Table of contents

An infinite number of exact bound state solutions and corresponding energy eigenvalues of the one-dimensional Schrödinger equation with symmetric screened Coulomb potential V_a,λ(r) = a/r - a/(r - λ) is computed. The square integrability of the solutions is discussed and correlated to certain properties of the potential. To calculate the bound states and energies on a computer, a suitable program for MATHEMATICA 3.0 is presented.

This work is an extension of S K Bose and N Gupta, Nuovo Cimento113 299 (1998).

The optical emission a from laser produced plasma generated by 1064 nm irradiation of Sn/Pb alloys targets at a flux of 2 · 10¹⁰ W cm^-2 was recorded and analyzed between 200 and 700 nm. The Local Thermodynamic Equilibrium (LTE) conditions and plasma homogeneity have been checked. The analysis of Sn II was checked, with the support of parametric studies of the mixed configurations in both parities, by means of a self-consistent-field method to generate one-electron orbitals. The parametric description of the 5s5p² configuration is improved by taking into account 5s²5d, 5s²6d and 5s²7d mixing effects. Eigenfunctions were used to derive theoretical values of the transition probabilities. Experimental transition probabilities for 36 lines of Sn II arising from the 5s²ns, 5s²np, 5s²nd, 5s²nf, and 5s5p² configurations of Sn II have been determined. Some values have been compared with the available data in the literature and are in a good agreement. The coincidence between several experimental and theoretical transition probabilities obtained in this work is remarked.

Zinc is an element of importance in many research fields within astronomy and astrophysics, from cosmology to stellar atmosphere dynamics. With the aim of improving three decades old measurements of zinc lines of astrophysical interest, emission spectra of Zn I and Zn II have been recorded using a Fourier Transform Spectrometer with a hollow cathode light source. Revised energies for previously known levels are derived from the measurements for Zn I 3d¹⁰4snl and for Zn II 3d¹⁰nl and 3d⁹4s². Isotope shifts are observed in Zn II lines involving the 3d⁹4s² configuration. The accuracy of prominent lines and energy levels are about 0.001–0.003 cm^-1 and 0.002–0.005 cm^-1 respectively.

A detailed calculation in the framework of first Born approximation has been presented for the study of anti-hydrogen formation in antiproton-positronium collisions in presence of a laser field considered classically in the dipole approximation. The projectile-laser field interaction and the dressing of the bound states are considered to first order. The anti-hydrogen formation amplitudes are obtained in closed forms in the A·p gauge, the field direction being parallel to the incident momentum. The differential as well as total cross-sections are presented for no photon (l = 0) and one photon (l = ±1) exchange with field strengths ε₀ = 10⁶ V/cm (0.0002 a.u.) and ε₀ = 10⁷ V/cm (0.002 a.u.) and compared with the corresponding field free results.

General formulas for the spin-angular part of the second-order effective operator for open-shell atoms are derived for LS and jj coupling. To obtain the perturbation theory expansion for a particular problem only a specification of ranks of the atomic interactions involved in the consideration is required. The expressions for matrix elements of one-particle and two-particle operators are derived in second quantization representation when the N-electron wavefunction has the consecutive order of coupling for angular momenta of shells. The matrix element is expressed as a sum of the products of 6-j and/or 9-j symbols and matrix elements of operators acting in the space of states formed from a shell of equivalent electrons. The expression for the matrix element does not contain the summation either over the resultant angular momenta of shells or over the intermediate angular momenta of N-electron wavefunction.

Ab initio theoretical calculations are reported for the electric (E1) dipole allowed and intercombination fine structure transitions in Fe V using the Breit–Pauli R-matrix (BPRM) method. We obtain 3865 bound fine structure levels of Fe V and 1.46 × 10⁶ oscillator strengths, Einstein A-coefficients and line strengths. In addition to the relativistic effects, the intermediate coupling calculations include extensive electron correlation effects that represent the complex configuration interaction (CI). For bound-bound transitions the BPRM method, based on atomic collision theory, entails the computation of the CI wavefunctions of the atomic system as an (electron+target ion) complex. The target ion Fe VI is represented by an eigenfunction expansion of 19 fine structure levels dominated by the spectroscopic configuration 3d³, and a number of correlation configurations. Fe V bound levels are obtained with angular and spin symmetries SLπ and Jπ of the (e + Fe VI) system such that 2S + 1 = 5,3,1, L ≤ 10, J ≤ 8. The bound levels are obtained as solutions of the Breit-Pauli (e + ion) Hamiltonian for each Jπ, and are designated according to the 'collision' channel quantum numbers. A major task has been the identification of these large number of bound fine structure levels in terms of standard spectroscopic designations. A new scheme, based on the analysis of quantum defects and channel wavefunctions, has been developed. The identification scheme aims particularly to determine the completeness of the results in terms of all possible bound levels with n ≤ 10, l ≤ n - 1, for applications to analysis of experimental measurements and plasma modeling. Sample results are presented and the accuracy of the results is discussed. A comparison of the dipole length and velocity oscillator strengths is presented, indicating an uncertainty of 10–20% for most transitions.

The resonance energies and widths for doubly-excited (1s²3d², 3p4f, 3d4d) ¹G^e states of beryllium-like ions are determined by calculating the density of resonance states using the stabilization method. A model potential is used to represent the interaction between the outer electrons and the core electrons. Products of Slater Orbitals are used to represent the two-electron wave functions. We present results for some lower-lying doubly-excited states for Z = 5-10. Comparisons are made with other calculations in the literature.

The spectrum of antimony was recorded in the 300–2040 Å region on a 3-m normal incidence spectrograph. Three odd configurations 5p³, 5s5p5d and 5s5p6s of Sb III were investigated. 34 out of possible 35 levels of these configurations have been established. 114 lines have been classified in this spectrum. The Hartree–Fock calculations with relativistic corrections and parametric levels fitting calculations were carried out to interpret the spectrum satisfactorily.

We found the exact electromagnetic fields of point-like electric and magnetic dipoles and elementary toroidal solenoids moving in a non-dispersive medium. The investigation is performed for different velocities and orientations of these moments relative to their velocities. For motion with a velocity smaller than the light velocity in the medium, the electromagnetic field differs from zero everywhere (even for toroidal solenoids). When the velocity is greater than the light velocity in the medium, the electromagnetic field is confined to the interior and surface of the Cherenkov cone.

The kinematic induction equation of MHD is solved numerically in the case of the normal "111" ABC flow using a general staggered mesh method. Careful 3-D visualizations of the topology of the magnetic field reveal that previous conclusions about the modes of operation of this type of kinematic dynamo must be revised. The two known windows of dynamo action at low and high magnetic Reynolds number, correspond to two distinct modes, both relying crucially on the replenishing of the magnetic field near a discontinuity at the β type stagnation points in the flow. One of these modes display double magnetic structures that were previously found only to obscure the physics of the dynamo: They turn out, however, to play an important part in the process of amplifying the magnetic field. Invariant properties of the mode in the second magnetic Reynolds number window support the case for the normal ABC flow as a fast dynamo.

The electric response field of a small metallic sphere to fluctuating dipolar and quadrupolar momenta is determined from spherical-tensor theory. This allows us to systematically describe the physisorbed atom polarization by introducing the various dipolar and quadrupolar propagators between two points outside the sphere. The non-local character of the electron response inside the sphere is included by using the random-phase approximation and by introducing a Jellium model. Numerical application on the magnitude of the physisorbed atom polarization is presented for typical systems (Xe, Kr, Ar) on (Al, Cu, Ag).

We consider two quantum cosmological models in higher dimension – one has a space with topology Sⁿ⁺¹ and the other a space with topology S¹ × Sⁿ. The classical solutions in the Euclidean region have been discussed and probability measures have been calculated from wave functions in the semi-classical approximation with Hartle–Hawking (H–H) boundary conditions.