Narrow Results

The hydrogen binding energy in the Pauli–Fierz model with the spin Zeeman term is determined up to the order α³, where α denotes the fine-structure constant.

In this paper, a numerical method optimizing the coefficients of the semi empirical mass formula or those of similar mass formulas is presented. The optimization is based on the least-squares adjustments method and leads to the resolution of a linear system which is solved by iterations according to the Gauss–Seidel scheme. The steps of the algorithm are given in detail. In practice, the method is very simple to implement and is able to treat large data in a very fast way. In fact, although this method has been illustrated here by specific examples, it can be applied without difficulty to any experimental or statistical data of the same type, i.e. those leading to linear system characterized by symmetric and positive-definite matrices.

The hyper-spherical adiabatic expansion is a representation for the investigation of the muonic three-body bound states. In this research we have used the method of hyper-spherical "surface" functions for charge-nonsymmetric muonic molecules (isotopes of helium-deuterium-muon). Through this approach, the binding energy of the ground state and the lowest eigenpotentials for the muonic molecular ions are calculated in extreme adiabatic approximation. The obtained results are close to other's calculation.

An approximate analytic solution for the ground electron state is found to the Schrödinger equation for a combination of a uniform magnetic field and a single attractive -λδ(r) potential. The effect of the magnetic field on this loosely localized electron state is studied. We show that this effect leads to the appearance of the probability current density in some region centered at the point r = 0 as well as changing the localization region of electron in the plane perpendicular to the magnetic field. The effect of a constant crossed uniform electromagnetic field on the loosely localized electron state is also discussed.

The α-cluster model is based on two assumptions that the proton–neutron pair interactions are responsible for adherence between α-clusters and that the NN-interaction in the α-clusters is isospin independent. It allows one to estimate the Coulomb energy and the short range inter-cluster bond energy in dependence on the number of clusters. The charge radii are calculated from the number of α-clusters too. Unlike the Weizsäcker formula in this model the binding energies of alpha-clusters and excess neutrons are estimated separately. The calculated values are in a good agreement with the experimental data.

Study of Coulombian three-body system is a basic phenomenon in muon catalyzed fusion (μCF). In this investigation, separation of variables in the base of adiabatic expansion, have been applied to the mesic three-body molecule, ³Heμd using hyper-spherical elliptic coordinate system. The corresponding eigenvalue problem has been solved and the adiabatic potential and the binding energy of this system are calculated. The obtained results agreed with the expected values of various theoretical methods.

The parton densities which are dependent on transverse momentum, open a way to understand better the structure of quarks and gluons in a more complete way. We are investigating a method based on the covariant quark model which enables us to extract the transverse momentum dependent (TMD) densities from the usual parton densities which are just dependent on the longitudinal momentum. In continuation, we obtain the dependence of the TMDs on binding energy and the mass of quarks. We do some calculations to obtain the TMDs in the unpolarized case while the mass and binding energy of partons are varying. Considering these effects, the results for TMDs are in good agreement with the results of the recent related models.

In this paper, we study four-quark states as di-hadronic molecular states. For this purpose, we apply the Nikiforov–Uvarov method to solve the Schrödinger equation in the presence of the Woods–Saxon plus Coulomb-type potential and we obtain the binding energies and masses of heavy di-mesons. We calculate the root mean square (r.m.s) radius and the wave function for some observed tetraquarks.

Recently, Harko et al. [Phys. Rev. D88, 044032 (2013)] have derived an exact solution of the spherically symmetric field equations in EiBI gravity, describing a compact star with decreasing pressure but increasing energy density. We have explored some features of this solution by restricting the range of the parameter $\kappa$ which satisfies four energy conditions for 10 equation of states (EOSs). Viability and deviations of these features in the light of updated observed properties of neutron stars (NS) have been explored completely. A comparison of those features with recent observations may uncover the future implication of this paper. Analysis of our results indicates that this solution may be used as an alternative EOS.

In this study, we consider baryons as three-body bound systems according to hypercentral constituent quark model in configuration space and solve three-body Klein–Gordon equation. Then we analyze perturbative spin-dependent and isospin-dependent interaction effects. To find the analytical solution, we used screened potential and calculate the eigenfunctions and eigenvalues of triply heavy baryons by using Nikiforov–Uvarov method. We compute the ground and excited state masses of triply heavy baryons with quantum numbers $J^P={\frac{1}{2}}^{\pm }$, ${\frac{3}{2}}^{\pm }$, ${\frac{5}{2}}^{\pm }$ via constituent quark model approach.

The behavior of an electrically charged massive particle (an electron) is studied in a constant uniform magnetic field and a single attractive λδ(r) potential. A simple transcendental equation that determines the electron energy spectrum is derived. The approximate wave function of a loosely bound state is constructed in a very simple form. The model under consideration makes it possible to study the effect of magnetic fields on a loosely bound electron. It is shown that the sizes of the electron localization region change and the probability current density arises when the electron is in the loosely bound state in the presence of a constant uniform magnetic field. The above current must involve (and exercise influence on) the electron scattering. The probability current resembles a stack of "pancake vortices" whose circulating (around the z-axes) "currents" are mostly confined within the plane z = 0 in the weak magnetic field. The equation for determining the energy levels of the electron states is obtained for the model under study in two spatial dimensions and the energy of the loosely bound state is found for the two-dimensional model.

In this work, we study meson systems consisting of quark–antiquark. We solve Lippman–Schwinger equation numerically for heavy meson systems. We attempt to find a nonrelativistic potential model through which we can solve the quark–antiquark bound state problem. The coefficients obtained are in agreement with Martin potential coefficients. Via this method we also determine the strong coupling constant of Cornell and Yukawa potentials for the heavy meson.

In this paper, we employed the quasi-particle (QP) Debye mass at finite baryonic chemical potential which can be used in the medium modified heavy quark potential to solve the $N$-dimensional Schrödinger equation. The bound state solution of the Schrödinger equation using Cornell potential been obtained by Super-Symmetry Quantum Mechanics (SUSYQM) method. The thermodynamical properties of quark matter are calculated by using baryonic chemical potential ($\mu$). We found that the binding energy of quarkonia dissociates more with QP Debye mass in comparison to nonperturbative and leading order Debye mass. The medium modified form of potential (real part) has been used to study the thermodynamical properties of quark matter with different equation of states (EoSs) (i.e. pressure, energy density and speed of sound) with $\mu$. The mass spectra of quarkonia have been also calculated in the $N$-dimensional space and compared with the experimental data at $N=3$. We have also calculated the dissociation temperature ($T_D$) for the ground states of quarkonium using the dissociation criteria of thermal width.

The temperature dependent binding energy of some low lying excited states for a compositional Quantum Well have been calculated for various impurity locations by extending the investigation of Elabsy.⁴ It has been observed that the temperature plays an important role in the binding energy of low lying excited states also.

Energy levels of an impurity atom and its binding energy in a quantum dot with electron–phonon interactions are obtained by the second-order Rayleigh–Schrodinger perturbation theory. The energy correction is expressed as a function of the temperature, the applied magnetic field, and the effective confinement length of the quantum dot. We apply our calculations to GaAs.

The binding energy of a bound polaron in an anisotropic quantum dot (QD) subject to electric and magnetic fields along the growth axis has been investigated by using a variational method of Pekar type, taking into account the electron-bulk LO-phonon interaction. The results show that the binding energy decreases with increasing electric field strength and increases with increasing confinement strengths in the lateral and the longitudinal direction, the magnetic field strength, and the Coulomb potential.

A variational calculation is given within the effective mass approximation of the binding energy of a hydrogenic donor impurity located on the axis of an infinitely long circular quantum well wire. A uniform magnetic field is applied along the axis of the wire. The different effective masses of the wire and the barrier are taken into consideration. This has not been done hitherto in the presence of the magnetic field. New analytical expressions for the electron energy levels and the binding energies of the hydrogenic impurity in the ground and the first four excited states have been derived.

Moreover, the form of the binding energy reported in earlier works in the special case of zero magnetic field has been amended. A new form of the trial wavefunction has also been introduced. It has the advantage of satisfying the required boundary conditions in the case of different masses of the wire and barrier, and thus it resembles the exact solution in this respect. The new form of the trial wavefunction has been applied to the case of the ground state. It has improved the results of binding energy considerably as they tend to approach the exact solution from below.

The ground-state binding energies of a hydrogenic impurity in cylindrical quantum dots (QDs) subjected to external electric and magnetic fields are investigated using the finite-difference method within the quasi-one-dimensional effective potential model. The QD is modeled by superposing a square-well potential and a strong lateral confinement potential by the combination of a parabolic potential and a changeable magnetic field. We define an effective radius of a cylindrical QD which can describe the strength of the lateral confinement. The effects of the electric fields are less important when the effective radius is very tiny, and the effects are manifested as the effective radius increases. Meanwhile, one finds that the binding energies highly depend on the impurity positions under the applied transverse fields. When the impurity is located at the right half of the cylinder, the electric field pushes the electron to the left side, then the binding energy decreases; when the impurity is located at the left, the binding energy first increases and reaches a peak value, then deceases with the electric field.

Using a variational approach within the effective-mass approximation, we investigate the ground-state binding energy of a donor impurity in the GaAs quantum rings (QR) in the infinite confinement potential. A trial wave function with two variational parameters is used in the calculation. The binding energy as a function of the QR structure parameters and the impurity position is investigated. The results indicate that the binding energy decreases gradually as the QR structure parameters increase in the infinite confinement potential. In addition, the binding energy of the impurity exhibits a maximum as the impurity position moves along the symmetry axis of the QR from the bottom of the QR to the top. The impurity binding energy firstly increases and then decreases as the impurity moves from the internal surface of the QR to the external surface, indicating that there is a maximum.

Ultra-thin platinum (Pt) films were deposited on Si(100) substrates at 160°C by magnetron sputtering and subsequently annealed to form silicides. The thickness of the Pt_xSi films was found to be approximately 4 nm as determined by transmission electron microscopy (TEM). X-ray photoelectron spectroscopy (XPS) analysis shows that these films consist of PtSi and Pt₂Si phases, and a multi-layer configuration of SiO_x/PtSi/Pt₂ Si/Si was detected by angle-resolved XPS. However, the Pt₃Si phase was not detected by X-ray diffraction (XRD).