CK(8–16) do not share these systematic. We correct these discrepancies by modifying [Formula: see text] tensor force two-body matrix elements (TBMEs) of CK(8–16) by the analytically calculated tensor force TBMEs. With some additional modification of single-particle energies and TBMEs, the revised effective interaction is named as CKN. The effective interaction CKN has been tested for the calculations of p-shell nuclei of normal parity states from various physics viewpoints such as excitation spectra, electromagnetic moments, and electromagnetic and Gamow–Teller (GT) transitions. The obtained results are found to be satisfactory with respect to the experimental results.

A nonlocal optical potential with a Gaussian nonlocality for proton elastic scattering off light 1p-shell nuclei

In a recent work we used the nonlocal optical model of Perey and Buck (Nucl Phys A 32:353, 1962) to fit the angular distribution data corresponding to neutron elastic scattering off light nuclei from $$^6\hbox {Li}$$ to $$^{18}\hbox {O}$$ over the 9–35 MeV energy range. Although such nuclei posses diffuse edges that complicate the scattering process, the model resulted in improved angular distribution fits compared to those obtained using local optical models. In this work we extend the treatment to the case of proton elastic scattering off light 1p-shell nuclei, but consider the wider 10–70 MeV energy range. No single global set of nonlocal parameters adequately described the measured data across the entire energy range. Instead, we obtained two global sets of fixed nonlocal parameters; one corresponds to the 10–39 MeV range, the other is for the higher 40–70 MeV incident energies. Each set resulted in angular distribution fits which are in very good agreement with experimental data even in the large-angle scattering region, which is usually endowed by nonlocal effects. The fits were improved even further by expressing the imaginary volume and imaginary surface depths as linear functions of energy and the $$(N-Z)/A$$ asymmetry term. This indicates that there is still need for energy-dependent parameters even when nonlocality is explicitly included in the potential. We also used the model to predict elastic angular distributions for proton scattering off nuclei not included in the fitting procedure. The theoretical predictions showed very good agreement with experiment. As a further test of the nonlocal model, we calculated total reaction cross sections for proton scattering off light 1p-shell nuclei. Our predictions are in fair overall agreements with the experimental data.

Family of chiral two- plus three-nucleon interactions for accurate nuclear structure studies

We present a family of nucleon-nucleon (NN) plus three-nucleon (3N) interactions up to N3LO in the chiral expansion that provides an accurate ab initio description of ground-state energies and charge radii up to the medium-mass regime with quantified theory uncertainties. Starting from the NN interactions proposed by Entem, Machleidt and Nosyk, we construct 3N interactions with consistent chiral order, non-local regulator, and cutoff value and explore the dependence of nuclear observables over a range of mass numbers on the 3N low-energy constants. By fixing these constants using the 3H and 16O ground-state energies, we obtain interactions that robustly reproduce experimental energies and radii for a large range from p-shell nuclei to the nickel isotopic chain and resolve many of the deficiencies of previous interactions. Based on the order-by-order convergence and the cutoff dependence of nuclear observables, we assess the uncertainties due the interaction, which yield a significant contribution to the total theory uncertainty.

P-shell hypernuclear energy spectra using the Gogny-interaction shell model

Recent high-resolution experiments at JLab give the energy spectra of the hypernuclei , , and . However, their spins and parities of the excited states have not been known experimentally. In the present paper, we make a systematical theoretical investigation for the p-shell hypernuclei, within the shell model based on the nucleon–nucleon (NN) and hyperon–nucleon interactions. The effective NN interaction takes the finite-range density-dependent Gogny force, and the hyperon–nucleon interaction takes an empirical ΛN interaction which includes the ΛN–ΣN and ΣN–ΣN coupling effects. The shell model with the Gogny force without parameters being refitted can reasonably describe both spectra and binding energies of the p-shell nuclei, which gives a confidence for the further calculations of hypernuclei. We compare our results with experimental data as well as various theoretical calculations, and explain the recent experimental hypernuclear spectra observed at JLab.

Ab initio calculations of p-shell nuclei up to N2LO in chiral Effective Field Theory

Nuclear structure and reaction theory are undergoing a major renaissance with advances in many-body methods, realistic interactions with greatly improved links to Quantum Chromodynamics, the advent of high performance computing, and improved computational algorithms. State-of-the-art two- and three-nucleon interactions obtained from chiral Effective Field Theory provide a theoretical foundation for nuclear theory with controlled approximations. With highly efficient numerical codes, tuned to the current generation of supercomputers, we can perform ab-initio nuclear structure calculations for a range of nuclei to a remarkable level of numerical accuracy, with quantifiable numerical uncertainties. Here we present an overview of recent results for No-Core Configuration Interaction calculations of p-shell nuclei using these chiral interactions up to next-to-next-to-leading order, including three-body forces. We show the dependence of the ground state energies on the chiral order; we also present excitation spectra for selected nuclei and compare the results with experimental data.

A nonlocal optical model for neutron scattering from light 1p-shell nuclei

Nonlocal effects result in complications when predicting scattering observables. This is usually seen when one analyses the data for nucleon scattering off light 1p-shell nuclei using local optical model potentials. In this work we employ the nonlocal optical model of Perey and Buck (1962) [10] to study the neutron-light nucleus scattering process. By fitting the individual elastic angular distributions we determine energy-dependent, target-specific potential parameters. Then, for each nucleus, a constant set of nonlocal parameters is obtained by simultaneously fitting the corresponding elastic angular distributions. The good quality of the fits prompted us to search for a global constant set of nonlocal parameters by simultaneously fitting a large number elastic angular distribution sets for neutron scattering off light nuclei from 6Li to 18O over the energy range 9 to 35 MeV. We also show that the implicit inclusion of nonlocality in the optical model does not fully remove the need for energy-dependent potential parameters. This is achieved by expressing the nonlocal imaginary volume and surface depths of the constant global set as linear functions of energy and the asymmetry term. The effectiveness of this set is tested by applying it to additional light nuclei and energies outside the fitted range. The predicted elastic angular distributions compared well with the measured data.

Natural orbitals for ab initio no-core shell model calculations

We explore the impact of optimizations of the single-particle basis on the convergence behavior and robustness of ab initio no-core shell model calculations. Our focus is on novel basis sets defined by the natural orbitals of a correlated one-body density matrix that is obtained in second-order many-body perturbation theory. Using a perturbatively improved density matrix as starting point informs the single-particle basis about the dominant correlation effects on the global structure of the many-body state, while keeping the computational cost for the basis optimization at a minimum. Already the comparison of the radial single-particle wavefunctions reveals the superiority of the natural-orbital basis compared to a Hartree-Fock or harmonic oscillator basis, and it highlights pathologies of the Hartree-Fock basis. We compare the model-space convergence of energies, root-mean-square radii, and selected electromagnetic observables with all three basis sets for selected p-shell nuclei using chiral interactions with explicit three-nucleon terms. In all cases the natural-orbital basis provides the fastest and most robust convergence, making it the most efficient basis for no-core shell model calculations. As an application we present no-core shell model calculations for the ground-state energies of all oxygen isotopes and assess the accuracy of the normal-ordered two-body approximation of the three-nucleon interaction in the natural-orbital basis.

Chiral three-body force and monopole properties of shell-model Hamiltonian

So far, the nature of three-nucleon forces (3NFs) derived by the chiral effective field theory has been intensively investigated by various theoretical approaches. In this work, to address the chiral 3NF within the shell-model framework, three-body matrix elements are formulated in terms of the harmonic oscillator basis functions, by adopting the nonlocal regulator. We perform a benchmark test for p-shell nuclei inorder to confirm our framework. Then we show that the contribution of the 3NF to the monopole component of the effective shell model Hamiltonian plays an essential role to account for the shell evolution of f p-shell nuclei.

7Li(d,p)8Li transfer reaction in the NCSM/RGM approach

Recently, we applied an ab initio method, the no-core shell model combined with the resonating group method, to the transfer reactions with light p-shell nuclei as targets and deuteron as the projectile. In particular, we studied the elastic scattering of deuterium on 7Li and the 7Li(d,p)8Li transfer reaction starting from a realistic two-nucleon interaction. In this contribution, we review of our main results on the 7Li(d,p)8Li transfer reaction, and we extend the study of the relevant reaction channels, by showing the dominant resonant phase shifts of the scattering matrix. We assess also the impact of the polarization effects of the deuteron below the breakup on the positive-parity resonant states in the reaction. For this purpose, we perform an analysis of the convergence trend of the phase and eigenphase shifts, with respect to the number of deuteron pseudostates included in the model space.

Isoscalar and isovector spin responses in p-shell and sd-shell nuclei

We study the spin magnetic dipole transitions in sd-shell even-even nuclei with N=Z and a p-shell nucleus 12C by modern shell model calculations. The shell model wave functions take into account enhanced isoscalar (IS) spin-triplet pairing as well as the effective spin operators. We point out that the IS pairing and the effective spin operators give a large quenching effect on the isovector (IV) spin transitions to be consistent with observed data by (p, p′) experiments. On the other hand, the observed IS spin strengths do not show large quenching effect suggested by the calculated investigation. The IS pairing gives a substantial quenching effect on the spin magnetic dipole transitions, especially on the IV ones.

Investigation of interaction processes of light nuclei with 14N

Elastic scattering of 3He on 14N as an example of 1p-shell nuclei at 50 and 60 MeV has been investigated within the framework of Optical Model. In the Optical Model analysis, both microscopic double-folding and phenomenological potentials for the real part of the complex nuclear potential have been used. For both microscopic double-folding and phenomenological analyses, the imaginary potential has taken to be WS volume shaped. It is noticed that while a normalization of the strength of the double-folding real potential is needed to explain the structure observed in the experimental data, a good agreement between experimental data is obtained for the phenomenological potential case.