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.

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

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

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.

\(^{12}\mathrm{C}(\alpha , \gamma )^{16}\)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

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

Unfortunately, corrections to equations 3.19 and 3.20 were published incorrect in the original publication.

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

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

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

Unfortunately during proofing, corrections to equations 5 and 6 have not been incorporated into the final version before online publication as requested by author.

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

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.

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

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

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

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

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

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

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

The Green function for Dirac oscillator in \((1+1)\) dimension in the context of the extended uncertainty principle (EUP) is calculated exactly via the path integral formalism. The spectrum energy is determined, the corresponding wave functions suitably normalized are derived and they are expressed by the Gegenbauer’s polynomials. Special cases are considered.

We present a work which is meant to inspire the few-body practitioners to venture into the study of new, more exotic, systems and to hadron physicists, working mostly on two-body problems, to move in the direction of studying related few-body systems. For this purpose we devote the discussions in the introduction to show how the input two-body amplitudes can be easily obtained using techniques of the

The exciting discovery by LHCb of the \(P_c(4312)^+\) and \(P_c(4450)^+\) pentaquarks, or the suggestion of a tetraquark nature for the \(Z_c(3900)\) state seen at BESIII and Belle, have triggered a lot of activity in the field of hadron physics, with new experiments planned for searching other exotic mesons and baryons, and many theoretical developments trying to disentangle the true multiquark nature

The existence of a kinematic long range component in the one particle transfer three-body potential or so-called “general particle transfer (GPT) potential” was proposed several years ago. In this investigation the mass dependence of the exchanged particle and the index number of the long range property are clarified. On the basis of the GPT potential, a new long range three-body force is proposed

It is shown, that fitting parameters of a \(\bar{K}N\) interaction model to different sets of experimental data can lead to physical conclusions which might provide a deeper insight into the physics of this multichannel system. The available experimental data are divided into three parts: the “classical” set consisting of the low-energy \(K^-p\) cross sections and the threshold branching ratios, the

In recent years, study of pentaquarks as the exotic states of multiquark particles have been in progress experimentally and theoretically. A motivation for studying these new particles has been to better understanding of the strong interactions and the QCD theory. In this work, our aim is to calculate the mass spectrum of possible heavy pentaquarks for which we consider a two-body system containing

In this work, we present approximate solutions of the modified Klein–Gordon containing an interaction of the modified unequal mixture scalar vector Hulthén–Yukawa potentials model (MUMSVHYa-PM) using the procedure of improved approximation of the centrifugal term, Bopp’s shift method and perturbation theory. This study is realized in the relativistic noncommutative three-dimensional real-space (RNC:

Studies of the spectrum of hadrons and their structure in experiments with electromagnetic probes offer unique insight into many facets of the strong interaction in the regime of large quark-gluon running coupling, i.e. the regime of strong QCD. The experimental program within Hall B at Jefferson Laboratory based on data acquired with the CLAS spectrometer using electron and photon beams with energies

We suggest a framework based on the rainbow approximation to the Dyson–Schwinger and Bethe–Salpeter equations with effective parameters adjusted to lattice QCD data to calculate the masses of the ground and excited states of pseudo-scalar glueballs. The structure of the truncated Bethe–Salpeter equation with the gluon and ghost propagators as solutions of the truncated Dyson–Schwinger equations is

It was found that NN potential could influence the results of the quasi-bound state search in the \(K^- d\) system, where the corresponding pole is situated close to the threshold. Three-body Faddeev-type calculations of the \(\bar{K}NN - \pi \varSigma N\) system performed with a new model of nucleon-nucleon interaction predict the existence of the quasi-bound \(K^- d\) state caused by strong interactions

We study central configurations of 5-body problem with one dominant particle and four infinitesimal particles. In 2013, Oliveira (Celest Mech Dyn Astron 116:11–20, 2013) showed that the configurations are symmetric when two infinitesimal particles are diametrically opposite. Moreover, in the case of these two particles have the same mass he proved that the number of central configurations is one or

In this study, we have extended the idea of fractional spin introduced recently in literature based on two orders fractional derivative operator. Generalizations of the fractional spin, the fractional angular momentum and the fractional momentum operators were obtained. The theory is characterized by a noncommutativity between the generalized fractional angular momentum and the fractional Hamiltonian

We discuss the stability of hidden and open heavy-flavor hadronic states made of either two or three mesons. References are made in passing to studies regarding two and three-body systems containing baryons. We perform a comparative study analyzing the results in terms of quark and hadron degrees of freedom. Compact and molecular states are found to exist in very specific situations. We estimate the

The hadronic vacuum polarization function \(\Pi _h\) for two light flavors is computed on the entire domain of spacelike and timelike momenta using a framework of Dyson–Schwinger equations. The analytical continuation of the function \(\Pi _h\) is based on the utilization of the Gauge Technique with the entry of QCD Green’s functions determined from generalized quark spectral functions. For the first

Properties of the positronium negative ion embedded in non-ideal classical plasmas have been studied theoretically. A pseudopotential, derived from a solution of Bogolyubov’s hierarchy equations, is used to describe the interaction potentials of the charged particles in the ion. A large basis set is employed in Rayleigh–Ritz variational method to compute accurately various quantities, such as binding

The explicit expression of the vibrational partition function for the modified Pöschl–Teller plus Woods–Saxon potential has been presented in a closed-form. The analytical expression for the vibrational mean energy have also been calculated were other thermodynamic functions like the vibrational specific heat, free energy, and the entropy for the gallium nitride wurtzite crystal structure have been

Since the pioneering work of Lüscher in the 1980s it is well known that considering quantum systems in finite volume, specifically, finite periodic boxes, can be used as a powerful computational tool to extract physical observables. While this formalism has been worked out in great detail in the two-body sector, much effort is currently being invested into deriving analogous relations for systems with

The eigensolutions of many-body quantum systems are always difficult to compute. The envelope theory is a method to easily obtain approximate, but reliable, solutions in the case of identical particles. It is extended here to treat systems with different particles (bosons or fermions). The accuracy is tested for several systems composed of identical particles plus a different one.

The Alt–Grassberger–Sandhas equations for the five-body problem are solved for the case of the driving two-body potentials limited to s-waves. The separable pole expansion method is employed to convert the equations into the effective quasi-two-body form. Numerical results are presented for five identical bosons as well as for the system containing an \(\eta \)-meson and four nucleons. Accuracy of

In this work we study the Schrödinger equation in the presence of the Hartmann potential with a generalized uncertainty principle. We pertubatively obtain the matrix elements of the hamiltonian at first order in the parameter of deformation \(\beta \) and show that some degenerate states are removed. We give analytic expressions for the solutions of the diagonal matrix elements. Finally, we derive

By attaining an accuracy of 30 significant figures, in the present work we have calculated the expectation values of \(\langle {r^{ - 2}}\rangle \) of a few states for the confined hydrogen atom and the confined harmonic oscillator, as a function of the confinement radius \(R_{c}\). In comparison to other calculations reported in the literature, our results are found to be more accurate. This numerical

We present and analyzed bi-circular restricted four-body problem model that accounts for dissipative forces. Specifically, the model for Sun–Earth–Moon-Spacecraft system is formulated with inclusion of Stokes drag and Poynting–Robertson (P–R) drag. The Lagrange points are seen to be dependent on the strength and the kind of the dissipative force involved, comparatively, the P–R drag is found to exert

Our present understanding of the structure of the Hoyle state in \(^{12}\)C and other near-threshold states in \(\alpha \)-conjugate nuclei is reviewed in the framework of the \(\alpha \)-condensate model. The \(^{12}\)C Hoyle state, in particular, is a candidate for \(\alpha \)-condensation, due to its large radius and \(\alpha \)-cluster structure. The predicted features of nuclear \(\alpha \)-particle

We probe the convergence of the configuration interaction (CI) approach for harmonically trapped one-dimensional Fermi–Fermi mixtures. Existing scientific papers that apply the CI approach to study such systems typically use harmonic oscillator eigenfunctions with fixed frequency parameter values as bases. We show that CI’s optimisation is the key to reducing the computational cost of the numerical

We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schrödinger models with energy-dependent potentials, conventional Schrödinger models using the supersymmetry formalism, and two-dimensional Dirac systems. In addition, we derive Wronskian integral formulas for Lambert-W functions.

Based on \( 3\times 3\) irreducible representation of Duffin–Kemmer–Petiau (DKP) algebras, we obtain the bound-states energy spectrum, the wave function and the probability density of DKP oscillator with linear potential under the effect of Generalized Uncertainty Principle in the momentum space representation. In addition, the numerical results of the bound-states energy spectrum are discussed. It

Dirac equation with spatially or position-dependent mass and an attractive Coulomb-like field is constructed in Hausdorff dimension of order \(0<\alpha \le 1\). The lower and upper components of the spinor wave function were derived in addition to the corresponding energy eigenvalues of the resulting relativistic equation. It was observed that, in Hausdorff radial dimension, the ground state energy

In this paper, we try to solve the Schrödinger equation in a quasi-exact solvable method for a three-body problem with a special interaction and by adding an anharmonic perturbation term. We consider the interaction and perturbation theory in the Calogero model by the roots of algebra \(A_{2}\) and rewrite the Hamiltonian in terms of Lie algebra \(gl_{3} \) and \(g^{2}\) generators. Indeed, we show

As a two-body system, hydrogen atom with quantum exact solution played an important role for explaining shell structure of multi-electron atoms. Inspired by this, we suggest an alternative interpretation of the integer and fractional quantum Hall effect (QHE) by establishing a direct connection between the exact solutions of a two-dimensional (2D) magnetically trapped electron-pair and the “fundamental”

In this paper, Duffin–Kemmer–Petiau (DKP) for spin-1 equation has been investigated in the q-deformed quantum mechanics. After rewriting DKP equation and its elements, this equation has been rewritten in the new formalism. After an algebraic processes for decoupling of components wave function, some scattering and bound states problems have been studied in detail. To show effects of the deformation

Kinetic, potential and overlap matrix elements of one dimensional correlated Gaussians multiplied by polynomial factors are presented. These matrix elements can be used to calculate energies of one dimensional cold atom systems, or to construct a tensorial product to calculate energies in 2 or 3 dimensional systems with a nonspherical potential.

In this letter, we present the exact solution of the three-dimensional Klein–Gordon oscillator on the (anti)-de Sitter spaces, the energy spectrum and the associated wave functions are extracted and the wave functions are expressed according to the Jacobi polynomial. On the other hand, we have investigated the three-dimensional the Klein–Gordon equation with a Coulomb plus scalar potential, we use

In this paper the q-deformed Schrödinger equation is derived from the q-translation symmetry in space. The correct unitary q-translation operator is constructed for q-deformed quantum mechanics with q-translation symmetry. The supersymmetric q-deformed quantum mechanics with q-translation symmetry is also discussed.

It is shown that the Hankel transform of the s-wave Hulthén physical Green’s function satisfies a second-order differential equation. This equation is solved by applying the proper boundary conditions in association with the properties of the special functions of mathematics to get a closed form expression for the same. The Hankel transform of the physical Green’s function is exploited to extract off-shell

We study the Massless Semi-Relativistic Harmonic Oscillator within the framework of quantum mechanics with a Generalized Uncertainty Principle (GUP). The latter derives from the idea of minimal observable length, a quantity whose existence is expected to affect the energy eigenvalues and the eigenfunctions of the system. These effects are worked out, to the first order in the deformation parameter

In the context of new type of the extended uncertainty principle using the displacement operator method, we present an exact solution of some problems such as: the Klein–Gordon particle confined in a one dimensional box, the scalar particle with linear vector and scalar potentials and the case of inversely linear vector and scalar potentials of Coulomb-type. The expressions of bound state energies

Trigonometric Rosen–Morse potential is suggested as a quark–antiquark interaction potential for studying thermodynamic properties and masses of heavy and heavy–light mesons. For this purpose, the N-radial Schrödinger equation is analytically solved using an exact-analytical iteration method. The energy eigenvalues and corresponding wave functions are obtained in the N-space. The present results are

We propose a solution method for studying relativistic spin-0 particles. We adopt the Feshbach–Villars formalism of the Klein–Gordon equation and express the formalism in an integral equation form. The integral equation is represented in the Coulomb–Sturmian basis. The corresponding Green’s operator with Coulomb and linear confinement potential can be calculated as a matrix continued fraction. We consider

The envelope theory is a simple technique to obtain approximate, but reliable, solutions of many-body systems with identical particles. The accuracy of this method is tested here for two systems in one dimension with pairwise forces. The first one is the fermionic ground state of the analytical Calogero model with linear forces supplemented by inverse-cube forces. The second one is the ground state

Confinement induced resonance (CIR) is a useful tool for the control of the interaction between ultracold atoms. In most cases the CIR occurs when the characteristic length \(a_\mathrm{trap}\) of the confinement is similar as the scattering length \(a_{s}\) of the two atoms in the free three-dimensional (3D) space. If there is a CIR which can occur with weak bare interaction, i.e., under the condition