NN Interaction Research Articles

Machine Learning in the Problem of Extrapolating Variational Calculations in Nuclear Physics

A modified machine learning method is proposed, utilizing an ensemble of artificial neural networks for the extrapolation of energies obtained in variational calculations, specifically in the No-core Shell Model (NCSM), to the case of the infinite basis. A new neural network topology is employed, and criteria for selecting both the data used for training and the trained neural networks for statistical analysis of the results are formulated. The approach is tested by extrapolating the deutron ground state energy in calculations with the Nijmegen II NN interaction and provides statistically significant results. This technique is applied to obtain extrapolated ground state energies of 6Li and 6He nuclei based on the NCSM calculations with Daejeon16 NN interaction.

Direct ab initio calculation of the 4He nuclear electric dipole polarizability

The calculation of nuclear electromagnetic sum rules by directly solving for numerous eigenstates in a large basis is numerically challenging and has not been performed for A>2 nuclei. With the significant progress of high performance computing, we show that calculating sum rules using numerous discretized continuum states obtained with the ab initio no-core shell model in the harmonic oscillator basis is achievable numerically. Specifically, we calculate the 4He electric dipole (E1) polarizability, that is an inverse energy weighted sum rule, employing the Daejeon16 NN interaction. We demonstrate that the calculations are numerically tractable as the dimension of the basis increases and are convergent. Our results for the 4He electric dipole polarizability are consistent with the most recent experimental data and are compared with those of other theoretical studies employing different techniques and various interactions.

Mass–radius relation of neutron stars and massive pulsars with realistic equation of state

We use up-to-date constraints on the mass and radius of 15 neutron star objects and pulsars, from electromagnetic and gravitational wave observables and different theoretical schemes, to extend the nuclear equation of state (EOS) based on realistic Michigan-three-Yukawa (M3Y) nucleon–nucleon interaction, which truly accounts for the low-density EOS of nuclear matter (NM), to describe dense NM. The considered EOSs are employed to map the mass–radius profiles using the Tolman–Oppenheimer–Volkoff equations of hydrostatic equilibrium. We found that the EOSs from CDM3Y-230 to CDM3Y-270, with saturation incompressibility K 0 = 230–270 MeV, successfully reproduce most of the recent constraints on the NS masses and radii. Based on both M3Y-Paris and M3Y-Reid NN interactions, these EOSs indicate radius of 11.67 ± 0.34 km for the NS of 1.4 M ʘ mass, and the expected maximum NS mass (M max) to be 1.93 ± 0.21 M ʘ. The upper limits of constraints indicated stiffer EOSs of K 0 = 300–330 MeV, which have estimated 1arger radii of 12.29 ± 0.14 km for NS (1.4 M ʘ) and heavier M max of 2.31 ± 0.14 M ʘ. Increasing the stiffness of the employed EOS is found to increase the indicated maximum mass of NS, its radius and maximum compactness, the core–crust transition density, the speed of sound in its interior, and slightly the transition proton-fraction, but to decrease the abundance of the proton, muon, and electron over npeμ core matter of NS, as well as the estimated central density.

Core-polarization effects on electron scattering in 10B, 19F and 39K nuclei

In the study of NN interactions, calculations are performed from the longitudinal shape factor through inelastic scattering of electrons. The determination of the longitudinal shape factor in the inelastic scattering of electrons is based on the transfer momentum and angular momentum. We delve into the analysis of electron scattering shape factors as well as CP — standing for nuclear polarization — in longitudinal inelastic shell models. This is done using NuShellX, where we employ a sum potential HO to look at 10B, 39K, and 19F nuclei. Among the computations carried out include those of Single Particle Matrix Elements and Inelastic Electron Scattering Shape Factors which are then pitted against experimental data. The outcomes depict a scenario where the model space provides a full explanation on NushellX shape factor compared to nuclear polarization; this thereby implies less contribution from certain quarters towards shaping this factor. On another front, the comparison shows that results from longitudinal form factor polarization for NuShellX core find resonance with what is already available experimentally— a pointer towards reliability if not outright correctness.

Quasi-deuterons in light nuclei

The role of pairing correlations for nucleon pairs with isospin T = 1 and T = 0 is investigated for ground-states of nuclei in the mass region 12 ≤ A ≤ 42. For that purpose, the two-nucleon densities resulting from nuclear shell-model calculations in one and two major shells are analyzed. Various tools are applied in this analysis including the sensitivity of correlation effects on components of the NN interaction. Significant effects on the resulting energies are observed due to the formation of T = 0 pairs. The formation of quasi-deuterons is maximal for symmetric nuclei with N = Z. The formation of T = 0 pairs is less sensitive to the density of single-particle states close to the Fermi energy than the T = 1 pairing. Therefore the correlations in T = 0 pairs are relevant also for excitations across shell closures. This robustness also explains why T = 0 pairing does not lead to such clear evidence in comparing energies of neighbored nuclei as the ‘odd–even mass staggering’ due to the formation of T = 1 pairing.

Phase behavior and percolation in an equilibrium system of symmetrically interacting Janus disks on the triangular lattice

A Janus particle has two distinct areas on its surface. Denoting the two areas as P (patch) and N (nonpatch), when two particles come close to each other, the strength of the PP interaction is usually different from that of the NN interaction. Recently the interplay between a rotational-symmetry-breaking continuous phase transition and percolation has been explored for an equilibrium system of asymmetrically interacting (i.e., attractive PP interaction, zero NN and PN interactions) Janus disks on the triangular lattice. By Monte Carlo simulation and finite-size scaling analysis, in this work we study an equilibrium system of symmetrically interacting (i.e., attractive PP and NN interactions with the same strength, zero PN interaction) Janus disks on the same lattice. By definition, the phase diagram in the T–θ plane is symmetric for systems with patch sizes θ below and above 90°. We determine the phase diagram and compare it with that of the asymmetric system. Similar to the latter system, for 60° < θ < 90°, a rotational-symmetry-breaking continuous phase transition and an anisotropic percolation transition are found in the symmetric system, though the transition points in the two systems are quite different. Phase crossover curves are found to be different, e.g., a continuous varying crossover line extends between θ = 0° and 90° for the symmetric model; and in the range 0° < θ ≤ 30°, along the crossover lines of the two models, the trends of 1/T vs. θ are opposite in the two systems. We understand the latter by analytically solving the models with two particles in 0° < θ ≤ 30°. These results are helpful for understanding close-packed systems of Janus disks with more complex interactions.

Geometrical properties of ΩNN three-body states by realistic NN and first principles Lattice QCD ΩN potentials

The Faddeev equations in coordinate space are solved to study the ΩNN and ΩΩN three-body systems using the latest ΩNS25 and ΩΩ S01 interactions developed by the HAL QCD Collaboration. We recalculate the binding energy of the ΩNN system by examining three NN potentials, i.e., modern realistic AV18 potential, Yukawa-type Malfliet-Tjon (MT) interaction, and Gogny-Pires-Tourreil (GPT) soft and local potential. We take into account the contribution of the Coulomb potential. Our numerical calculations for Ωd(T=0) in maximum spin 5/2+ confirm ground state binding energy of 20.953, 19.368, and 20.439 MeV and a matter radius of 1.097, 1.373, and 1.309 fm using MT, GPT, and AV18 NN potentials, respectively. In the case of Ωd(0)5/2+ system, our numerical analysis shows that considering higher partial waves than s wave in NN interactions leads to an increase of about 0.2 MeV using GPT and about 0.1 MeV reduction with AV18 potentials. We study the convergence of three-body binding energies in a cluster model using the hyperspherical harmonics method and investigate the geometrical properties of Ωd(0)5/2+ ground states.

Ab initio no-core shell-model study of 18-24Ne isotopes

We report ab initio no-core shell-model (NCSM) study of 18−24Ne isotopes for energy spectra, electromagnetic properties, and point-proton radii using three realistic NN interactions. We have used inside nonlocal outside Yukawa (INOY), charge-dependent Bonn 2000 (CDB2K) and the chiral next-to-next-to-next-to-leading order (N3LO) interactions. We are able to reach basis size up to N max = 6 for 18Ne and N max = 4 for the 19−24Ne isotopes with m-scheme dimensions up to 1.0 × 109 in case of 24Ne. We observed better results for INOY interaction in terms of the binding energies of the ground state, and overall all three interactions provide good agreement with the experimental low-energy spectra. Our results for reduced M1 transition strengths and magnetic moments are close to the experimental values. We found that for long-range observables such as the E2 transition strengths, the electric quadrupole moments, and the point-proton radii (r p ), we need higher N max calculations to obtain results comparable to the experimental data. We have observed almost 6% increment in the converged r p as we increase the model space from N max = 4 to N max = 6.

Cluster folding model analysis of the 7Be+28Si elastic scattering in the near-barrier

In the framework of the optical model, the elastic scattering of the radioactive projectile 7Be on the 28Si target at four energies near the Coulomb barrier has been analyzed. The cluster folding model is used to determine the real part of the nuclear optical potential. For comparison, two microscopic optical potentials have been generated using the DDM3Y effective NN interaction based upon two different forms for 7Be density distribution. All the obtained real potentials, in conjunction with phenomenological Woods-Saxon imaginary parts, have successfully reproduced the elastic scattering angular distributions over the measured angular range. The energy dependence of the real and imaginary strengths that are produced by the best-fit of the experimental data was examined. Neither the usual threshold anomaly nor the breakup threshold anomaly can be observed at the considered energy range. The obtained cross sections have been reduced and compared with earlier theoretical and experimental data of 7Li on the same target near the Coulomb barrier.

Toward observation of three-nucleon short-range correlations in high- Q2 A(e,e′)X reactions

We present a detailed study of the kinematical and dynamical conditions necessary for probing highly elusive three-nucleon short-range correlations (3N-SRCs) in nuclei through inclusive electron scattering. The kinematic requirements that should be satisfied in order to isolate 3N-SRCs in inclusive processes are derived. We demonstrate that a sequence of two short-range NN interactions is the main mechanism for 3N-SRCs in such processes. With this mechanism we predict a quadratic dependence of the cross section ratios of nuclei to $^{3}\mathrm{He}$ in the 3N-SRC region to the same ratio measured in the 2N-SRC domain. An extended analysis of the available data which satisfies the required 3N-SRC kinematical conditions is presented. This analysis reveals tantalizing signatures of the scaling associated with the onset of 3N-SRC dominance. The same data are also consistent with the prediction of the quadratic relation between the ratios measured in the 3N- and 2N-SRC regions for nuclei ranging $4\ensuremath{\le}A\ensuremath{\le}197$. This agreement made it possible to extract ${a}_{3}(A)$, the probability of 3N-SRCs relative to the $A=3$ nucleus. We find ${a}_{3}(A)$ to be significantly larger in magnitude than the analogous parameter, ${a}_{2}(A)$, for 2N-SRCs.

How does thickness affect magnetic coupling in Ti-based MXenes.

The magnetic nature of Ti2C, Ti3C2, and Ti4C3 MXenes is determined from periodic calculations within density functional theory and using the generalized gradient approximation based PBE functional, the PBE0 and HSE06 hybrids, and the on-site Hubbard corrected PBE+U one, in all cases using a very tight numerical setup. The results show that all functionals consistently predict a magnetic ground state for all MXenes, with spin densities mainly located at the Ti surface atoms. The analysis of solutions corresponding to different spin orderings consistently show that all functionals predict an antiferromagnetic conducting ground state with the two ferromagnetic outer (surface) Ti layers being antiferromagnetically coupled. A physically meaningful spin model is proposed, consistent with the analysis of the chemical bond, with closed shell, diamagnetic, Ti2+ like ions in inner layers and surface paramagnetic Ti+ like centers with one unpaired electron per magnetic center. From a Heisenberg spin model, the relevant isotropic magnetic coupling constants are extracted from an appropriate mapping of total energy differences per formula unit to the expected energy values of the spin Hamiltonian. While the numerical values of the magnetic coupling constants largely depend on the used functional, the nearest neighbor intralayer coupling is found to be always ferromagnetic, and constitutes the dominant interaction, although two other non-negligible interlayer antiferromagnetic terms are involved, implying that the spin description cannot be reduced to NN interaction only. The influence of the MXene thickness is noticeable for the dominant ferromagnetic interaction, increasing its value with the MXene width. However, the interlayer interactions are essentially due to the covalency effects observed in all metallic solutions which, as expected, decay with distance. Within the PBE+U approach, a U value of 5 eV is found to closely simulate the results from hybrid functionals for Ti2C and less accurately for Ti3C2 and Ti4C3.

Dibaryon resonances and short-range NN interaction* *The work has been partially supported by RFBR, grants Nos. 19-02-00011 and 19-02-00014. M.N.P. also appreciates support from the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”

The dibaryon concept for nuclear force is presented, assuming that the attraction between nucleons at medium distances is mainly due to the s-channel exchange of an intermediate six-quark (dibaryon) state. To construct the respective NN interaction model, a microscopic six-quark description of the NN system is used, in which symmetry aspects play a special role. It is shown that the NN interaction in all important partial waves can be described by the superposition of long-range t-channel one-pion exchange and s-channel exchange by an intermediate dibaryon. The model developed in this study provides a good description of both elastic phase shifts and inelasticities of NN scattering in all S, P, D, and F partial waves at energies from zero to 600–800 MeV and even higher. The parameters of the intermediate six-quark states, corresponding to the best fit of NN scattering data, are found to be consistent with the parameters of the known dibaryon resonances in those NN partial configurations, where their existence has been experimentally confirmed. Predictions for new dibaryon states are given as well.

Alpha decay around shell closures and correlation of half-life times with the neutron energy levels of the emitting nuclei

The α-decay half-lives (T1/2) for 16 isotopic chains of even-even and even-odd nuclei, from 52Te to 82Pb were investigated by employing the density dependent cluster model. The α-nucleus potential was calculated by the double-folding model (DFM) using the M3Y-Reid NN interaction with the zero-range exchange part assuming spherical and deformed density distributions of the daughter nuclei. In the framework of the WKB approximation, the half-lives of the α-emitters were calculated and compared using six analytic formulas (UDL, Horoi, BKAG, UNIV, NRDX and TM formulas). We found a clear similarity in the behavior of log10⁡T1/2 versus the neutron daughter number (Nd) when the calculations performed using both DFM and these mentioned analytical formulas for each isotopic chain. In addition, the theoretical results of log10⁡T1/2 obtained with the UDL and UNIV formulas slightly better agree with the DFM calculations than those calculated from the other analytical methods. Moreover, the present work pointed out some magic or semi-magic neutron numbers of the daughter nuclei corresponding to dips in the behavior of log10⁡T1/2 with variation in Nd. The interplay of these magic (semi-magic) numbers is inspected as the total number of neutrons filling the upper neutron level in the parent nucleus. We test the predicted results of the above mentioned models by comparing them with the available experimental α-decay half-lives. Starting from the number of neutrons needed for level closure and the small available values of the confirmed spin of parent and daughter nuclei, we predicted the level schemes around the known magicities N=50, 82 and 126. We found changes in the neutron levels for isotopes of the same element which become too large for heavy nuclei. Example for these changes is the repetition of the spin value 1/2− for the three isotopes 195−199Hg and their daughters, we need five different neutron level arrangements with 3p1/2 level at the top.

Data on the Neutron–Neutron Scattering Length from the nd-Breakup Reaction at En = 8 MeV and En = 11 MeV

A kinematically complete experiment devoted to studying the nd-breakup reaction at energies of 8 and 11 MeV via detecting all three secondary particles was performed. The {}^{1}S_{0} neutron–neutron (nn) scattering-length values of a_{nn}={-}19.8pm 0.4 and {-}19.0pm 0.5 fm at, respectively, E_{n}=8 and 11 MeV were obtained from a comparison of the experimental dependence of the yield of the nd-breakup reaction on the relative energy of the nn pair with the results of a simulation. An analysis of the values obtained for the nn scattering length, together with data from other experiments, confirms the hypothesis that three-nucleon forces affect the parameters of nn interaction that are extracted from reactions involving few-nucleon systems and gives a new asymptotic nn scattering length, a_{nn}={-}16.1pm 0.1 fm.

Systematic study of fusion barrier characteristics within the relativistic mean-field formalism

Background: The nuclear interaction potential and hence the fusion barrier formed between the interacting nuclei are the keys to understanding the complex fusion process dynamics. Purpose: This work intends to explore the fusion barrier characteristics of different target-projectile combinations within the relativistic mean-field (RMF) formalism. Methods: The density distributions of interacting nuclei and the microscopic R3Y NN interaction are obtained from relativistic mean-field (RMF) formalism for non-linear NL1, NL3, TM1, and relativistic-Hartree-Bogoliubov (RHB) approach for DDME2 parameter sets. The fusion and/or capture cross-section for the different reaction systems is calculated using the well-known $\ell$-summed Wong model. Results: The barrier height and position of 24 heavy-ion reaction systems are obtained for different nuclear density distributions and effective NN interaction potentials. The comparison of fusion and/or capture cross-section obtained from the $\ell$-summed Wong model is made with the available experimental data. Conclusions: The phenomenological M3Y NN potential is observed to give higher barrier heights than the relativistic R3Y NN potential for all the reaction systems. The comparison of results obtained from different relativistic parameter sets shows that the densities from NL1 and TM1 parameter sets give the lowest and highest barrier heights for all the systems under study. We observed higher barrier heights and lower cross-sections for DDR3Y NN potential as compared to density-independent R3Y NN potentials obtained for considered non-linear NL1, NL3 and TM1 parameter sets. According to the present analysis, it is concluded that the NL1 and NL3 parameter sets provide comparatively better overlap with the experimental fusion and/or capture cross-section than the TM1 and DDME2 parameter sets.

Cluster radioactivity around shell closures: correlation of half-lives with the energy levels of daughter nuclei

The emission of Be, C, O, and Ne clusters from seven parent nuclei with neutron numbers around the neutron magicities N = 82 and 126 are considered. The universal decay law (UDL) formula, as well as the double-folding model derived from the Michigan three-range Yukawa–Paris NN interaction with zero- and finite-range exchange components, are utilized to compute the half-life time for 23 cluster decay processes. The calculations utilizing the UDL formula show satisfactory agreement with the experimental data. The reliable UDL formula is used to calculate log T c for more than 1500 cluster emitters and its variation with the neutron number, N d, of the daughter nuclei is presented. The behavior of log T c with neutron number variation is studied and correlated to the energy levels of the daughter nuclei. For a neutron number N d larger than the neutron magic number, log T c increases almost linearly with increasing N d, leaving the daughter nuclei in most cases with the same nuclear spin value. This linear behavior of log T c results from equal nuclear spin values of the daughter nuclei. At the magic neutron number, the nuclear spin changes strongly and as a result log T c increases as N d decreases. Log T c reaches to a maximum value when all the neutrons in the cluster are emitted from levels below the neutron gap. Leaving the daughter nuclei in the same spin produces almost linear variation of log T c. For protons in various clusters emitted from the same level or the same group of levels, log T c has almost the same value and the same behavior of variation with N d. Also, the values of log T c for specific types of cluster depend on the N to Z ratio for different isotopes of this cluster. From the available nuclear spin values, the neutron energy levels around the magic numbers are presented.

Antinucleon-nucleon interaction from chiral effective field theory and its application to neutron-antineutron oscillations

An $\bar N$N potential is reviewed which has been derived within chiral effective field theory by the Jülich-Bonn group. By construction it reproduces $\bar N$N phase shifts and inelasticities, provided by an elaborate phase-shift analysis of available $\bar p$p scattering data. This interaction is then employed in a study of neutron-antineutron oscillations in the deuteron. In particular, the deuteron lifetime is considered, and results for it are presented in terms of the free-space n – $\bar n$ oscillation time, based on that $\bar N$N potential in combination with an NN interaction likewise derived within chiral effective field theory.

The α-decay half-lives of heavy nuclei via the double folding model with the use of relativistic NN interactions

In this study, the half-lives of [Formula: see text]-decay from some heavy nuclei in the range [Formula: see text] have been studied using the WKB semi-classical approximation. The nuclear interaction potential between the [Formula: see text]-particle and the daughter nuclei is obtained within the double folding model. The [Formula: see text] interactions employed are those derived from relativistic mean field (RMF) theory, called as R3Y [Formula: see text] interactions. Six different R3Y [Formula: see text] interactions are considered in the study to determine the most appropriate R3Y parametrization for heavy nuclei. Some of the R3Y interactions (such as R3Y-HS, R3Y-L1, R3Y-Z, R3Y-W) contain only linear [Formula: see text], [Formula: see text], and [Formula: see text] mesons, while the others (such as R3Y-NL2, R3Y-NLSH) contain nonlinear terms, in addition to the linear terms. All the R3Y [Formula: see text] interactions used are found to be efficient in describing the [Formula: see text]-decay half-lives data. However, R3Y [Formula: see text] interactions containing nonlinear terms are found to perform better than those containing only linear terms of the mesons.

NN interaction from chiral effective field theory and its application to neutron-antineutron oscillations

An N¯N potential is introduced which is derived within chiral effective field theory and fitted to up-to-date N¯N phase shifts and inelasticities, provided by a proper phase-shift analysis of available p¯p scattering data. As an application of this interaction neutron-antineutron oscillations in the deuteron are considered. In particular, results for the deuteron lifetime are presented, evaluated in terms of the free-space n−n¯ oscillation time, utilizing that N¯N potential together with an NN interaction likewise derived within chiral effective field theory.

Possible Studies at the First Stage of the NICA Collider Operation with Polarized and Unpolarized Proton and Deuteron Beams

This paper contains suggestions for experiments with usage of the Spin Physics Detector (SPD) at the first stage of the SPD NICA Programme developing at JINR. Double polarized pp-, dd- and pd- collisions at c.m.s. NN energies of 3.4-10 GeV, which will be accessible at the initial stage of experiments, allow one to study spin dependence of the NN interaction, search for multiquark states at double strangeness, charm and beauty thresholds, study the short-range structure of the deuteron. Double polarized pd scattering offer a possibility to test the Standard Model through the search for T-invariance violation.