The Schrodinger and Pauli-Dirac Oscillators in Noncommutative Phase Space

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bound states of the Dirac equation for a class of effective quadratic plus inversely quadratic potentials

The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schrodinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case. (C) 2004 Elsevier B.V. All rights reserved.

A spin Hamiltonian for non-relativistic electrons and their interaction with an external field

We investigate the spin of the electron in a non-relativistic context by using the Galilean covariant Pauli-Dirac equation. From a non-relativistic Lagrangian density, we find an appropriate Dirac-like Hamiltonian in the momentum representation, which includes the spin operator in the Galilean covariant framework. Within this formalism, we show that the total angular momentum appears as a constant of motion. Additionally, we propose a non-minimal coupling that describes the Galilean interaction between an electron and the electromagnetic field. Thereby, we obtain, in a natural way, the Hamiltonian including all the essential interaction terms for the electron in a general vector field.

Electron-impact excitation of Fe2: a comparison of intermediate coupling frame transformation, Breit-Pauli and Dirac R-matrix calculations

Modeling the spectral emission of low-charge iron group ions enables the diagnostic determination of the local physical conditions of many cool plasma environments such as those found in H II regions, planetary nebulae, active galactic nuclei etc. Electron-impact excitation drives the population of the emitting levels and, hence, their emissivities. By carrying-out Breit-Pauli and intermediate coupling frame transformation (ICFT) R-matrix calculations for the electron-impact excitation of Fe$^{2+}$ which both use the exact same atomic structure and the same close-coupling expansion, we demonstrate the validity of the application of the powerful ICFT method to low-charge iron group ions. This is in contradiction to the finding of Bautista et al. [Ap.J.Lett, 718, L189, (2010)] who carried-out ICFT and Dirac R-matrix calculations for the same ion. We discuss possible reasons.

Energy levels and transition probabilities for nitrogen-like Fe xx

Energies of the 700 lowest levels in Fe XX have been obtained using the multiconfiguration Dirac-Fock method. Configuration interaction method on the basis set of transformed radial orbitals with variable parameters taking into account relativistic corrections in the Breit-Pauli approximation was used to crosscheck our presented results. Transition probabilities, oscillator and line strengths are presented for electric dipole (E1), electric quadrupole (E2) and magnetic dipole (M1) transitions among these levels. The total radiative transition probabilities from each level are also provided. Results are compared with data compiled by NIST and with other theoretical work.

Oscillator strengths and transition probabilities for the W xlv ion

In this paper we present oscillator strengths and transition probabilities for W xlv transitions between levels arising from configurations 3d¹⁰4s²,4p²,4d², 3d¹⁰4k4l (k = s,p,d,f and l = p,d,f), 3d⁹4s²4l (l = p,d,f) and 3d⁹4s4p². The model used to calculate these contained all configurations which can be constructed from the available orbitals (up to n = 4), with either a 3d¹⁰ or 3d⁹ core. The calculations were performed with the configuration interaction CIV3 program with the inclusion of relativistic effects achieved through the use of the Breit-Pauli approximation. We compare our ab initio energy levels, oscillator strengths and transition rates with other experimental and theoretical values available in the literature. There is generally good agreement when only levels with 3d¹⁰ cores are considered. The literature is sparse for levels in which the 3d-subshell is opened: for the majority of the fine-structure lines considered, there is either no comparison data available or substantial differences are found. This paper also investigates how the inclusion of relativistic effects can result in a significant redistribution of the oscillator strength from the LS calculations.

Comment on "multiconfiguration Dirac-Fock energy levels and radiative rates for Br-like tungsten" by S. Aggarwal, A.K.S. Jha, and M. Mohan [Can. J. Phys. 91, 394 (2013)]

We report calculations of energy levels and oscillator strengths for transitions in W XL, undertaken with the general-purpose relativistic atomic structure package (GRASP) and flexible atomic code (FAC). Comparisons are made with existing results and the accuracy of the data is assessed. Discrepancies with the most recent results of S. Aggarwal et al. (Can. J. Phys. 91, 394 (2013)) are up to 0.4 Ryd and up to two orders of magnitude for energy levels and oscillator strengths, respectively. Discrepancies for lifetimes are even larger, up to four orders of magnitude for some levels. Our energy levels are estimated to be accurate to better than 0.5% (i.e., 0.2 Ryd), whereas results for oscillator strengths and lifetimes should be accurate to better than 20%.

Position-dependent effective mass Dirac equations with PT-symmetric and non-PT-symmetric potentials

We present a new procedure to construct the one-dimensional non-Hermitian imaginary potential with a real energy spectrum in the context of the position-dependent effective mass Dirac equation with the vector-coupling scheme in 1 + 1 dimensions. In the first example, we consider a case for which the mass distribution combines linear and inversely linear forms, the Dirac problem with a PT-symmetric potential is mapped into the exactly solvable Schrodinger-like equation problem with the isotonic oscillator by using the local scaling of the wavefunction. In the second example, we take a mass distribution with smooth step shape, the Dirac problem with a non-PT-symmetric imaginary potential is mapped into the exactly solvable Schrodinger-like equation problem with the Rosen-Morse potential. The real relativistic energy levels and corresponding wavefunctions for the bound states are obtained in terms of the supersymmetric quantum mechanics approach and the function analysis method.

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator

We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and gamma(5) chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry-related problems have the same spectrum but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector, and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.

Extension of PT-symmetric quantum mechanics to the Dirac theory with position-dependent mass

We present a new method to construct the exactly solvable PT-symmetric potentials within the framework of the position-dependent effective mass Dirac equation with the vector potential coupling scheme in 1 + 1 dimensions. In order to illustrate the procedure, we produce three PT-symmetric potentials as examples, which are PT-symmetric harmonic oscillator-like potential, PT-symmetric potential with the form of a linear potential plus an inversely linear potential, and PT-symmetric kink-like potential, respectively. The real relativistic energy levels and corresponding spinor components for the bound states are obtained by using the basic concepts of the supersymmetric quantum mechanics formalism and function analysis method. (C) 2007 Elsevier B.V. All rights reserved.

Dirac's hole theory versus quantum field theory

Dirac's hole theory and quantum field theory are usually considered equivalent to each other. The equivalence, however, does not necessarily hold, as we discuss in terms of models of a certain type. We further suggest that the equivalence may fail in more general models. This problem is closely related to the validity of the Pauli principle in intermediate states of perturbation theory.

Pauli blocking and medium effects in nucleon knockout reactions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Pseudospin symmetry and the relativistic harmonic oscillator

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U linear in r. Setting either or both combinations Σ=5+V and δ=V-S to zero, analytical solutions for bound states of the corresponding Dirac equations are found. The eigenenergies and wave functions are presented and particular cases are discussed, devoting a special attention to the nonrelativistic limit and the case Σ=0, for which pseudospin symmetry is exact. We also show that the case U=δ=0 is the most natural generalization of the nonrelativistic harmonic oscillator. The radial node structure of the Dirac spinor is studied for several combinations of harmonic-oscillator potentials, and that study allows us to explain why nuclear intruder levels cannot be described in the framework of the relativistic harmonic oscillator in the pseudospin limit.