Relativistic particle scattering

In the presence of competing relativistic formalisms for interacting particle dynamics, a model-independent axiomatic approach is proposed for the study of the following asymptotic aspects of relativistic classical particle dynamics: the definition of the scattering operator, scattering angle and time-delay, and the specification of a general functional interdependence between the objects so defined.     

Relativistic potential scattering

Relativistic potential scattering by a superposition of Yukawa potentials is reexamined. In particular high-energy asymptotic expansions are obtained for the wave-functions and the Regge trajectories. Finally the behaviour of the Regge poles is discussed.     

Relativistic symmetry of position-dependent mass particle in Coulomb field including tensor interaction

The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction under the spin and pseudospin symmetric limit. Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ. Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit in the absence of tensor interaction.     

Relativistic quarks bound with a one-body tensor potential

A dipole fit to electromagnetic form factors is used to determine a quark density in the nucleon. A radial tensor potential is used to bind the quarks into states of goodJ, J _z, and parity. The tensor potential radial component is taken to satisfy the equationT = T ₀, whereT ₀ is a parameter of the model. This linear divergence equation can be simultaneously solved with the Dirac equation for the bound quark wave functions. A self-consistent solution is possible where the mass density used as the source for the binding potential is the same as that determined from the solution for the quark wave functions.     

Relativistic effects on the tensor polarization in electron-deuteron scattering

The tensor analysing power P_e in electron deuteron scattering is calculated including relativistic corrections to the deuteron form factor as determined by Friar and Gross. These effects are found to be quite comparable to the differences between various potentials, and should therefore not be ignored.     

Relativistic symmetries with the trigonometric Poeschl-Teller potential plus Coulomb-like tensor interaction

The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Poeschl-Teller （tPT） potential including a Coulomb-like tensor interaction with arbitrary spin-orbit quantum number κ using an approximation scheme to substitute the centrifugal terms κ（κ± i 1）r^-2. In view of spin and pseudo-spin （p-spin） symmetries, the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method （AIM）. We present numerical results in the absence and presence of tensor coupling A and for various values of spin and p-spin constants and quantum numbers n and κ. The non-relativistic limit is also obtained.     

Relativistic linear response wave functions and dynamic scattering tensor for the ns1/2 states in hydrogenlike atoms

We report a novel closed-form analytic representation for the linear response relativistic wave function of the hydrogenic ns(1/2) level that is exposed to dipole radiation of frequency omega. This result is derived by means of a direct analytical solution of the inhomogeneous omega-dependent Dirac equation. The utility of the formulas obtained is demonstrated by new analytic and numerical calculations of the static and dynamic relativistic dynamic polarizabilities of the lowest hydrogenic ns(1/2) states.     

Exact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass Coulomb potential including a Coulomb-like tensor interaction via asymptotic iteration method

In this Letter, the Dirac equation is exactly solved for spatially-dependent mass Coulomb potential including a Coulomb-like tensor potential under pseudospin symmetry limit by using asymptotic iteration method with arbitrary spin-orbit coupling number κ. The energy eigenvalues and corresponding eigenfunctions are obtained and some numerical results are given.     

Relativistic wave and particle mechanics formulated without classical mass

The fact that the concept of classical mass plays an important role in formulating relativistic theories of waves and particles is well-known. However, recent studies show that Galilean invariant theories of waves and particles can be formulated with the so-called ‘wave mass’, which replaces the classical mass and allows attaining higher accuracy of performing calculations [J.L. Fry and Z.E. Musielak, Ann. Phys. 325 (2010) 1194]. The main purpose of this paper is to generalize these results and formulate fundamental (Poincaré invariant) relativistic theories of waves and particles without the classical mass. In the presented approach, the classical mass is replaced by an invariant frequency that only involves units of time. The invariant frequencies for various elementary particles are deduced from experiments and their relationship to the corresponding classical and wave mass for each particle is described. It is shown that relativistic wave mechanics with the invariant frequency is independent of the Planck constant, and that such theory can attain higher accuracy of performing calculations. The choice of natural units resulting from the developed theories of waves and particles is also discussed.     

Relativistic bounds states for a neutral particle confined to a parabolic potential induced by noninertial effects

We obtain the solutions of the Dirac equation when the noninertial effects of the Fermi-Walker reference frame break the relativistic Landau-Aharonov-Casher quantization, but they provide bound states in an analogous way to a Dirac neutral particle subject to Tan-Inkson quantum dot potential [W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11 (1996) 1635].     

Relativistic symmetries with the trigonometric Pschl-Teller potential plus Coulomb-like tensor interaction

The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Pschl-Teller(tPT) potential including a Coulomb-like tensor interaction with arbitrary spin-orbit quantum number κ using an approximation scheme to substitute the centrifugal terms κ(κ± 1)r-2.In view of spin and pseudo-spin(p-spin) symmetries,the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method(AIM).We present numerical results in the absence and presence of tensor coupling A and for various values of spin and p-spin constants and quantum numbers n and κ.The non-relativistic limit is also obtained.     

Relativistic symmetries in the Rosen-Morse potential and tensor interaction using the Nikiforov-Uvarov method

Approximate analytical bound-state solutions of the Dirac particle in the fields of attractive and repulsive Rosen- Morse (RM) potentials including the Coulomb-like tensor (CLT) potential are obtained for arbitrary spin-orbit quantum number κ. The Pekeris approximation is used to deal with the spin-orbit coupling terms κ(κ± 1)r 2 . In the presence of exact spin and pseudospin (p-spin) symmetries, the energy eigenvalues and the corresponding normalized two-component wave functions are found by using the parametric generalization of the Nikiforov-Uvarov (NU) method. The numerical results show that the CLT interaction removes degeneracies between the spin and p-spin state doublets.     

Relativistic symmetry of position-dependent mass particles in a Coulomb field including tensor interaction

The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials,including a tensor interaction under the spin and pseudospin symmetric limits.Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ.Some numerical results are also given,and the effect of tensor interaction on the bound states is presented.It is shown that tensor interaction removes the degeneracy between two states in the spin doublets.We also investigate the effects of the spatially-dependent mass on the bound states under spin symmetric limit conditions in the absence of tensor interaction.     

Alpha particle scattering to negative parity states of14N

Inelastic⁴He scattering on melamine targets is studied for negative parity excitations of¹⁴N. ElevenΔL=3 excitations are presented, for states up to 15.41 MeV; threeΔL=1 transitions are also studied. A microscopic DWBA calculation accounts for several of the octupole excitations, requiring an isoscalar effective strength about twice that expected for free alpha-nucleon scattering. Great purity of the structure of the three lowest 2^? states is noted, with the 5.11 MeV and 9.13 MeV levels excited byΔL=3, but with the 7.97 MeV state excited purely byΔL=1.     

An energy-independent nonlocal potential model for bound and scattering states

The general expression of the nucleon-nucleus optical potential has been obtained using Watson's multiple scattering theory and Wolfenstein's parametrization of the nucleon-nucleon scattering amplitude. The resulting theoretical potential is nonlocal and consists of an energy-independent central volume plus surface real and imaginary potential and of a Thomas-like spin-orbit term. The analysis has been restricted to N = Z spherical nuclei, so that neither isospin-isospin nor spin-spin interactions have been included. The widely used Perey-Buck, Greenlees, and Watson expressions of the optical potential are easily obtained as particular cases. For practical purposes, the nonlocal potential has been parametrized in the Frahn-Lemmer form, using Woods-Saxon radial form factors, and the equivalent local potential (ELP) has been calculated by a Perey-Buck-like transformation.The ELP has a radial behavior very similar to the original nonlocal one, but the potential depths and radii are energy dependent. The six free parameters in the ELP have been adjusted to fit the available experimental data in the ?70 to + 150 MeV range of interest in nuclear reactions, namely, energies of single hole and single particle states, charge distributions, proton elastic scattering cross sections, and polarizations. The fitted potential depths show an energy dependence in remarkable agreement with the model predictions with a central nonlocality range β ? 1 F and a spin-orbit nonlocality range β₃ ? 0.8 F. The relative importance of surface and volume dependence in the real central potential in also discussed.     

Application of the real Weinberg states in potential scattering

This work is the first step in a systematic application of a resonant scattering theory due to Huby in which the real Weinberg state is the crucial feature. The scattering cross sections ofl=0,1, 2 partial waves in a square well potential are calculated with the aid of the real Weinberg states. Perfect agreement with the exact calculation is obtained. Approximate cross sections resulting from a schematic approximation in the formalism which, apart from other desirable features, display the Breit-Wigner energy factor in the phase shifts, are also found to agree perfectly with the exact calculation. Some simple approximations of the complex and real Weinberg states are investigated, but none is found to be satisfactory forl>0 partial waves in complete contrast to works of previous authors on thel=0 partial wave.     

Relativistic effect of pseudospin symmetry and tensor coupling on the Mie-type potential via Laplace transformation method

A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S（r） and a vector V（r） Mie-type potential in the radial coordinates, as well as a tensor potential U（r） in the form of Coulomb potential. In the pseudospin（p-spin） symmetry setting Σ = Cps and Δ = V（r）, an analytical solution for exact bound states of the corresponding Dirac equation is found. The eigenenergies and normalized wave functions are presented and particular cases are discussed with any arbitrary spin–orbit coupling number κ. Special attention is devoted to the caseΣ = 0 for which p-spin symmetry is exact. The Laplace transform approach（LTA） is used in our calculations. Some numerical results are obtained and compared with those of other methods.