Yukawa Potential Research Articles

Constraining velocity-dependent self-interacting dark matter with the Milky Way’s dwarf spheroidal galaxies

ABSTRACT The observed anticorrelation between the central dark matter (DM) densities of the bright Milky Way (MW) dwarf spheroidal galaxies (dSphs) and their orbital pericentre distances poses a potential signature of self-interacting dark matter (SIDM). In this work, we investigate this possibility by analysing the range of SIDM scattering cross-section per unit mass, σ/mχ, able to explain such anticorrelation. We simulate the orbital evolution of dSphs subhaloes around the MW assuming an analytical form for the gravitational potential, adopting the proper motions from the Gaia mission and including a consistent characterization of gravitational tidal stripping. The evolution of subhalo density profiles is modelled using the gravothermal fluid formalism, where DM particle collisions induce thermal conduction that depends on σ/mχ. We find that models of dSphs, such as Carina and Fornax, reproduce the observed central DM densities with fixed σ/mχ ranging between 30 and 50 cm2 g−1, whereas other dSphs prefer larger values ranging between 70 and 100 cm2 g−1. These cross-sections correlate with the average collision velocity of DM particles within each subhalo’s core, so that systems modelled with large cross-sections have lower collision velocities. We fit the cross-section–velocity correlation with a SIDM particle model, where a DM particle of mass mχ = 53.93 ± 9.81 GeV interacts under the exchange of a light mediator of mass mϕ = 6.6 ± 0.43 MeV, with the self-interactions being described by a Yukawa potential. The outcome is a cross-section–velocity relation that explains the diverse DM profiles of MW dSph satellites and is consistent with observational constraints on larger scales.

Semi-classical methods, angular momentum, and non-analytic problems

We explore the semi-classical Sommerfeld method of quantization as applied to states with nonzero angular momentum, and show that it leads to qualitatively and quantitatively useful information about systems with spherically symmetric potentials. We begin by reviewing the traditional application of this model to hydrogen, and discuss the way Einstein–Brillouin–Keller (EBK) quantization resolves a mismatch between Sommerfeld states and true quantum mechanical states. We then analyze systems with logarithmic and Yukawa potentials, and compare the results of Sommerfeld and EBK quantization to those from solving Schrödinger’s equation. We show that the semi-classical quantization techniques provide insight into the spread of energy levels associated with a given principle quantum number, as well as giving quantitatively accurate approximations for the energies. We also argue that analyzing systems in this manner involves an interesting application of numerical methods, as well as providing insight into the connections between classical and quantum mechanical physics.

Analytical Bound State Solutions of the Klein-Fock-Gordon Equation for the Sum of Hulthén and Yukawa Potential within SUSY Quantum Mechanics

The relativistic wave equations determine the dynamics of quantum fields in the context of quantum field theory. One of the conventional tools for dealing with the relativistic bound state problem is the Klein-Fock-Gordon equation. In this work, using a developed scheme, we present how to surmount the centrifugal part and solve the modified Klein-Fock-Gordon equation for the linear combination of Hulthén and Yukawa potentials. In particular, we show that the relativistic energy eigenvalues and corresponding radial wave functions are obtained from supersymmetric quantum mechanics by applying the shape invariance concept. Here, both scalar potential conditions, which are whether equal and nonequal to vector potential, are considered in the calculation. The energy levels and corresponding normalized eigenfunctions are represented as a recursion relation regarding the Jacobi polynomials for arbitrary l states. Beyond that, a closed form of the normalization constant of the wave functions is found. Furthermore, we state that the energy eigenvalues are quite sensitive with potential parameters for the quantum states. The nonrelativistic and relativistic results obtained within SUSY QM overlap entirely with the results obtained by ordinary quantum mechanics, and it displays that the mathematical implementation of SUSY quantum mechanics is quite perfect.

A multi-center quadrature scheme for the molecular continuum

A common way to evaluate electronic integrals for polyatomic molecules is to use Becke’s partitioning scheme (Becke and Chem, 1988) in conjunction with overlapping grids centered at each atomic site. The Becke scheme was designed for integrands that fall off rapidly at large distances, such as those approximating bound electronic states. When applied to states in the electronic continuum, however, Becke scheme exhibits slow convergence and it is highly redundant. Here, we present a modified version of Becke scheme that is applicable to functions of the electronic continuum, such as those involved in molecular photoionization and electron–molecule scattering, and which ensures convergence and efficiency comparable to those realized in the calculation of bound states. In this modified scheme, the atomic weights already present in Becke’s partition are smoothly switched off within a range of few bond lengths from their respective nuclei, and complemented by an asymptotically unitary weight. The atomic integrals are evaluated on small spherical grids, centered on each atom, with size commensurate to the support of the corresponding atomic weight. The residual integral of the interstitial and long-range region is evaluated with a central master grid. The accuracy of the method is demonstrated by evaluating integrals involving integrands containing Gaussian Type Orbitals and Yukawa potentials, on the atomic sites, as well as spherical Bessel functions centered on the master grid. These functions are representative of those encountered in realistic electron-scattering and photoionization calculations in polyatomic molecules.

Semiclassical regime for dark matter self-interactions

Many particle physics models for dark matter self-interactions - motivated to address long-standing challenges to the collisionless cold dark matter paradigm - fall within the semi-classical regime, with interaction potentials that are long-range compared to the de Broglie wavelength for dark matter particles. In this work, we present a quantum mechanical derivation and new analytic formulas for the semi-classical momentum transfer and viscosity cross sections for self-interactions mediated by a Yukawa potential. Our results include the leading quantum corrections beyond the classical limit and allow for both distinguishable and identical dark matter particles. Our formulas supersede the well-known formulas for the momentum transfer cross section obtained from the classical scattering problem, which are often used in phenomenological studies of self-interacting dark matter. Together with previous approximation formulas for the cross section in the quantum regime, our new results allow for nearly complete analytic coverage of the parameter space for self-interactions with a Yukawa potential. We also discuss the phenomenological implications of our results and provide a new velocity-averaging procedure for constraining velocity-dependent self-interactions. Our results have been implemented in the newly released code CLASSICS.

Analytical bound state solutions of the Dirac equation with the Hulthén plus a class of Yukawa potential including a Coulomb-like tensor interaction

We examine the bound state solutions of the Dirac equation under the spin and pseudospin symmetries for a new suggested combined potential, Hulthén plus a class of Yukawa potential including a Coulomb-like tensor interaction. An improved scheme is employed to deal with the centrifugal (pseudocentrifugal) term. Using the Nikiforov–Uvarov and SUSYQM methods, we analytically develop the relativistic energy eigenvalues and associated Dirac spinor components of wave functions. We find that both methods give entirely the same results. Modification of our results to fit some particular potentials, which are useful in some other systems, is also discussed. We obtain complete agreement with the findings of previous works. The spin and pseudospin bound state energy spectra for various levels are presented in the absence as well as the presence of tensor coupling. Both energy spectrums are sensitive with regard to the quantum numbers $$\kappa $$ and n, as well as the parameter $$\delta $$ . We also notice that the degeneracies between Dirac spin and pseudospin-doublet eigenstate partners are completely removed by the tensor interaction. Finally, we present the parameter space of allowable bound state regions of potential strength $$V_0$$ with constants $$C_{S}$$ and $$C_{PS}$$ for both symmetry limits.

Approximate solutions of D-dimensional Klein–Gordon equation with Yukawa potential via Nikiforov–Uvarov method

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 $$ c\bar{c} $$ and bottomonium $$ b\bar{b} $$ , 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.

DMRG study of FQHE systems in the open cylinder geometry

The study of the fractional quantum Hall liquid state of two-dimensional electrons requires a non-perturbative treatment of interactions. It is possible to perform exact diagonalizations of the Hamiltonian provided one considers only a small number of electrons in an appropriate geometry. Many insights have been obtained in the past from considering electrons moving on a sphere or on a torus. In the Landau gauge it is also natural to impose periodic boundary conditions in only one direction, the cylinder geometry. The interacting problem now looks formally like a one-dimensional problem that can be attacked by the standard DMRG algorithm. We have studied the efficiency of this algorithm to study the ground state properties of the electron liquid at lowest Landau level filling factor v = 1/3 when the interactions are truncated to the two most important repulsive hard-core components. Use of finite-size DMRG allows us to conclude that the ground state is a compressible two-electron bubble phase in agreement with previous Hartree-Fock calculations. We discuss the treatment of Coulomb interactions in the cylinder geometry. To regularize the long-distance behavior of the Coulomb potential, we compare two methods : using a Yukawa potential or forbidding arbitrary long distances by defining the interelectron distance as the chord distance through the cylinder. This allows us to observe the Wigner crystal state for small filling factor.

Energy spectra and magnetic properties of diatomic molecules in the presence of magnetic and AB fields with the inversely quadratic Yukawa potential

Within the framework of non-relativistic quantum mechanics, the inversely quadratic Yukawa potential is investigated in the presence of external magnetic and Aharonov–Bohm (AB) fields. The Schrodinger equation is solved via the Nikiforov–Uvarov functional analysis (NUFA) method, and the obtained energy eigenvalues are discussed. It is shown that the presence of the magnetic and AB fields removes the degeneracy. The partition function of the system and the thermodynamic properties of the system such as Helmholtz free energy, entropy, internal energy, specific heat and the magnetization and magnetic susceptibility of the system are calculated in detail. The magnetic properties of the QYP in the presence of the magnetic and AB fields are also discussed. The variation of the magnetic field as a function of temperature plays an importance role in understanding of many quantum systems in physics and chemistry

Approximate Bound State Solutions for Certain Molecular Potentials

We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number l and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthen potentials along with their bound state energies are obtained.

New bound-state solutions of the deformed Klein–gordon and Schrödinger equations for arbitrary l-state with the modified equal vector and scalar Manning–Rosen plus a class of Yukawa potentials in RNCQM and NRNCQM symmetries

New bound-state solutions of the deformed Klein–gordon and Schrödinger equations for arbitrary l-state with the modified equal vector and scalar Manning–Rosen plus a class of Yukawa potentials in RNCQM and NRNCQM symmetries

Analytical Investigation of the Single-Particle Energy Spectrum in Magic Nuclei of ⁵⁶Ni and ¹¹⁶Sn

The analytical solutions of the radial D-dimensional Schrödinger equation for the Yukawa potential plus spin-orbit and Coulomb interaction terms are presented within the framework of the Nikiforov-Uvarov method by using the Greene-Aldrich approximation scheme to the centrifugal barrier. The energy eigenvalues obtained are employed to calculate the single-energy spectrum of ⁵⁶Ni and ¹¹⁶Sn for distinct quantum states. We have also obtained corresponding normalized wave functions for the magic nuclei manifested in terms of Jacobi polynomials. However, the energy spectrum without Spin-orbit and Coulomb interaction terms precisely matches the quantum mechanical system of the Yukawa potential field at any arbitrary state.

Analytical Solutions of the Schrödinger Equation with Class of Yukawa Potential for a Quarkonium System Via Series Expansion Method

A class of Yukawa potential is adopted as the quark-antiquark interaction potential for studying the mass spectra of heavy mesons. The potential was made to be temperature-dependent by replacing the screening parameter with Debye mass. We solved the radial Schrödinger equation analytically using the series expansion method and obtained the energy eigenvalues. The present results are applied for calculating the mass spectra of heavy mesons such as charmonium and bottomonium . Two special cases were considered when some of the potential parameters were set to zero, resulting into Hellmann potential, and Coulomb potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.

On plasma neutralization of the ion beam

Simulation of the thermal motion of ions in a spherical bunch was performed on the basis of the molecular dynamics. The Yukawa potential was used to describe the ion interactions. Obtained data showed good agreement with results of theoretical investigation. The conclusion was done that INURA accelerator needs good plasma neutralization in order to keep transverse size of the ion beam.

Evaluation of the bound state energies of some diatomic molecules from the approximate solutions of the Schrodinger equation with Eckart plus inversely quadratic Yukawa potential.

We have obtained analytically the bound state solutions for the non-relativistic Schrodinger equation for the Eckart plus inversely quadratic Yukawa potential (EIQYP) using the parametric Nikiforov-Uvarov (NU) method. In order to validate our approximation, the bound state energies were computed and predicted for some selected diatomic molecules at different adjustable screening parameters from the available spectroscopic model parameters. The fact-finding obtained are in agreement with previously reported results available in literature. Furthermore, the graphs of the effective potential against inter-nuclear distance for low and high values of the screening parameters were reported. From our graphs, we observed that the approximation is best fit for very low values of the screening parameter α ≪ 1.

Study of bottom and charmed baryons in quark-diquark model

In this work, we study the properties of charm- and bottom-flavored baryons in the approximative quark-diquark modelin which the structure of baryons is considered as the bound states of quark-diquark pairs instead of the usual three equivalent quarks. To this aim, we use the Bethe-Salpeter equation including the Yukawa potential between the constituent quarks of baryons. Performing a fit procedure on the baryon masses in their ground state, we first determine the free parameters in the Yukawa potential and then compute the heavy baryons masses and energies in their excited states. We will also compute the magnetic moments of single heavy baryons as well as their semileptonic decay widths by evaluating the Isgur-Wise functions (IWF) for heavy baryons. Our results will be compared with available experimental data and other models so that the consistencies between them ensure the validity of IWF parameters extracted for the transitions of bottom baryons into charmed ones. Relying on the diquark model, we shall also predict the properties of some levels which have not yet observed.

Dynamics of two-dimensional binary dusty plasma in liquid-like state

Using a driven-dissipative Langevin dynamics simulation, the dynamics of two-dimensional binary dusty plasma in the liquid-like state has been investigated. The system consists of charge-asymmetric microparticles with an identical charge-mass ratio. To include the effect of particle size on the dynamics of the system, a modified Yukawa potential with consideration of the particle radius is employed to account for the electrostatic interaction between the charged particles. It is found that the mean squared displacement (MSD) of the system changes little when the ratio of particle radius to interparticle spacing is up to the order of magnitude of one tenth. By analyzing MSD at different time scales, coexistence of the distinct self-diffusion regimes for the two species is observed. The compositions of the two species together with the effective coupling strength of the system are responsible for the motion separation of the two species.

Calculation of information entropies for the 1s2 state of helium‐like ions

AbstractThis 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.

Solution of the Ultra Generalized Exponential–Hyperbolic Potential in Multi-dimensional Space

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 Schrodinger equation for UGEHP have been presented using the parametric Nikiforov–Uvarov method. The approximate analytical bound state energy eigenvalues and the corresponding un-normalized eigenfunctions expressed in terms of hypergeometric functions were obtained. We also investigated the rotational vibrational (RV) partition function from the eigenvalue of UGEHP. By the setting parameters, we obtained eigenvalue spectrum and RV partition function for the screened cosine Kratzer potential, screened Kratzer potential, attractive radial potential, quadratic exponential-type potential, Manning Rosen with class of Yukawa potential and Yukawa potential, class of Yukawa potential, mixed class of Yukawa potential, quantum interaction potential or Hulthen–Yukawa inversely quadratic potential, Hulthen plus inversely quadratic exponential Mie-type potential and Hulthen plus exponential Coulombic potential with centrifugal potential barrier. We studied the behavior of energy eigenvalues and RV partition function for the UGEHP. We computed and tabulated numerical results for $$CO, NO, I_2$$ , HCl and LiH diatomic molecules and compared with numerical results available in literature for same diatomic molecules.

The application bispherical coordinate in Schrödinger equation for Mobius square plus modified Yukawa potential using Nikiforov Uvarov Functional Analysis (NUFA) method

<p class="Abstract">The application bispherical coordinates in Schrödinger equation for the Mobius square plus modified Yukawa potential have been obtained. The Schrödinger equation in bispherical coordinates for the separable Mobius square plus modified Yukawa potential consisting of the radial part and the angular part for the Mobius square plus modified Yukawa potential is solved using the variable separation method to reduce it to the radial part and angular part Schrödinger equation. The aim of this study was to solve the Schrödinger's equation of radial in bispherical coordinates for the Mobius square plus modified Yukawa potential using the Nikiforov Uvarov Functional Analysis (NUFA) method. Nikiforov Uvarov Functional Analysis (NUFA) method used to obtained energy spectrum equation and wave function for the Mobius square plus modified Yukawa potential. The result of energy spectrum equation for Mobius square plus modified Yukawa potential can be shown in Equation (50). The result of un-normalized wave function equation for Mobius square plus modified Yukawa potential can be shown in Table 1.</p>