Arbitrary Solution of the Schrödinger Equation Interacting with the Superposition of Hulthen with Spin-orbit Plus Adjusted Coulomb Potential Model

In this study, we solve the non-relativistic radial part of the Schrödinger wave equation for the superposition of the Hulthen with spin-orbit plus adjusted Coulomb potential (SHSC) potential using the Nikiforov-Uvarov (NU) method for arbitrary states. The Hulthen with spin-orbit plus adjusted Coulomb (SHSC) potential is the simplest potential field for a nuclear system and has been used to obtain the single particle energy spectrum for both nucleon species orbiting a closed nuclear core. We also obtained in this study the corresponding single particle normalized wave function expressed in terms of the Jacobi polynomial. Besides, we obtained two special cases of the energy spectra for the SHSC potential.

Existence and asymptotics of ground states to the nonlinear Dirac equation with Coulomb potential

In this paper we study the Dirac equation with Coulomb potential − i α · ∇ u + a β u − μ | x | u = f ( x , | u | ) u , x ∈ R 3 where a is a positive constant, μ is a positive parameter, α = ( α 1 , α 2 , α 3 ), α i and β are 4 × 4 Pauli–Dirac matrices. The Dirac operator is unbounded from below and above so the associate energy functional is strongly indefinite. Under some suitable conditions, we prove that the problem possesses a ground state solution which is exponentially decay, and the least energy has continuous dependence about μ. Moreover, we are able to obtain the asymptotic property of ground state solution as μ → 0 + , this result can characterize some relationship of the above problem between μ > 0 and μ = 0.

Erratum to: Magnetic dominance of axion electrodynamics: photon capture effect and anisotropy of Coulomb potential

A Correction to this paper has been published: 10.1140/epjc/s10052-021-09046-3

Bound States in the Continuum (BIC) Protected By Self-Sustained Potential Barriers in a Flat Band System

In this work, we investigate the bound states in the continuum (BIC) of a one-dimensional spin-1 flat band system with a potential of type III, which has a unique non-vanishing matrix element in basis |1⟩. It is found that, for such a kind of potential, there exists an effective attractive potential well surrounded by infinitely high self-sustained barriers. Some bound states in the continuum (BIC) can appear for sufficiently strong potential. These bound states (BIC) are protected by the infinitely high potential barriers, which could not decay into the continuum. Taking a long-ranged Coulomb potential and a short-ranged exponential potential as two examples, the bound state energies are obtained. For a Coulomb potential, there exists a series of critical potential strength, near which the bound state energy can goes to infinite. For a sufficiently strong exponential potential, there exists two different bound states with a same number of wave function nodes. The existences of BIC protected by the self-sustained potential barriers is quite a universal phenomenon in the flat band system under a strong potential. A necessary condition for existence of BIC is that the maximum value of potential is larger than two times band gap.

Nonrelativistic Electron–Ion Bremsstrahlung: An Approximate Formula for All Parameters

The evaluation of the electron–ion bremsstrahlung cross section—exact to all orders in the Coulomb potential—is computationally expensive due to the appearance of hypergeometric functions. Therefore, tabulations are widely used. Here, we provide an approximate formula for the nonrelativistic dipole process valid for all applicable relative velocities and photon energies. Its validity spans from the Born to the classical regime and from soft-photon emission to the kinematic endpoint. The error remains below 3% (and widely below 1%) except at an isolated region of hard-photon emission at the quantum-to-classical crossover. We use the formula to obtain the thermally averaged emission spectrum and cooling function in a Maxwellian plasma and demonstrate that they are accurate to better than 2%.