NN Potential Research Articles

Inverse-scattering separable NN potential constrained to phase-shift data up to 2.5 GeV. I.—Uncoupled states

Inverse-scattering separable NN potential constrained to phase-shift data up to 2.5 GeV. I.—Uncoupled states

Nonautonomous Volterra Series Expansion of the Variable Phase Approximation and its Application to the Nucleon-Nucleon Inverse Scattering Problem

Abstract In this paper, the nonlinear Volterra series expansion is extended and used to describe certain types of nonautonomous differential equations related to the inverse scattering problem in nuclear physics. The nonautonomous Volterra series expansion lets us determine a dynamic, polynomial approximation of the variable phase approximation (VPA), which is used to determine the phase shifts from nuclear potentials through first-order nonlinear differential equations. By using the first-order Volterra expansion, a robust approximation is formulated to the inverse scattering problem for weak potentials and/or high energies. The method is then extended with the help of radial basis function neural networks by applying a nonlinear transformation on the measured phase shifts to be able to model the scattering system with a linear approximation given by the first-order Volterra expansion. The method is applied to describe the ${}^1S_0$ NN potentials in neutron+proton scattering below 200 MeV laboratory kinetic energies, giving physically sensible potentials and below $1\%$ averaged relative error between the recalculated and the measured phase shifts.

The Nuclear EOS of PNM and sensitivity of Neutron Star Properties to modern NN Potentials

The Nuclear EOS of PNM and sensitivity of Neutron Star Properties to modern NN Potentials

Quest for a universal cluster preformation formula: A new paradigm for estimating the cluster formation energy

This study presents a holistic picture of the preformation of nuclear clusters with credence to the kinematics of their emissions. Besides the fitting of the preformation formula to reproduce the experimental half-lives, we have investigated the interrelationship between the parameters involved in the cluster decay process for medium, heavy and superheavy nuclei. Based on the established conceptual findings, we propose a new cluster preformation probability (P 0) formula that incorporates all influential parameters of the cluster radioactivity and thus has an edge over the existing formulae in the literature. Further, we hypothesize that a fraction of the decay energy is needed for cluster formation within the parent nucleus. The proposed formula opens a new paradigm to separately estimate the energy contributed during the cluster formation from its emission and thus shows that the contribution of the Q-value splits into three major parts accounting for the energy contributed during the cluster preformation, its emission and recoil of the daughter nucleus. Moreover, the expression P 0 is adept at accommodating the theorized concept of heavy particle radioactivity (HPR). The result reveals that, like α-decay, a proper estimation of the P 0- and Q-value in the cluster studies is enriched with qualitative information about the nuclear structure. However, from the analysis, the Geiger-Nuttall law is not the best compromise in the clustering due to the non-linearity between log10 T 1/2 and , unlike in α-decay. We have demonstrated that with the inclusion of the proposed formula, the half-life predictions from both microscopic R3Y and phenomenological M3Y NN potentials closely agree with the available experimental data and that the slight variation can be traced to their peculiar barrier characteristics.

Are Neural Network Potentials Trained on Liquid States Transferable to Crystal Nucleation? A Test on Ice Nucleation in the mW Water Model.

Neural network potentials (NNPs) are increasingly being used to study processes that happen on long time scales. A typical example is crystal nucleation, which rate is controlled by the occurrence of a rare fluctuation, i.e., the appearance of the critical nucleus. Because the properties of this nucleus are far from those of the bulk crystal, it is yet unclear whether NN potentials trained on equilibrium liquid states can accurately describe nucleation processes. So far, nucleation studies on NNPs have been limited to ab initio models whose nucleation properties are unknown, preventing an accurate comparison. Here we train a NN potential on the mW model of water─a classical three-body potential whose nucleation time scale is accessible in standard simulations. We show that a NNP trained only on a small number of liquid state points can reproduce with great accuracy the nucleation rates and free energy barriers of the original model, computed from both spontaneous and biased trajectories, strongly supporting the use of NNPs to study nucleation events.

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.

The α-particle clustering and half-lives of the newly discovered 207,208Th decay chains within relativistic-Hartree-Bogoliubov approach

The structural and decay properties of the ground state of recently discovered neutron-deficient 207Th and remeasured 208Th isotopes Yang et al. (2022) [26] is examined using the Relativistic-Hartree-Bogoliubov (RHB) formalism using the DD-ME2 parameter set within the preformed cluster-decay model (PCM). The relativistic medium-dependant R3Y so-called DD-R3Y NN potentials are for the first time used to obtain the nucleus-nucleus potential as input into the PCM. The penetration probability is calculated using the WKB approximation, and the preformation probability (Pα) is estimated using our newly derived formula, which is based on parameters well known to influence the α -particle radioactivity. A close correlation is observed between the α-preformation factor and the crucial role of the pairing correlation in the α-decay process. Furthermore, the Pα values for the even-even nuclei are generally found to be of higher magnitude than those for the odd-A nuclei. Our results further affirm that the odd-even staggering effect on the Qα values and its accompanying effects on other observables such as the charge radii and the decay half-lives, which can be largely attributed to the pairing correlation and Pauli blocking of the unpaired valence nucleons.

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.

Preformation probability and kinematics of cluster emission yielding Pb-daughters* *Supported by the Fundamental Research Grant Scheme (FRGS/1/2019/STG02/UNIMAP/02/2) from the Ministry of Education Malaysia stipulated with the Institute of Engineering Mathematics (IMK) of the Faculty of Applied and Human Sciences UniMAP as the beholder, Science and Engineering Research Board (SERB, CRG/2021/001229), FOSTECT Project (FOSTECT.2019B.04), FAPESP Project (2017/05660-0)

In the present study, the newly established preformation formula is applied for the first time to study the kinematics of the cluster emission from various radioactive nuclei, especially those that decay to the double shell closure Pb nucleus and its neighbors as daughters. The recently proposed universal cluster preformation formula has been established based on the concepts that underscore the influence of mass and charge asymmetry ( and ), cluster mass , and the Q-value, paving the way to quantify the energy contribution during preformation as well as during the tunneling process separately. The cluster-daughter interaction potential is obtained by folding the relativistic mean-field (RMF) densities with the recently developed microscopic R3Y using the NL and the phenomenological M3Y NN potentials to compare their adaptability. The penetration probabilities are calculated from the WKB approximation. With the inclusion of the new preformation probability , the predicted half-lives of the R3Y and M3Y interactions are in good agreement with the experimental data. Furthermore, a careful inspection reflects slight differences in the decay half-lives, which arise from their respective barrier properties. The for systems with double magic shell closure Pb daughter are found to be an order of higher than those with neighboring Pb daughter nuclei. By exploring the contributions of the decay energy, the recoil effect of the daughter nucleus is evaluated, in contrast to several other conjectures. Thus, the centrality of the -value in the decay process is demonstrated and redefined within the preformed cluster-decay model. Additionally, we have introduced a simple and intuitive set of criteria that governs the estimation of recoil energy in the cluster radioactivity.

Theoretical Investigation of α-decay Chains of Fm-isotopes

Background: The theoretical and experimental investigations of decay properties of heavy and superheavy nuclei are crucial to explore the nuclear structure and reaction dynamics.
 Purpose: The aim of this study is to probe the α-decay properties of 243Fm and 245Fm isotopic chains using relativistic mean-field (RMF) approach within the framework of preformed cluster-decay model (PCM).
 Methods: The RMF densities are folded with the relativistic R3Y NN potential to deduce the nuclear interaction potential between the α particle and daughter nucleus. The penetration probability is calculated within the WKB approximation.
 Results: The α-decay half-lives of even-odd 243Fm and 245Fm isotopes and their daughter nuclei are obtained from the preformed cluster-decay model. These theoretically calculated half-lives are found to be in good agreement with the recent experimental measurements.
 Conclusions: The novel result here is the applicability of the scaling factor within the PCM as a signature for shell/sub-shell closures in α-decay studies. As such, we have also demonstrated that N=137, 139 and Z=94 corresponding to 231,233Pu could be shell/sub-shell closures. The least T1/2 is found at 243,245Fm which indicate their individual stability and α-decay as their most probable decay mode.

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.

Nature of the Active Sites of Copper Zinc Catalysts for Carbon Dioxide Electroreduction

AbstractThe electrochemical CO2 reduction (CO2ER) to multi‐carbon chemical feedstocks over Cu‐based catalysts is of considerable attraction but suffers with the ambiguous nature of active sites, which hinder the rational design of catalysts and large‐scale industrialization. This paper describes a large‐scale simulation to obtain realistic CuZn nanoparticle models and the atom‐level structure of active sites for C2+ products on CuZn catalysts in CO2ER, combining neural network based global optimization and density functional theory calculations. Upon analyzing over 2000 surface sites through high throughput tests based on NN potential, two kinds of active sites are identified, balanced Cu−Zn sites and Zn‐heavy Cu−Zn sites, both facilitating C−C coupling, which are verified by subsequent calculational and experimental investigations. This work provides a paradigm for the design of high‐performance Cu‐based catalysts and may offer a general strategy to identify accurately the atomic structures of active sites in complex catalytic systems.

Nature of the Active Sites of Copper Zinc Catalysts for Carbon Dioxide Electroreduction.

The electrochemical CO2 reduction (CO2 ER) to multi-carbon chemical feedstocks over Cu-based catalysts is of considerable attraction but suffers with the ambiguous nature of active sites, which hinder the rational design of catalysts and large-scale industrialization. This paper describes a large-scale simulation to obtain realistic CuZn nanoparticle models and the atom-level structure of active sites for C2+ products on CuZn catalysts in CO2 ER, combining neural network based global optimization and density functional theory calculations. Upon analyzing over 2000 surface sites through high throughput tests based on NN potential, two kinds of active sites are identified, balanced Cu-Zn sites and Zn-heavy Cu-Zn sites, both facilitating C-C coupling, which are verified by subsequent calculational and experimental investigations. This work provides a paradigm for the design of high-performance Cu-based catalysts and may offer a general strategy to identify accurately the atomic structures of active sites in complex catalytic systems.

Spin correlation coefficients in lepton–deuteron elastic scattering and their sensitivity to realistic NN potentials

Spin correlation coefficients in the elastic scattering of leptons on the deuteron, [Formula: see text], are studied in the one-photon-exchange approximation within the limit of zero lepton mass. Numerical estimations for the spin correlation coefficients caused by a polarized beam and a vector polarized target are given. The estimated spin correlation coefficients are analyzed at various values of beam energy and scattering angle. The sensitivity of the obtained results to the choice of realistic NN potential used for the deuteron wave function is investigated. We found a considerable dependence of the results on the realistic deuteron wave functions at incident beam energies greater than 0.4 GeV and backward scattering angles. The estimated results are of particular interest for encouragement of experimental measurements of lepton–deuteron scattering which aim for accurate calculation of the charge radius of the proton to a high degree of precision. These results may also stimulate new generation of measurements of different physical observables very sensitive to the spin structure of the nucleon and light nuclei.

Polarization observables in elastic lepton-deuteron scattering and their sensitivity to realistic NN potentials

Polarization effects in the elastic lepton scattering on the deuteron process are studied in the one-photon-exchange Born approximation within the limit of zero mass of the lepton. Numerical estimations for the spin asymmetries with an unpolarized lepton beam and a tensor polarized target are given. The estimated results are analysed at various lepton beam energies and scattering angles. For the first time, the sensitivity of the results for tensor spin asymmetries to the choice of modern NN potential used for the deuteron wave function (DWF) is investigated. A considerable influence of the results on the realistic and modern DWFs at incident beam energies greater than 0.6 GeV and scattering angles greater than 30 is obtained.

Particle configurations in the NNK̅ system

Three-body AAB model for the NNK(snn = 0) kaonic cluster is considered based on the configuration space Faddeev equations. Within a singlechannel approach, the difference between masses of nucleons and kaons and the charge independence breaking of nucleon-nucleon interaction are taken into consideration. We definite the particle configurations in the system according to the particle masses and pair potentials. There are two sets of the particle configurations, ppK, npK and nnK°, npK, charged and neutral. The three-body calculations are performed by applying NN and NK phenomenological isospin-dependent potentials. The mass and energy spectra related to the particle configurations are presented. We evaluate the mass and energy uncertainties for the NNK model. An analogy to NNN model for the H and He nuclei is proposed.

Description for N = 126 Isotones 210Po and 212Rn with Particle-Hole Excited Nucleon-Pair Approximation and Realistic Effective Interaction

In this paper, we study yrast states of two N=126 isotones 210Po and 212Rn using the nucleon-pair approximation with particle–hole excitations and using a low-momentum interaction Vlow–k renormalized from the free CD-Bonn NN potential. An overall good agreement with experimental level structures, B(E2)s, and B(E3)s, is achieved. We also calculate the probabilities of neutron particle–hole excitations in these yrast states, with a focus on negative-parity states, which reflect the roles played by the neutron negative-parity configurations of one-particle-one-hole excitations across the N=126 shell gap and the negative-parity configurations of valence proton particles involving the 0i13/2 orbit. The N=126 shell gap is discussed in terms of energies of neutron one-particle-one-hole excitations.

Divergence in the Relativistic Mean Field Formalism: A Case Study of the Ground State Properties of the Decay Chain of 214,216,218U Isotopes

A new α-emitting 214U has been recently observed experimentally. This opens the window to theoretically investigate the ground-state properties of the lightest known even–even neutron deficient 214,216,218U isotopes and to examine α-particle clustering around the shell closure. The decay half-lives are calculated within the preformed cluster-decay model (PCM). To obtain the α-daughter interaction potential, the RMF densities are folded with the newly developed R3Y and the well-known M3Y NN potentials for comparison. The alpha preformation probability (Pα) is calculated from the analytic formula of Deng and Zhang. The WKB approximation is employed for the calculation of the transmission probability. The individual binding energies (BE) for the participating nuclei are estimated from the relativistic mean-field (RMF) formalism and those from the finite range droplet model (FRDM) as well as WS3 mass tables. In addition to Z=84, the so-called abnormal enhancement region, i.e., 84≤Z≤90 and N<126, is normalised by an appropriately fitted neck-parameter ΔR. On the other hand, the discrepancy sets in due to the shell effect at (and around) the proton magic number Z=82 and 84, and thus a higher scaling factor ranging from 10−8–10−5 is required. Additionally, in contrast with the experimental binding energy data, large deviations of about 5–10 MeV are evident in the RMF formalism despite the use of different parameter sets. An accurate prediction of α-decay half-lives requires a Q-value that is in proximity with the experimental data. In addition, other microscopic frameworks besides RMF could be more reliable for the mass region under study. α-particle clustering is largely influenced by the shell effect.

Nucleon-nucleon potentials from Δ -full chiral effective-field-theory and implications

We closely investigate NN potentials based upon the Delta-full version of chiral effective field theory. We find that recently constructed NN potentials of this kind, which (when applied together with three-nucleon forces) were presented as predicting accurate binding energies and radii for a range of nuclei from A=16 to A=132 and providing accurate equations of state for nuclear matter, yield a chi^2/datum of 60 for the reproduction of the pp data below 100 MeV laboratory energy. This chi^2 is more than three times what the Hamada-Johnston potential of the year of 1962 achieved already some 60 years ago. We perceive this historical fact as concerning in view of the current emphasis on precision. We are able to trace the very large chi^2 as well as the apparent success of the potentials in nuclear structure to unrealistic predictions for P-wave states, in which the Delta-full NNLO potentials are off by up to 40 times the NNLO truncation errors. In fact, we show that, the worse the description of the P-wave states, the better the predictions in nuclear structure. Thus, these potentials cannot be seen as the solution to the outstanding problems in current miscroscopic nuclear structure physics.

Integral equations and binding energies for Λ − NN and Λ − NNN systems

A systematic treatment of the procedure used to construct and solve the Faddeev-Yakubovsky integral equations for three and four different particles with nonzero spin is introduced. The four-body T-matrices are written in terms of solutions of the three-body Faddeev integral equations in total angular momenta representation. General spin-angular structure of the four-body Faddeev-Yakubovsky equations is written down and reduced to a spin-angular structure of the three-body system by elimination of one body. Partial-wave expansion performed for the system of four-body integral equations gives an infinite system of one-dimensional coupled equations with integral kernels containing four types of partial components of the three-body Faddeev integral equation solutions. The given method is tested on Λ−NN and Λ−NNN systems with two-body potential written down in only separable form. Both separable NN potential and ΛN potential rewritten in separable form for s-wave are used to determine the Λ-hyperon binding energies in Λ−NN and Λ−NNN systems. Calculation also includes the hyperon conversion in ΛN→ΣN process. Λ-hyperon separation energies were calculated from binding energies and turned out to be 0.147 MeV in Λ−NN system and 2.04 MeV in Λ−NNN system, respectively, that is in close coincidence with experimental ones.