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Our purpose in this paper is to modify the original proximity potential by universal function available in the literature. A potential model with Yukawa proximity potential has been considered according to the modified model fusion reactions of ${}^{92}\mathrm{\text{Zr}}+{}^{12}\mathrm{\text{C}}$, ${}^{16}\mathrm{\text{O}}+{}^{92}\mathrm{\text{Zr}}$, ${}^{28}\mathrm{\text{Si}}+{}^{92}\mathrm{\text{Zr}}$, ${}^{16}\mathrm{\text{O}}+{}^{144}\mathrm{\text{m}}$, ${}^{28}\mathrm{\text{Si}}+{}^{28}\mathrm{\text{Si}}$, ${}^{28}\mathrm{\text{Si}}+{}^{29}\mathrm{\text{Si}}$, ${}^{28}\mathrm{\text{Si}}+{}^{30}\mathrm{\text{Si}}$, ${}^{24}\mathrm{\text{Mg}}+{}^{24}\mathrm{\text{Mg}}$, ${}^{24}\mathrm{\text{Mg}}+{}^{26}\mathrm{\text{Mg}}$ and ${}^{24}\mathrm{\text{Mg}}+{}^{28}\mathrm{\text{Si}}$, ${}^{26}\mathrm{\text{Mg}}+{}^{28}\mathrm{\text{Si}}$, ${}^{24}\mathrm{\text{Mg}}+{}^{30}\mathrm{\text{Si}}$, ${}^{26}\mathrm{\text{Mg}}+{}^{30}\mathrm{\text{Si}}$ which have been discussed in detail. The results have a good agreement with the experimental data.

This paper presents the results of the nuclear electrical quadrupole moment of the ¹⁷O and ²H before and after their scattering interaction near the Coulomb barrier. The distribution of nuclei’s charge (the quadrupole moment of nuclei) was examined for ²H and ¹⁷O when interacting together. The interaction potential between the nuclei was achieved using the double-folding model. Also, the wave functions of the interacting nuclei were replaced with the density functions. The wave functions of the interacting nuclei were obtained through the D-dimensional Schrödinger equation with the pseudo-Coulomb potential plus ring-shaped potential and Yukawa potential by the Nikiforov–Uvarov solution method.

Many precision experiments have been done in the Casimir regime and in short range gravity when the separation between the interacting bodies is in the sub-micron range. Experimental complexity is minimized when one of the bodies is a sphere and the other one is a plate, making the alignment between the two bodies ubiquitous. Our group has produced the most precise Casimir measurements, and the best limits on predicted Yukawa-like potentials by measuring a force between a $R\sim 150\mu \mathrm{\text{m}}$ sphere attached to a ${(500\mu \mathrm{\text{m}})}^2$ micro-mechanical oscillator and a planar source mass. By replacing the spherical surface with a fraction of a $500\mu \mathrm{\text{m}}$ long cylinder with $R\sim 150\mu$m, the force sensitivity can be greatly enhanced. Here, it is paramount to know the angular deviation between the long axis of the cylinder and both the axis of rotation of the oscillator and the plate. Tests between a cylinder and a structure etched into a silicon wafer show that deviations of $20\mu$rad are readily accessible. Additionally, a scaled up experiment is used to investigate if capacitance measurements can determine the orientation of the cylinder with respect to a plane with the required precision.

Similar to how general relativity emerged, quantum mechanics resulted from experimental observations that made us radically rethink our previous assumptions. Scientists who study atoms need to solve these three equations. They are for a system with N electrons affected by the nucleus’s attractive Coulomb force and the repulsive force between each pair of electrons and other potentials. While general relativity has upended our large-scale conception of the universe, quantum mechanics calls into question all our intuition regarding particle physics. The Klein–Gordon (KG) resolution helps determine some physical systems and their properties by finding their bound states and eigenfunctions. These are resolved using analytical and numerical methods, as well as Coulomb and Yukawa potentials. In order to extract some of the first eigenvalues of the quantum mechanical system, we applied the Nikiforov–Uvarov (NU) method to the KG equation. The findings are significant for understanding nuclear charge radius, spin, nuclear diffusion and other topics in numerous theoretical physics and quantum chemistry fields because they are more generic and helpful.

Energy levels of neutral atoms have been reexamined by applying an alternative perturbative scheme in solving the Schrödinger equation for the Yukawa potential model with a modified screening parameter. The predicted shell binding energies are found to be quite accurate over the entire range of the atomic number Z up to 84 and compare very well with those obtained within the framework of hypervirial-Padé scheme and the method of shifted large-N expansion. It is observed that the new perturbative method may also be applied to the other areas of atomic physics.

Noticing renewed or increasing interest in the possibility to describe semirelativistic bound states (of either spin-zero constituents or, upon confining oneself to spin-averaged features, constituents with nonzero spin) by means of the spinless Salpeter equation generalizing the Schrödinger equation toward incorporation of effects caused by relativistic kinematics, we revisit this problem for interactions between bound-state constituents of Yukawa shape, by recalling and applying several well-known tools enabling to constrain the resulting spectra.

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 work, we use the approach recently introduced by Barros to study hadron spectra and some quark confinement properties in a Schwarzchild-like space–time generated by a nongravitational field. As a starting point, for the nongravitational field, we make the choice of a strong Yukawa-like field whose associated potential is a generalized Yukawa-like potential, typical of strong interactions. Then, from the latter field, the energy momentum tensor is constructed, the Einstein field equations are solved and the curvature function of the Schwarzchild metric is obtained. The correspondence principle applied to the Schwarzchild metric has enable us to construct the Dirac equation in the latter space. The resolution of the coupled differential equations of Dirac made it possible to obtain the energy spectrum of the strong interaction. The latter is obtained in a more general form than in the previous investigations. Then, the energy spectrum, masses and confinement radius of few hadrons are estimated and compared with experimental data and other theoretical studies. In most considered cases, our predictions are found to be in good agreement with experimental data. The good agreement observed between our outcomes and the experiment can be attributed to the choice of our potential, which has more free parameters than in past studies with the same approach.

Within the context of nonlinear electromagnetism, we consider the Yukawa extension of a Reissner–Nordström black hole. Exact solution is given which modifies certain characteristics of the latter. Some thermodynamical aspects are given for comparison. The model which is based on a nonpolynomial Lagrangian implicitly may be considered as a useful agent to describe a short-ranged, charged and massive interaction.

We apply the asymptotic iteration method to solve the radial Schrödinger equation for the Yukawa type potentials. The solution of the radial Schrödinger equation by using different approaches requires tedious and cumbersome calculations; however, we present that it is possible to obtain the bound state energy eigenvalues for any n and ℓ values easily within the framework of this method. We also show the perturbed application of this method for the same potential. Our results are in excellent agreement with the findings of the SUSY perturbation, 1/N expansion and numerical methods.

We obtain analytical solutions of the two-body spinless Salpeter (SS) equation with the Yukawa potential within the conventional approximation scheme to the centrifugal term for any l-state. The semirelativistic bound-state energy spectra and the corresponding normalized wave functions are calculated by means of the Nikiforov–Uvarov (NU) method. We also obtain the numerical energy spectrum of the SS equation without any approximation to centrifugal term for the same potential and compare them with the approximated numerical ones obtained from the analytical expressions. It is found that the exact numerical results are in good agreement with the approximated ones for the lower energy states. Special cases are treated like the nonrelativistic limit and the solution for the Coulomb problem.

We intend to study the alpha-decay half-lives of some nuclei from ground state to ground state. We consider a potential model with Yukawa proximity potential. We see that the results are in good agreement with the experimental data.

The paper investigates the alpha-decay half-lives of some nuclei by modifying the Coulomb potential with Yukawa proximity potential for the excited state decays. A new relation is found for the width diffuseness of the nuclear surface $b_T$ and the sharp radii $R_{\mathrm{\text{i}}}$ for the excited system. The parameters are fitted to the experimental data for the nuclear temperature in the range $0\le T\le 1$ (MeV). A comparison of half-life indicates that the probability of decay increases with increasing nuclear temperature for the excited system. The comparison of the results with the existing experimental data is motivating.

We use the basis expansion method to solve the Schrödinger equation with the Yukawa potential, which is popular in most areas of physics but which cannot be solved analytically. This method is based on the basic principle in quantum physics that all particle states are represented by the complete set of eigenbases. We use the Coulomb eigenstates as a basis set for a particle state under the Yukawa potential and find the bound energies within more accuracy than ever using matrix representation. We justified the validity of this method in the choice of coupling constant of the Coulomb potential and in the choice of the number of bases included in the numerical calculation. We present the eigenenergies for $n=1\sim 20$ states and compare our results to published ones. We find that the results are relatively precise with relative errors less than 2.2%. Our method is very efficient in a sense that all bound energies and eigenstates are obtained at the same time, which is not tried in other methods. The precision in calculation should be taken at least smaller than the energy difference between states.

The Yukawa potential has an important and significant rule in some branches of physics such as nuclear, plasma and solid state. However, there is no analytical solution for Schrödinger equation with this potential without approximation, therefore, other ways, such as numerical, perturbation, variation and so on, are taken to deal with this potential. In this work, the variation principle is taken to obtain some of its energy eigenvalues. In the arbitrary $l$-state, the Yukawa potentials with centrifugal term are taken together as effective potential and then by choosing the wave functions of the Hulthen potential as trial function which are obtained in this work from the Nikiforov–Uvarov method, and then by applying the variation principle, the energy eigenvalues are obtained. After that, the result is compared with the former numerical result. The comparison shows excellent agreement between our result and the former numerical ones.

In this paper, we investigate the energy spectra, wave functions and the $B(E2)$ transition rates for ${}^{98–112}$Ru atomic nuclei, using the conformable fractional Bohr Hamiltonian model. For the $\beta$-part of the potential, the newly proposed Yukawa plus modified exponential potential is considered and the harmonic oscillator potential in $\gamma$-part, with $\gamma$ fixed around $\frac{\pi }{6}$. By using the conformable fractional Nikiforov–Uvarov method, energy spectra and wave functions are obtained analytically. The sensitivity of the potential parameters and the spectra with respect to the fractional order parameter is investigated. The normalized fractional energies and fractional electric quadrupole transition rates are compared with the available experimental predictions and those from existing theoretical studies. Comparisons are made at different values of the fractional derivative order. The results are presented across a broader range of values of $\alpha$, providing a systematic analysis of how variations in this parameter influence the energy spectra, wave functions, and $B(E2)$ transition rates in Ru nuclei. Overall, the comparison of our results with experimental data shows the good accuracy of our model, especially when the fractional parameter goes to lower values. It can be concluded that the order of fractional derivative plays a crucial role in refining theoretical predictions of electric quadrupole transition rates, especially for transitions involving higher multipolarities.

In this paper, we present a complete solution for the problem of a relativistic particle without spin, of mass M and charge e, subject to linear combination of the Yukawa and Deformed Hulthén Potentials. In particular, we assess the radial Green’s function for the l states by introducing appropriate approximations of the terms (1/r) and (1/(r)). By choosing an appropriate spacetime transformation, the energy spectrum and the normalized wave functions of the bound states are obtained from the poles of Green’s function and its residues.