Abstract: Abstract In this paper the search for \(\eta \) -mesic nuclei with particular focus on light \(\eta \) -He bound states is reviewed. A brief description of recent experimental results is presented. PubDate: 2021-01-09

Abstract: Abstract We investigated the relativistic dynamics of oppositely charged two fermions interacting with an external uniform magnetic field, without considering any charge-charge interaction between the fermions. We chose the interaction of each fermion with the external magnetic field in the symmetric gauge, and obtained a precise solution of the corresponding fully-covariant two-body Dirac equation that derived from Quantum Electrodynamics via Action principle. The dynamic symmetry of the system we deal with allowed us to determine the relativistic Landau levels of such a spinless composite system, without using any group theoretical method. As a result, we determined the eigenfunctions and eigenvalues of the corresponding two-body Dirac Hamiltonian. PubDate: 2021-01-09

Abstract: Abstract The measurement of nuclear generalized parton distributions (GPDs) in hard exclusive processes, such as deeply virtual Compton Scattering (DVCS), will be one of the main achievements of a new generation of experiments at high luminosity. Let us mention those under way at the Jefferson Laboratory (JLab) with the 12 GeV electron beam and, above all, those planned at the future Electron Ion Collider. The CLAS collaboration at JLab has recently demonstrated the possibility to disentangle the the coherent and incoherent channels of nuclear DVCS, a first step towards the measurement of GPDs of nuclei and of bound nucleons, respectively, opening new exciting perspectives in the field. In this scenario, accurate calculations, ultimately realistic, become mandatory. Light nuclei, for which realistic studies are affordable and conventional nuclear effects can be safely estimated, so that possible exotic effects can be exposed, play an important role. The status of the calculation of GPDs for light nuclei will be summarized, in particular for \(^3\) He and \(^4\) He, and some updates will be presented. The prospects for the next years, related to the new series of measurements at future facilities, will be addressed. PubDate: 2021-01-08

Abstract: Abstract The mass relation \({M_{0^{+}}+3M_{1^{+\prime }}+5M_{2^{+}}= 9M_{1^{+}}}\) miraculously holds for the P-wave charmonium \((c\bar{c})\) and bottomonium \((b\bar{b})\) systems with soaring precision. The origin of such relation can be addressed from Quark Models, and have been confirmed experimentally in a limited number of cases. In this connection, we propose \(M_{0^{+}}+5M_{2^{+}}=3(M_{1^{+\prime }}+M_{1^{+}})\) as an extension to the P-wave \(B_{c}\) case. In order to test its applicability, we employ a variety of Quark Model predictions for the \(B_c\) mass spectrum. Our numerical analysis confirms such formula is accurate up to very small deviations. PubDate: 2021-01-08

Abstract: Abstract \(^{12}\mathrm{C}(\alpha , \gamma )^{16}\) O radiative-capture process is a key reaction to produce the element of oxygen in stars. Measuring the cross section near the Gamow window is extremely hard because it is too small. To make a theoretical contribution towards resolving the long-standing problem, I present a microscopic formulation that aims at providing all materials needed to calculate the cross section. The states of \(^{12}\mathrm{C}\) and \(^{16}\mathrm{O}\) relevant to the reaction are respectively described with fully microscopic 3 \(\alpha \) -particle and 4 \(\alpha \) -particle configurations, in which the relative motion among the \(\alpha \) particles is expanded in terms of correlated Gaussian basis functions. The configuration space has the advantage of being able to well describe the reduced \(\alpha \) -width amplitudes of the states of \(^{16}\) O. Both electric dipole and electric quadrupole transitions are responsible for the radiative-capture process. The \(\alpha \) particle is described with a \((0s)^4\) configuration admixed with a small amount of an isospin \(T=1\) impurity component, which is crucially important to account for the isovector electric dipole transition. The isoscalar electric dipole operators are also taken into account up to the first order beyond the long-wavelength approximation. All the necessary ingredients are provided to make the paper self-contained and ready for numerical computations. PubDate: 2021-01-03

Abstract: Abstract The standard way to demonstrate the relevance of chiral symmetry for the NN interaction is to consider higher partial waves of NN scattering which are controlled entirely by chiral pion-exchanges (since contacts vanish). However, in applications of NN-potentials to nuclear structure and reactions, the lower partial waves are the important ones, making the largest contributions. Lower partial waves are sensitive to the short-range potential, and so, when the short-range contacts were to dominate over the chiral pion-contributions in lower partial waves, then the predictions from “chiral potentials” would have little to do with chiral symmetry. To address this issue, we investigate systematically the role of the (chiral) one- and two-pion exchanges, on the one hand, and the effect of the contacts, on the other hand, in the lower partial waves of NN scattering. We are able to clearly identify the signature of chiral symmetry in lower partial waves. Our study has also a pedagogical spin-off as it demonstrates in detail how the reproduction of the lower partial-wave phase shifts comes about from the various ingredients of the theory. PubDate: 2021-01-02

Abstract: Abstract We introduce the transition-density formalism, an efficient and general method for calculating the interaction of external probes with light nuclei. One- and two-body transition densities that encode the nuclear structure of the target are evaluated once and stored. They are then convoluted with an interaction kernel to produce amplitudes, and hence observables. By choosing different kernels, the same densities can be used for any reaction in which a probe interacts perturbatively with the target. The method therefore exploits the factorisation between nuclear structure and interaction kernel that occurs in such processes. We study in detail the convergence in the number of partial waves for matrix elements relevant in elastic Compton scattering on \({}^3\hbox {He}\) . The results are fully consistent with our previous calculations in Chiral Effective Field Theory. But the new approach is markedly more computationally efficient, which facilitates the inclusion of more partial-wave channels in the calculation. We also discuss the usefulness of the transition-density method for other nuclei and reactions. Calculations of elastic Compton scattering on heavier targets like \({}^4\hbox {He}\) are straightforward extensions of this study, since the same interaction kernels are used. And the generality of the formalism means that our \({}^3\hbox {He}\) densities can be used to evaluate any \({}^3\hbox {He}\) elastic-scattering observable with contributions from one- and two-body operators. They are available at https://datapub.fz-juelich.de/anogga. PubDate: 2020-11-19

Abstract: Abstract We study the quantum relativistic wave equations (Klein–Gordon and Dirac) for the non-pure dipole potential \(V(r)=-Ze/r+D\cos \theta /r^{2}\) , in the case of two-dimensional systems. We consider either spin symmetry or anti-spin symmetry cases in our computations. We give the analytical expressions of the eigenfunctions, compute the exact values of the energies and study their dependence according to the dipole moment D. Our study generalizes the energies of the Kratzer potential as well as the magnetic quantum number m, which is replaced with the Mathieu characteristic values obtained during the resolution of the angular equations. For each magnetic quantum number, we demonstrate the existence of a critical value for the dipole moment, beyond which the corresponding bound state can no longer exist. We find that the critical value is null when \(m=0\) ; this means that these s-states cannot exist for this system and this is in agreement with non-relativistic studies. PubDate: 2020-11-19

Abstract: Abstract We study the prospects of using femtoscopic low-momentum correlation measurements at the Large Hadron Collider to access properties of the \(J/\psi \) -nucleon interaction. The QCD multipole expansion in terms of the \(J/\psi \) chromopolarizability relates the forward scattering amplitude to a key matrix element to the origin of the nucleon mass problem, the average chromoelectric gluon distribution in the nucleon. We use information on the \(J/\psi \) -nucleon interaction provided by lattice QCD simulations and phenomenological models to compute \(J/\psi \) -nucleon correlation functions. The computed correlation functions show clear sensitivity to the interaction, in particular to the \(J/\psi \) chromopolarizability. PubDate: 2020-11-19

Abstract: Unfortunately during proofing, corrections to equations 5 and 6 have not been incorporated into the final version before online publication as requested by author. PubDate: 2020-11-12

Abstract: Abstract Using advanced stochastic methods (time-dependent quantum Monte Carlo, TDQMC) we explore the ground state of 1D and 2D artificial atoms with up to six bosons in harmonic trap where these interact by long-range and short-range Coulomb-like potentials (bosonic quantum dots). It is shown that the optimized value of the key variational parameter in TDQMC named nonlocal correlation length is close to the standard deviation of the Monte Carlo sample for one boson and it is slightly dependent on the range of the interaction potential. Also it is almost independent on the number of bosons for the 2D system thus confirming that the spatial quantum non-locality experienced by each particle is close to the spatial uncertainty exhibited by the rest of the particles. The intimate connection between spatial non-locality and quantum correlations is clearly evidenced. PubDate: 2020-10-31

Abstract: Abstract We present a selection of topics with an interplay of hadron and few-body physics. This includes few-nucleon systems, light hypernuclei and quark dynamics for baryons and multiquarks. It is stressed that standard quark models predict very few stable multiquarks. PubDate: 2020-10-30

Abstract: Abstract An electron ion collider has been proposed in China (EicC). It is anticipated that the facility would provide polarised electrons, protons and ion beams, in collisions with large centre-of-mass energy. This discussion highlights its potential to address issues that are central to understanding the emergence of mass within the Standard Model, using examples that range from the exploration of light-meson structure, through measurements of near-threshold heavy-quarkonia production, and on to studies of the spectrum of exotic hadrons. PubDate: 2020-10-24

Abstract: Abstract A method of analytically calculating energy levels of He-like ions in an environment of dense plasma is given by using the angular momentum coupling theory and irreducible tensor theory under Hartree–Fock approximation. In order to obtain higher calculation precision, relativistic correction terms of the non-relativistic energy including corrections caused by relativistic mass, one- and two-body Darwin effect, spin–spin contact interaction and orbit–orbit interaction, are calculated. The binding energies of the ground state \(1s^2\) \(^1S\) and excited state 1snp \(^1P\) (n = 1 − 4) of He-like Cl ions and the transition energy between two energy levels in an environment of dense plasma are calculated. The scaling relationship between the energy shift of plasma and its temperature and density is given. According to our study, the energy shift of plasma conforms very well with the recent high-precision experimental result (Phys Rev A 100:012511, 2019). PubDate: 2020-10-22

Abstract: Abstract In this study, we obtain the recursive general solution of the Schrödinger equation \(y_{\nu }''(x;\lambda )+[\lambda -\nu (\nu +1)v(x)]y_{\nu }(x;\lambda )=0\) for some Pöschl–Teller type potentials when \(\nu =0,1,2,\ldots \) . As a by product of the general solution, the finitely many bound states of the squared hyperbolic secant and tangent potentials are also derived when equipped with some suitable boundary conditions over the real line. PubDate: 2020-10-20

Abstract: Abstract A nuclear model is proposed where the nucleons interact by emitting and absorbing mesons, and where the mesons are treated explicitly. A nucleus in this model finds itself in a quantum superposition of states with different number of mesons. Transitions between these states hold the nucleus together. The model—in its simplest incarnation—is applied to the deuteron, where the latter becomes a superposition of a neutron-proton state and a neutron-proton-meson state. Coupling between these states leads to an effective attraction between the nucleons and results in a bound state with negative energy, the deuteron. The model is able to reproduce the accepted values for the binding energy and the charge radius of the deuteron. The model, should it work in practice, has several potential advantages over the existing non-relativistic few-body nuclear models: the reduced number of model parameters, natural inclusion of few-body forces, and natural inclusion of mesonic physics. PubDate: 2020-10-16

Abstract: Abstract In this work, we proposed ultra generalized exponential–hyperbolic potential (UGEHP) and derived various well known exponential–hyperbolic type potentials by setting parameters in UGEHP and using approximation suggested by Greene–Aldrich. The bound state solutions of the multi (D)-dimensional Schrödinger equation for UGEHP have been presented using the parametric Nikiforov–Uvarov method. The approximate analytical bound state energy eigenvalues and the corresponding un-normalized eigenfunctions expressed in terms of hypergeometric functions were obtained. We also investigated the rotational vibrational (RV) partition function from the eigenvalue of UGEHP. By the setting parameters, we obtained eigenvalue spectrum and RV partition function for the screened cosine Kratzer potential, screened Kratzer potential, attractive radial potential, quadratic exponential-type potential, Manning Rosen with class of Yukawa potential and Yukawa potential, class of Yukawa potential, mixed class of Yukawa potential, quantum interaction potential or Hulthën–Yukawa inversely quadratic potential, Hulthën plus inversely quadratic exponential Mie-type potential and Hulthën plus exponential Coulombic potential with centrifugal potential barrier. We studied the behavior of energy eigenvalues and RV partition function for the UGEHP. We computed and tabulated numerical results for \(CO, NO, I_2\) , HCl and LiH diatomic molecules and compared with numerical results available in literature for same diatomic molecules. PubDate: 2020-10-12

Abstract: Abstract In this feature article we summarise and highlight aspects of the treatment of four-quark states with functional methods. Model approaches to those exotic mesons almost inevitably have to assume certain internal structures, e.g. by grouping quarks and antiquarks into (anti-)diquark clusters or heavy-light \(q{\bar{q}}\) pairs. Functional methods using Dyson–Schwinger and Bethe–Salpeter equations can be formulated without such prejudice and therefore have the potential to put these assumptions to test and discriminate between such models. So far, functional methods have been used to study the light scalar-meson sector and the heavy-light sector with a pair of charmed and a pair of light quarks in different quantum number channels. For all these states, the dominant components in terms of internal two-body clustering have been identified. It turns out that chiral symmetry breaking plays an important role for the dominant clusters in the light meson sector (in particular for the scalar mesons) and that this property is carried over to the heavy-light sector. Diquark-antidiquark components, on the other hand, turn out to be almost negligible for most states with the exception of open-charm heavy-light exotics. PubDate: 2020-10-07

Abstract: Abstract In this study, we have constructed a generalized momentum operator based on the notion of backward–forward coordinates characterized by a low dynamical nonlocality decaying exponentially with position. We have derived the associated Schrödinger equation and we have studied the dynamics of a particle characterized by an exponentially decreasing position-dependent mass following the arguments of von Roos. In the absence of magnetic fields, it was observed that the dynamics of the particle is similar to the harmonic oscillator with damping and its energy state is affected by nonlocality. We have also studied the dynamics of a charged particle in the presence of Morse–Coulomb potentials and external magnetic and Aharonov-Bohm flux fields. Both the energy states and the thermodynamical properties were obtained. It was observed that all these physical quantities are affected by nonlocality and that for small magnetic fields and high quantum magnetic numbers, the entropy of the system decreases with increasing temperature unless the nonlocal parameter is negative. For positive value of the nonlocal parameter, it was found that the entropy increases with temperature and tends toward an asymptotically stable value similar to an isolated system. PubDate: 2020-10-03