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Control of thermal transport in colloidal crystals plays an important role in modern technologies. A deeper understanding of the governing heat transport processes in various systems, such as polydisperse colloidal crystals, is required. This study shows how strongly the particle size polydispersity of a model colloidal crystal influences the thermal conductivity. The thermal conductivity of model colloidal crystals has been calculated using molecular dynamics simulations. The model crystals created by particles interacting through Yukawa (screened-Coulomb) interaction are assumed to have a face-centered cubic structure. The influence of the Debye screening length, contact potential, and particle size polydispersity on the thermal conductivity of Yukawa crystals was investigated. It was found that an increase in particle size polydispersity causes a strong—almost fivefold—decrease in the thermal conductivity of Yukawa crystals. In addition, the obtained results showed that the effect of the particle size polydispersity on reducing the thermal conductivity of Yukawa crystals is stronger than changes in values of the Debye screening length or the contact potential. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the energy spectra, wave functions and the B(E2) transition rates for 98–112Ru atomic nuclei, using the conformable fractional Bohr Hamiltonian model. For the β-part of the potential, the newly proposed Yukawa plus modified exponential potential is considered and the harmonic oscillator potential in γ-part, with γ fixed around π6. 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 α, 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. [ABSTRACT FROM AUTHOR]

The approximate bound state solutions of Schrödinger equation with linear combination of a four-parameter diatomic potential plus inversely quadratic Yukawa potential were obtained with the help of appropriate approximation to evaluate the centrifugal term. The Feynman path integral approach was used to obtain the analytical solutions. The energy spectrum and the normalized wave functions of the bound states are derived from the poles of the Green’s function and its residues. Particular cases of these potentials are also discussed briey and it is found that obtained results are in good agreement with those obtained in the literature. [ABSTRACT FROM AUTHOR]

Control of thermal transport in colloidal crystals plays an important role in modern technologies. A deeper understanding of the governing heat transport processes in various systems, such as polydisperse colloidal crystals, is required. This study shows how strongly the particle size polydispersity of a model colloidal crystal influences the thermal conductivity. The thermal conductivity of model colloidal crystals has been calculated using molecular dynamics simulations. The model crystals created by particles interacting through Yukawa (screened-Coulomb) interaction are assumed to have a face-centered cubic structure. The influence of the Debye screening length, contact potential, and particle size polydispersity on the thermal conductivity of Yukawa crystals was investigated. It was found that an increase in particle size polydispersity causes a strong—almost fivefold—decrease in the thermal conductivity of Yukawa crystals. In addition, the obtained results showed that the effect of the particle size polydispersity on reducing the thermal conductivity of Yukawa crystals is stronger than changes in values of the Debye screening length or the contact potential.

‎In this paper‎, ‎we present an exact analytical solution for five interacting quarks‎. ‎We solve the Schr\"{o}dinger equation for pentaquarks in the framework of five-body and two-body problems‎. ‎For this purpose‎, ‎we utilize Yukawa potential in Jacobi coordinates‎. ‎Also finding the relation between the reduced masses and coupling constants of pentaquarks‎, ‎we obtain the coupling constant of Yukawa potential for pentaquark systems‎. ‎We calculate the energy of these systems in their ground state‎. ‎The results are well consistent with the theoretical results‎. ‎Our procedure to obtain these results is appropriate for other potentials and $n$-body systems‎.

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We consider Cauchy problem of Hartree-type nonlinear Dirac equation with potentials given by Vb(x) = ... (b ≤ 0). In previous works regarding a global well-posedness of Dirac equation with these potentials, a standard argument is to utilize null form estimates in order to prove global well-posedness for Hs-data, s > 0. However, the null structure inside the equations is not enough to attain critical regularity. We impose an extra regularity assumption with respect to the angular variable. First, we prove the global well-posedness and scattering of Dirac equations with Hartree-type nonlinearity for b > 0 for small L²x-data with additional angular regularity. We also show that only a small amount of angular regularity is required to obtain the global existence of solutions. Second, we obtain nonscattering result for a certain class of solutions with the Coulomb potential V0(x). [ABSTRACT FROM AUTHOR]

In this manuscript, we review the motion of a two-body celestial system (planet–sun) for a Yukawa-type correction on Newton's gravitational potential using Hamilton's formulation. We reexamine the stability using the corresponding linearization Jacobian matrix, and verify that the conditions of Bertrand's theorem are met for radii ≪ 10 15 m, meaning that bound closed orbits are expected. Applied to the solar system, we present the equation of motion of the planet, then solve it both analytically and numerically. Making use of the analytical expression of the orbit, we estimate the Yukawa strength α and find it to be larger than the nominal value ( 10 − 8 ) adopted in previous studies, in that it is of order ( α = 10 − 4 − 10 − 5 ) for the terrestrial planets (Mercury, Venus, earth, Mars, and Pluto) and even larger ( α = 10 − 3 ) for the giant planets (Jupiter, Saturn, Uranus, and Neptune). Taking the inputs ( r m i n , v m a s , e ) observed by NASA, we analyse the orbits analytically and numerically for both the estimated and nominal values of α and determine the corresponding trajectories. For each obtained orbit, we recalculate the characterizing parameters ( r m i n , r m a x , a , b , e ) and compare their values according to the potential (Newton with/without Yukawa correction) and method (analytical and/or numerical) used. When compared to the observational data, we conclude that the path correction due to Yukawa correction is on the order of up to 80 million km (20 million km) as the maximum deviation occurring for Neptune (Pluto) for a nominal (estimated) value of α. [ABSTRACT FROM AUTHOR]

The MICROSCOPE experiment was designed to test the weak equivalence principle in space, by comparing the low-frequency dynamics of cylindrical ‘free-falling’ test masses controlled by electrostatic forces. We use data taken during technical sessions aimed at estimating the electrostatic stiffness of MICROSCOPE’s sensors to constrain a short-range Yukawa deviation from Newtonian gravity. We take advantage of the fact that in the limit of small displacements, the gravitational interaction (both Newtonian and Yukawa-like) between nested cylinders is linear, and thus simply characterised by a stiffness. By measuring the total stiffness of the forces acting on a test mass as it moves, and comparing it with the theoretical electrostatic stiffness (expected to dominate), it is a priori possible to infer constraints on the Yukawa potential parameters. However, we find that measurement uncertainties are dominated by the gold wires used to control the electric charge of the test masses, though their related stiffness is indeed smaller than the expected electrostatic stiffness. Moreover, we find a non-zero unaccounted for stiffness that depends on the instrument’s electric configuration, hinting at the presence of patch-field effects. Added to significant uncertainties on the electrostatic model, they only allow for poor constraints on the Yukawa potential. This is not surprising, as MICROSCOPE was not designed for this measurement, but this analysis is the first step to new experimental searches for non-Newtonian gravity in space. [ABSTRACT FROM AUTHOR]

The nonsequential double ionization of the argon atom is studied in this article using an orthogonal two-color laser pulse with different intensities. The results demonstrate that electron correlation is strongly dependent on the relative phase of the laser pulses. We also observe that the recollision time remains constant when analyzing the nonsequential double ionization signal at the relative phase 0:6π. Meanwhile, the contribution of each returning bunch of the first ionized electron and the final electron-electron repulsion highly depends on the laser intensity. Coulomb repulsion is most pronounced at low and high laser intensities. However, at moderate laser intensities, it does not sufficiently affect the momentum distribution. [ABSTRACT FROM AUTHOR]

Yukawa potential has garnered remarkable attention since its proposition. It is applied in condensed matter physics, plasma physics, high energy physics and related areas. Based on this widespread applicability, this study focused on the analysis of the effects of topological defect on the thermal and magnetic properties of this system. Non-relativistic treatment of this potential in the presence of magnetic fields and Aharonov–Bohm is performed using the functional analytical approach (FAA). The energy equation and the wavefunction are analytically derived. The accessible energy levels are summed up to obtain to get the partition function that is used to derive the expressions for the thermo-magnetic properties of the Yukawa potential. These properties are analysed in detail by means of graphical representations. It is observed that in the various settings of the analysis, the system has a diamagnetic characteristic and the behaviour of the heat capacity is in accordance with the recognized law of Dulong–Petit, although some anomalies are observed. This irregular behaviour could be attributed to Schottky anomaly. The results of our research will be helpful in many fields of physics: condensed matter physics, high energy physics, etc.

• A two-Yukawa potential is fitted to the repulsive part of the Buckingham potential. • The two-Yukawa analytic Ross perturbation theory with correcting terms is applied to the N 2 fluid. • The pressure is in good agreement with numerical simulations and experimental results. In this Short Communication an efficient procedure to fit closely the repulsive part of a given spherical intermolecular potential ϕ(r) with a two-Yukawa function is introduced and applied to the general Buckingham Exp(α , m) fluid. The method consists first in imposing the same minima and then equating the values of both potentials deep into the positive repulsive branch at a suitable distance. The recently developed Ross analytic (RA) variation perturbation theory for two-Yukawa (TY) fluids with correction terms (RAC theory) to account for the remaining discrepancies between both potentials is then applied to the analytic determination of the nitrogen N 2 pressure at high temperatures and high densities from its known Buckingham intermolecular potential Exp(α = 12.684, m = 6). The results compare favourably with experimental results and recent extensive molecular dynamic (MD) simulation data. [ABSTRACT FROM AUTHOR]

An inverse patchy colloid (IPC) refers to a particle having patches that are mutually repulsive while the bare particle–patch interactions are attractive. We model a system of charged IPCs with a single patch using Debye-Hückel theory. We derive the full analytical expression for the effective interaction energy for a pair of IPCs as a function of inter-particle separation and particle orientations. The model is applicable for various patch coverage, ionic strengths and dielectric permittivity of the medium. Approximate solutions are derived under high screening limit and the results are compared with the full solution. The model can be used in molecular simulations such as Monte Carlo simulations to accurately describe the interaction between a pair of IPCs for a given experimental conditions. [ABSTRACT FROM AUTHOR]

In this work, we obtain the Klein–Gordon equation solutions for the Yukawa potential using the Nikiforov–Uvarov method. The energy eigenvalues are obtained both in relativistic and non-relativistic regime. The corresponding eigenfunction are obtained in terms of Laguerre polynomial. We applied the present results to calculate heavy-meson masses of charmonium c c ¯ and bottomonium b b ¯ , and we got the numerical values for states 1S–1F. The results are in good agreement with experimental data and the work of other researchers. [ABSTRACT FROM AUTHOR]

In this manuscript, we review the motion of a two-body celestial system (planet–sun) for a Yukawa-type correction on Newton’s gravitational potential using Hamilton’s formulation. We reexamine the stability using the corresponding linearization Jacobian matrix, and verify that the conditions of Bertrand’s theorem are met for radii ≪1015 m, meaning that bound closed orbits are expected. Applied to the solar system, we present the equation of motion of the planet, then solve it both analytically and numerically. Making use of the analytical expression of the orbit, we estimate the Yukawa strength α and find it to be larger than the nominal value (10−8) adopted in previous studies, in that it is of order (α=10−4−10−5) for the terrestrial planets (Mercury, Venus, earth, Mars, and Pluto) and even larger (α=10−3) for the giant planets (Jupiter, Saturn, Uranus, and Neptune). Taking the inputs (rmin,vmas,e) observed by NASA, we analyse the orbits analytically and numerically for both the estimated and nominal values of α and determine the corresponding trajectories. For each obtained orbit, we recalculate the characterizing parameters (rmin,rmax,a,b,e) and compare their values according to the potential (Newton with/without Yukawa correction) and method (analytical and/or numerical) used. When compared to the observational data, we conclude that the path correction due to Yukawa correction is on the order of up to 80 million km (20 million km) as the maximum deviation occurring for Neptune (Pluto) for a nominal (estimated) value of α.

The probability density of the Yukawa particle at the origin plays significant roles in fundamental physical quantities such as the darkonium production cross sections and matter-anti-matter annihilation rates. Inspired by the recent work of Napsuciale and Rodríguez (2021) [12,13] where the authors proposed a complete analytical solution of the Yukawa problem at small screening parameters to analyze the bound state eigenenergies and probability densities at the origin, we perform in this work high-precision numerical calculation of these quantities by employing the generalized pseudospectral method. The variational method based on one-, two-, and three-parameter trial wave functions is also developed to provide an alternative analytical solution to the Yukawa problem. It is shown that these trial functions manifest simple implementation and high accuracy in the entire range of screening parameters.

Dust particles in magnetized plasma have generated considerable interest in the semiconductor industry, plasma crystals, Tokamaks, cosmological events, and so on. Upon introducing dust particles in dc glow discharge plasma, they get charged, and hence, a potential is developed surrounding the same. Coulomb potential or Yukawa potential is taken for the interaction of charged dust particles. The effect of magnetic field along the axis of the chamber and, subsequently, scattering cross section of charged dust particles due to the interaction of magnetic fields have been studied critically in this report. A generalized mathematical model is implemented, to find the scattering cross section of charged dust particles. The scattering parameter is introduced to reduce the complexity involved in the derivation of integral equations. Furthermore, to validate the mathematical model, the simulation of DC glow discharge plasma in COMSOL Multiphysics has been carried out. A rectangle chamber with charged dust particles is introduced and with varying magnetic fields, and the transport of dust particles is recorded. The scattering cross section of dust particles is determined from the velocity profile of dust particles and it has been observed that the scattering cross section decreases with the increase of the magnetic field. [ABSTRACT FROM AUTHOR]

Infinite families of new exact solutions to the Beltrami equation with a non-constant are derived. Differential operators connecting the steady axisymmetric Klein – Gordon equation and a special case of the Grad – Shafranov equation are constructed. A Lie semi-group of nonlinear transformations of the Grad – Shafranov equation is found. [ABSTRACT FROM AUTHOR]

We have studied the bound-state solutions of the spin and pseudospin limits of the Dirac equation with the generalised Morse potential and a class of Yukawa potential using the Nikiforov–Uvarov method and an appropriate approximation scheme. The energy eigenvalues and the corresponding normalised eigenfunction of the non-relativistic limits of the spin symmetry was obtained. By adjusting some potential parameters, six special potentials, namely, the generalised Morse, a class of Yukawa, Hellmann, inversely quadratic Yukawa, Hulthen and Coulomb potentials to which the generalised Morse potential plus a class of Yukawa potential ( GMP + CYP ) reduces to, were evaluated. The deduced corresponding energies of these special potentials were found to be in excellent agreement with those in the existing literature. We also studied and compared the energy spectra of the GMP + CYP with those of the special potentials with respect to internuclear distance. Moreover, we investigated and compared the behaviour of some selected diatomic molecules, when subjected to the ( GMP + CYP ) potential. Finally, the expectation values of some useful physical observables were deduced using the Hellmann–Feynman theorem. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The quasi-exact Bethe ansatz method has been examined for solving the radial Schrödinger equation with the Yukawa potential as an important central interaction for computing bound states of neutral atoms. The method, in spite of its simplicity with respect to other methods, leads to the ground state and low excited states of the radial Schrödinger equation with a good accuracy. It is found that the results are generally in agreement with the results of others and, therefore, this method can be used for solving the Schrödinger equation instead of other numerical and analytical methods. It was also found that the energy eigenvalues reach that of the Coulomb potential in the limit of zero screening parameter. The method has been briefly generalized to arbitrary dimension for the Yukawa potential inspiring the 3-dimensional trail wave function. [ABSTRACT FROM AUTHOR]

Recent astrophysical observations hint toward the need for an extended theory of gravity to explain puzzles presented by the standard cosmological model such as the need for dark matter and dark energy to understand the dynamics of the cosmos. This paper investigates the effect of a repulsive central universal force field on the behavior of celestial objects. Negative tidal effect on the solar and galactic orbits, like that experienced by Pioneer spacecrafts, was derived from the central force and was shown to manifest itself as dark matter and dark energy. Vertical oscillation of the sun about the galactic plane was modeled as simple harmonic motion driven by the repulsive force. The proposed universal field was used to infer the shape of dark matter halos as generated from a planar component of the universal force and to explain galactic warp, galactic halo density, and galactic rotation curves. It was found that the repulsive field addition to Newton’s gravity mimics the Yukawa potential correction employed by many current gravitational theories that modify gravity.

We present a complete analytical solution to the quantum problem of a particle in the Yukawa potential, using supersymmetry and a systematic expansion of the corresponding super-potentials. Results for the critical screening of the ground state improve in several figures existing results based on both numerical solutions and approximation methods. Our calculation to order (a0/D)2 for the squared ground state wavefunction at the origin, which enter in darkonium transitions, yields a correction of π4/216 to results based on variational techniques.

This work presents analytical and numerical results for the position‐ and momentum‐space information entropies of the 1s2 state of helium‐like ions using different interaction potentials. The potentials that we used are the Yukawa potential and the exponential‐cosine‐screened Coulomb potential. The investigated studies allow us to relate the position‐space information with the momentum‐space information of Shannon and Fisher, as well as Shannon entropy power and the Fisher‐Shannon information product, through different famous relations. The calculation is performed using the one‐electron charge density of entangled two‐parameter wavefunction. On one hand, the results that are presented for 10 members in the helium isoelectronic sequence demonstrate with precision the effect of correlation on bare charge distributions. On the other hand, it leads to some very important results for both the correlated and uncorrelated values of the informatic entropies. Analytical formulas for the momentum‐space information entropies are given. The effect of the nuclear charge and the screening parameter on the information expressions has been studied for both potentials. Detailed computational and numerical values and characteristics of these information quantities, as a function of the screening parameter, are reported here for the first time. New inequality has been proposed with Fisher's total value to measure the correlation of two electrons. [ABSTRACT FROM AUTHOR]

Abstract In this work we propose an alternative semiclassical iterative approach to obtain the Yukawa Potential, where the temporal evolution is replaced by the number of iterations. In addition, our analytical approach was able to provide an exact value very close to the adopted semi-empirically for the Yukawa magnitude scale constant.

We consider kinetic energy functionals that depend, beside the usual semilocal quantities (density, gradient, Laplacian of the density), on a generalized Yukawa potential, that is the screened Coulomb potential of the density raised to some power. These functionals, named Yukawa generalized gradient approximations (yGGA), are potentially efficient real-space semilocal methods that include significant non-local effects and can describe different important exact properties of the kinetic energy. In this work, we focus in particular on the linear response behavior for the homogeneous electron gas (HEG). We show that such functionals are able to reproduce the exact Lindhard function behavior with a very good accuracy, outperforming all other semilocal kinetic functionals. These theoretical advances allow us to perform a detailed analysis of a special class of yGGAs, namely the linear yGGA functionals. Thus, we show how the present approach can generalize the yGGA functionals improving the HEG linear behavior and leading to an extended formula for the kinetic functional. Moreover, testing on several jellium cluster model systems allows highlighting advantages and limitations of the linear yGGA functionals and future perspectives for the development of yGGA kinetic functionals.

Integral equation–based numerical methods are directly applicable to homogeneous elliptic PDEs and offer the ability to solve these with high accuracy and speed on complex domains. In this paper, such a method is extended to the heat equation with inhomogeneous source terms. First, the heat equation is discretised in time, then in each time step we solve a sequence of so-called modified Helmholtz equations with a parameter depending on the time step size. The modified Helmholtz equation is then split into two: a homogeneous part solved with a boundary integral method and a particular part, where the solution is obtained by evaluating a volume potential over the inhomogeneous source term over a simple domain. In this work, we introduce two components which are critical for the success of this approach: a method to efficiently compute a high-regularity extension of a function outside the domain where it is defined, and a special quadrature method to accurately evaluate singular and nearly singular integrals in the integral formulation of the modified Helmholtz equation for all time step sizes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper we study pattern formation for a physical local/nonlocal interaction functional where the local attractive term is given by the 1-perimeter and the nonlocal repulsive term is the Yukawa (or screened Coulomb) potential. This model is physically interesting as it is the Γ-limit of a double Yukawa model used to explain and simulate pattern formation in colloidal systems. Following a strategy introduced in [S. Daneri and E. Runa, Arch. Ration. Mech. Anal., 231 (2019), pp. 519-589] we prove that in a suitable regime minimizers are periodic stripes in any space dimension. [ABSTRACT FROM AUTHOR]

Generalized one‐particle propagator calculations were performed for fermions in atoms: neutrons, protons, and electrons. For this purpose, multicomponent Hartree‐Fock equations were implemented using Gaussian basis sets where, for nucleons, we consider a non‐Coulombic interaction, through a two‐term Yukawa scalar potential and the interaction between electrons and the electrons with positive charge (protons) through a Coulombic potential. The strategy for evaluating the required interaction integrals follows Obara‐Saika and Head‐Gordon recurrence relations combined with the generalized Boys function suggested by Ten‐no. Calculations on the isotopes 2H, 3H, 3He, 4He, 6Li, 6Be, 7Li, and 8Be were realized to test the accuracy of Koopmans' approximation and a second‐order generalized one‐particle propagator. Yukawa potentials were parametrized to reproduce nuclear properties as kinetic energies and radial distributions of density. These potentials produced the reference nuclear Hartree‐Fock calculations on which fully ab initio propagator calculations were performed for these non‐Coulombic potentials. This allowed us to explore the electronic structure of isotopes in an extended nucleus context. [ABSTRACT FROM AUTHOR]

We explore the dynamics and stability of the two-body problem by modifying the Newtonian potential with the Yukawa potential. This model may be considered a theory of modified gravity; where the interaction is not simply the Kepler solution for large distance. We investigate stability by deriving the Jacobian of the linearized matrix equation and evaluating the eigenvalues of the various equilibrium points calculated during the analysis. The subcases of a purely Yukawa and purely Newtonian potential are also explored. [ABSTRACT FROM AUTHOR]

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 ∼ 1 5 0 μ m sphere attached to a (5 0 0 μ m) 2 micro-mechanical oscillator and a planar source mass. By replacing the spherical surface with a fraction of a 5 0 0 μ m long cylinder with R ∼ 1 5 0 μ 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 2 0 μ 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. [ABSTRACT FROM AUTHOR]

This paper considers the Schrödinger–Newton (SN) equation with a Yukawa potential, introducing the effect of locality. We also include the interaction of the self-gravitating quantum matter with a radiation background, describing the effects due to the environment. Matter and radiation are coupled by photon scattering processes and radiation pressure. We apply this extended SN model to the study of Jeans instability and gravitational collapse. We show that the instability thresholds and growth rates are modified by the presence of an environment. The Yukawa scale length is more relevant for large-scale density perturbations, while the quantum effects become more relevant at small scales. Furthermore, coupling with the radiation environment modifies the character of the instability and leads to the appearance of two distinct instability regimes: one, where both matter and radiation collapse together, and others where regions of larger radiation intensity coincide with regions of lower matter density. This could explain the formation of radiation bubbles and voids of matter. The present work extends the SN model in new directions and could be relevant to astrophysical and cosmological phenomena, as well as to laboratory experiments simulating quantum gravity.

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 ∼ 2 0 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. [ABSTRACT FROM AUTHOR]

• Present the quasi-exactly solutions to the KG with the combination of Hulthén and Yukawa potentials. • New scheme to approximation of Yukawa potential. • NU approach to study this quantum system. • Consider two cases, equal and non-equal scalar and vector potentials. Based on a developed scheme we show how to deal with the centrifugal term and the Coulombic behavior part and then to solve the Klein-Gordon (KG) equation for the linear combination of Hulthén and Yukawa potentials. Two cases, i.e., the scalar potential which is equal and unequal to vector potential, are considered for arbitrary l state. With the aid of the Nikiforov-Uvarov (NU) method and the traditional approach, we present the eigenvalues and the corresponding radial wave functions expressed by the Jacobi polynomials or hypergeometric functions and find that the results obtained by them are consistent. For given values of potential parameters V 0 , V 0 ′ , S 0 , S 0 ′ and M = 1 , we notice that the energy levels E are sensitively relevant for the potential parameter δ and the energy levels E increase for δ > 0.1 as quantum numbers n r and l increase. However, for δ ∈ (0 , 0.1) the energy levels E do not always increase with the quantum numbers n r and l. We find that the energy levels E are inversely proportional to quantum numbers n r and l when δ ∈ (0 , 0.05). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We combine the Statistical Associating Fluid Theory for Potentials of Variable Range (SAFT-VR) and the Mean Spherical Approximation (MSA) to develop an equation of state to model asphaltene precipitation in petroleum fluids including the measured asphaltene onset pressures (AOP's) of a reservoir live oil. In this model, dispersive solvent–solvent and asphaltene–solvent interactions in reservoir fluid mixtures are represented by Yukawa potentials. The approach is based in the modeling of polar and ionic interactions via Yukawa potentials, as originally proposed by the Generalized Mean Spherical Approximation Theory, and also in recent studies in molecular simulation of charged fluids using non-Ewald effective pair interactions, as in the Wolf method. [ABSTRACT FROM AUTHOR]