Hellmann Potential in Spinless Salpeter Equation with Potential Barrier within the Framework of Nikiforov-Uvarov method

We have solved the Spinless Salpeter Equation (SSE) with a modified Hylleraas potential within the Nikiforov–Uvarov method. The energy eigenvalues and the corresponding wave functions for this system expressed in terms of the Jacobi polynomial are obtained. With the help of an approximation scheme, the potential barrier has been evaluated. The results obtained can be applied in nuclear physics, chemical physics, atomic physics, molecular chemistry, and other related areas, for example, can be used to study the binding energy and interaction of some diatomic molecules. By adjusting some potential parameters, our potential reduces to the Rosen–Morse and Hulthen potentials. We have present also the numerical data on the energy spectra for this system.

The Hellmann potential is simply a superposition of an attractive Coulomb poten- tial −a/r plus a Yukawa potential be −δr /r. The generalized parametric Nikiforov-Uvarov (NU) method is used to examine the approximate analytical energy eigenvalues and two-component wave function of the Dirac equation with the Hellmann potential for arbitrary spin-orbit quantum number κ in the presence of exact spin and pseudospin (p-spin) symmetries. As a particular case, we obtain the energy eigenvalues of the pure Coulomb potential in the non-relativistic limit.

Hulthen plus Hellmann potentials are adopted as the quark–antiquark interaction potential for studying the thermodynamic properties and the mass spectra of heavy mesons. The potential was rendered temperature dependent by replacing the screening parameter with Debye mass. We solved the radial Schrödinger equation analytically using the Nikiforov–Uvarov method. The energy eigenvalues and corresponding wave function in terms of Laguerre polynomials were obtained. The present results are applied for calculating the mass of heavy mesons, such as charmonium [Formula: see text] and bottomonium [Formula: see text], and thermodynamic properties, such as the mean energy, the specific heat, the free energy, and the entropy. Four special cases were considered when these potential parameters were set to zero, resulting in Hellmann potential, Yukawa potential, Coulomb potential, and Hulthen potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.

Within the framework of Nikiforov-Uvarov method, we obtained an approximate solution of the Schrodinger equation for the Energy Dependent Generalized inverse quadratic Yukawa potential model. The bound state energy eigenvalues for were computed for various vibrational and rotational quantum numbers. Special cases were considered when the potential parameters were altered, resulting into Energy Dependent Kratzer and Kratzer potential, Energy Dependent Kratzer fues and Kratzer fues potential, Energy Dependent Inverse quadratic Yukawa and Inverse quadratic Yukawa Potential, Energy Dependent Yukawa (screened Coulomb) and Yukawa (screened Coulomb) potential, and Energy Dependent Coulomb and Coulomb potential, respectively. Their energy eigenvalues expressions and numerical computations agreed with the already existing literatures.

In this study, we obtained bound state solutions of the radial Schrödinger equation by the superposition of Hulthén plus Hellmann potential within the framework of Nikiforov-Uvarov (NU) method for an arbitrary - states. The corresponding normalized wave functions expressed in terms of Jacobi polynomial for a particle exposed to this potential field was also obtained. The numerical energy eigenvalues for different quantum state have been computed. Six special cases are also considered and their energy eigenvalues are obtained. Our results are found to be in good agreement with the results in literature. The behavior of energy in the ground and excited state for different quantum state are studied graphically.

We study the approximate scattering state solutions of the Duffin-Kemmer-Petiau equation (DKPE) and the spinless Salpeter equation (SSE) with the Hellmann potential. The eigensolutions, scattering phase shifts, partial-waves transitions, and the total cross section for all the partial waves are obtained and discussed. The dependence of partial-waves transitions on total angular momentum number, angular momentum number, mass combination, and potential parameters was presented in the figures.

Hulthén plus Hellmann potentials are adopted as the quark-antiquark interaction potential for studying the mass spectra of heavy mesons. We solved the radial Schrödinger equation analytically using the Nikiforov-Uvarov method. The energy eigenvalues and corresponding wave function in terms of Laguerre polynomials were obtained. The present results are applied for calculating the mass of heavy mesons such as charmonium and bottomonium. Four special cases were considered when some of the potential parameters were set to zero, resulting into Hellmann potential, Yukawa potential, Coulomb potential, and Hulthén potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.

The Hellmann potential, which is a superposition of an attractive Coulomb potential −a/r and a Yukawa potential b e−δr/r, is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov—Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schrödinger equation (SE) for the Hellmann potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented, which show good agreement with a numerical amplitude phase method and also those previously obtained by other methods. As a particular case, we find the energy levels of the pure Coulomb potential.

Analytical solutions of the N-dimensional Schrödinger equation for the newly proposed Varshni-Hulthén potential are obtained within the framework of Nikiforov-Uvarov method by using Greene-Aldrich approximation scheme to the centrifugal barrier. The numerical energy eigenvalues and the corresponding normalized eigenfunctions are obtained in terms of Jacobi polynomials. Special cases of the potential are equally studied and their numerical energy eigenvalues are in agreement with those obtained previously with other methods. However, the behavior of the energy for the ground state and several excited states is illustrated graphically.

The Dirac equation for the combined Mobius square and inversely quadratic Yukawa potentials including a Coulomb-like interaction term has been investigated in the presence of spin and pseudospin symmetries with arbitrary spin-orbit quantum number κ .We have obtained the explicit energy eigenvalues and the corresponding eigenfunctions by the framework of Nikiforov-Uvarov method.

Topological defects on the bound state energy eigenvalues of the diatomic molecules HCl, LiH, CO, H 2 N 2 and NO embedded with Morse potential has been evaluated under the framework of Nikiforov-Uvarov method. Effect of Aharonov–Bohm (AB)-flux field on the diatomic molecules is also discussed here. For arbitrary l ≠ 0, Pekeris approximation is used to deal with the centrifugal barrier term. A comparison of vibrational energy levels for CO(X 1Σ+) diatomic molecule under modified shifted Morse potential (MSMP) with experimental Rydberg-Klein-Rees data has been shown in the Minkowski space. Present outcomes are good enough in accuracy in comparison of all available results found so far.

By using the Nikiforov-Uvarov (NU) method, the Schrodinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.

Today the applications of nuclear physics span a very broad range of topics and fields. This review discusses a number of aspects of these applications, including selected topics and concepts in nuclear reactor physics, nuclear fusion, nuclear non-proliferation, nuclear-geophysics, and nuclear medicine. The review begins with a historic summary of the early years in applied nuclear physics, with an emphasis on the huge developments that took place around the time of World War II, and that underlie the physics involved in designs of nuclear explosions, controlled nuclear energy, and nuclear fusion. The review then moves to focus on modern applications of these concepts, including the basic concepts and diagnostics developed for the forensics of nuclear explosions, the nuclear diagnostics at the National Ignition Facility, nuclear reactor safeguards, and the detection of nuclear material production and trafficking. The review also summarizes recent developments in nuclear geophysics and nuclear medicine. The nuclear geophysics areas discussed include geo-chronology, nuclear logging for industry, the Oklo reactor, and geo-neutrinos. The section on nuclear medicine summarizes the critical advances in nuclear imaging, including PET and SPECT imaging, targeted radionuclide therapy, and the nuclear physics of medical isotope production. Each subfield discussed requires a review article unto itself, which is not the intention of the current review; rather, the current review is intended for readers who wish to get a broad understanding of applied nuclear physics.

In this paper, the Born-Mayer potential is used to describe the core-shell polystyrene nanoparticle and the Schrodinger equation for this nanoparticle is solved rigorously using the Nikiforov-Uvarov (NU) method to obtain the exact bound state solutions and energy spectrum. This is achieved by inserting the Born-Mayer potential into the Time Independent Schrödinger Equation (TISE), obtaining the radial part and solving, exactly, for the expectation values of the energy spectrum and the corresponding eigenfunctions applying the Nikiforov Uvarov (NU) method. The eigenvalue expression obtained is similar to earlier work on Soliton solution in nonlinear lattice with the nearest neighbor Born-Mayer interaction.

Alexander Dalgarno