Wave-packet continuum discretisation for nucleon-nucleon scattering predictions

In this paper we analyse the efficiency, precision, and accuracy of computing elastic nucleon-nucleon (\NN) scattering amplitudes with the wave-packet continuum discretisation method (\wpcd). This method provides approximate scattering solutions at multiple scattering energies simultaneously. We therefore utilise a graphics processing unit (GPU) to explore the benefits of this inherent parallelism. From a theoretical perspective, the \wpcd{} method promises a speedup compared to a standard matrix-inversion method. We use the chiral NNLO$_{\rm opt}$ interaction to demonstrate that \wpcd{} enables efficient computation of \NN{} scattering amplitudes provided one can tolerate an averaged method error of $~1-5$ mb in the total cross section at scattering energies $0-350$ MeV in the laboratory frame of reference. Considering only scattering energies $\sim40-350$ MeV, we find a smaller method error of $\lesssim 1-2$ mb. By increasing the number of wave-packets we can further reduce the overall method error. However, the parallel leverage of the \wpcd{} method will be offset by the increased size of the resulting discretisation mesh. In practice, a GPU-implementation is mainly advantageous for matrices that fit in the fast on-chip shared memory. We find that \wpcd{} is a promising method for computationally efficient, statistical analyses of nuclear interactions from effective field theory, where we can utilise Bayesian inference methods to incorporate relevant uncertainties.

Role of inelastic couplings in the 4He + 208Pb elastic scattering in a wide energy range

The phenomenological strengths of the real part of the optical potential, obtained from elastic scattering data analyses within the optical model approach, present significant energy-dependence. This behavior has been associated to the intrinsic energy-dependence of the effective nucleon-nucleon interaction. However, in earlier works, we proposed that at least part of this dependence can arise from the effect of couplings to inelastic states of the nuclei. In order to deepen this study, in this paper we present extensive data analyses for the elastic scattering and inelastic excitation of 111 states of 208Pb, for the 4He + 208Pb system in a wide energy range. With the purpose of comparison, the theoretical cross sections are obtained in different approaches for the imaginary part of the potential, and within both contexts: optical model (distorted wave Born approximation) and coupled-channel calculations.

Symmetry Energy and the Pauli Exclusion Principle

In this article we present a classical potential that respects the Pauli exclusion principle and can be used to describe nucleon-nucleon interactions at intermediate energies. The potential depends on the relative momentum of the colliding nucleons and reduces interactions at low momentum transfer mimicking the Pauli exclusion principle. We use the potential with Metropolis Monte Carlo methods and study the formation of finite nuclei and infinite systems. We find good agreement in terms of the binding energies, radii, and internal nucleon distribution of finite nuclei, and the binding energy in nuclear matter and neutron star matter, as well as the formation of nuclear pastas, and the symmetry energy of neutron star matter.

Prediction of an ΩbbbΩbbb Dibaryon in the Extended One-Boson Exchange Model

Since Yukawa proposed that the pion is responsible for mediating the nucleon-nucleon interaction, meson exchanges have been widely used in understanding hadron-hadron interactions. The most studied mesons are the σ, π, ρ, and ω, while other heavier mesons are often argued to be less relevant because they lead to short range interactions. However, whether the range of interactions is short or long should be judged with respect to the size of the system studied. We propose that one charmonium exchange is responsible for the formation of the ΩcccΩccc dibaryon, recently predicted by lattice QCD simulations. The same approach can be extended to the strangeness and bottom sectors, leading to the prediction on the existence of ΩΩ and ΩbbbΩbbb dibaryons, while the former is consistent with the existing lattice QCD results, the latter remains to checked. In addition, we show that the Coulomb interaction may break up the ΩcccΩccc pair but not the ΩbbbΩbbb and ΩΩ dibaryons.

Quantum-Mechanical Substantiation of the Periodic System of Isotopes. Models of Nuclear Orbitals

The topic of this article lies in the field of problems: substantiating the periodic system of isotopes and the principle of multilevel periodicity using quantum mechanical calculations, combining strong and electromagnetic interactions, and searching for the fundamental cause of periodicity in general. This article is a theoretical section and a continuation of the article: "Periodic system of isotopes", in which the system was checked against 10 types of experimental data, the periodic change of properties at the level of nuclei and the vertical symmetry of subgroups of isotopes were found. Periodic system of isotopes was constructed with the help of a special algorithm, the principle of multilevel periodicity of the atom, from the electrons to the nucleus. As a description of the multilevel periodicity, this paper presents a unified system of quantum numbers, which is used to describe both electron and nucleon shells (binomial probabilistic interpretation). With the binomial interpretation the problem of a particle in a one-dimensional potential well has been solved; quantummechanical calculations for the probability functions of the orbitals and periods of both electrons and nucleons have been performed - characteristic equations have been obtained, the projections of electronic orbitals have been reproduced and the binomial interpretation has been shown to correspond to the family of spherical harmonics. For the electron orbitals the calculation and analysis of solutions of the Schrödinger equation for the binomial interpretation of quantum numbers have been performed. The spatial nature of quantum numbers, for this interpretation, in the form of degrees of freedom is shown. Based on the principle of multilevel periodicity, expressions are derived and planar projections of nucleon nucleon orbitals are constructed, and similarity of the forms with electron orbitals is analyzed and revealed. A critical analysis of the modern spherical coordinate system was made, possible errors in the construction of electron orbitals were shown and, taking into account the drawbacks, two alternative spherical coordinate systems were proposed, for which Lame coefficients were calculated and Laplace equations were derived. As a search for the fundamental cause of multilevel periodicity, a spatial model with changing degrees of freedom 0-n is presented, its manifestation in nature (crystal forms) is found; a number of experiments are proposed; the predictions about the applicability of the multilevel periodicity principle in quark theory are made

Study of the Strong Interaction Among Hadrons with Correlations at the LHC

The strong interaction among hadrons has been measured in the past by scattering experiments. Although this technique has been extremely successful in providing information about the nucleon–nucleon and pion–nucleon interactions, when unstable hadrons are considered the experiments become more challenging. In the last few years, the analysis of correlations in the momentum space for pairs of stable and unstable hadrons measured in pp and p+Pb collisions by the ALICE Collaboration at the LHC has provided a new method to investigate the strong interaction among hadrons. In this article, we review the numerous results recently achieved for hyperon–nucleon, hyperon–hyperon, and kaon–nucleon pairs, which show that this new method opens the possibility of measuring the residual strong interaction of any hadron pair.

Correspondence between isoscalar monopole strengths and α inelastic cross sections on 24Mg

The correspondence between the isoscalar monopole (IS0) transition strengths and α inelastic cross sections, the B(IS0)-(α,α′) correspondence, is investigated for 24Mg(α,α′) at 130 and 386 MeV. We adopt a microscopic coupled-channel reaction framework to link structural inputs, diagonal and transition densities, for 24Mg obtained with antisymmetrized molecular dynamics to the (α,α′) cross sections. We aim at clarifying how the B(IS0)-(α,α′) correspondence is affected by the nuclear distortion, the in-medium modification to the nucleon-nucleon effective interaction in the scattering process, and the coupled-channels effect. It is found that these effects are significant and the explanation of the B(IS0)-(α,α′) correspondence in the plane wave limit with the long-wavelength approximation, which is often used, makes no sense. Nevertheless, the B(IS0)-(α,α′) correspondence tends to remain because of a strong constraint on the transition densities between the ground state and the 0+ excited states. The correspondence is found to hold at 386 MeV with an error of about 20%–30%, while it is seriously stained at 130 MeV mainly by the strong nuclear distortion. It is also found that when a 0+ state that has a different structure from a simple α cluster state is considered, the B(IS0)-(α,α′) correspondence becomes less valid. For a quantitative discussion on the α clustering in 0+ excited states of nuclei, a microscopic description of both the structure and reaction parts will be necessary.