STUDY OF ELASTIC AND INELASTIC PROCESSES IN ATOMIC SYSTEMS

Abstract

Maximum attention has focused on the studies of electron impact elastic and inelastic processes with atoms, ions as well as molecules in the field of atomic collisions physics. The specific interest in such electron induced fundamental processes have been due to their wide applications in various areas viz. plasma physics, astrophysics, laser physics, fusion research etc. Although to study such processes the experimental measurements as well as the theoretical calculations have started from very early time but the main progress has been achieved in the recent past with the availability of advanced experimental techniques. We can prepare now atomic targets in different selected states and the electron impact collision experiment can be performed with various available efficient detection systems. In fact, projectile electrons in the various spin polarize states can be produced whose collision with lighter and heavier atomic systems with well resolved states have been considered. The sophisticated experimental data have led to advance theoretical calculations to progress and thus accurate theoretical model have come up on the basis of which one can explain the newly reported experimental data. In spite of the advancement in experimental techniques, report on experimental data has been scarce and thus the theoretical studies have dominated the field to meet the demand of the required data of various electron induced processes. A complete quantum mechanical description of an electron atom collision process requires the determination of all the scattering amplitudes for the process. The differential cross section (DCS) and total cross section (TCS) for the process are obtained by taking the squared modulus of complex scattering amplitudes and averaging over the magnetic sub-states. Thus the complete information about the scattering amplitudes is not available. For example, in an electron impact excitation process one can get more information by analyzing the polarization of photons, emitted from the atom after the excitation, in coincidence with the scattered electrons. This is achieved in an experiment called scattered electron-emitted photon coincidence experiment where one measures the polarization of the emitted photon in terms of differential Stokes parameters. If the scattered electrons are iv not observed and only the polarization of the emitted photon is analyzed, such measurements lead to integrated Stokes parameters. By measuring of the Stokes parameters, we have the information about the shape and orientation of the charge cloud of the excited state of the atom (ion). In the present thesis, one of our aims has been to theoretically study the electron impact excitation processes in different heavier atoms and ions where spin-orbit interaction is very important and gives rise to the various fine structure levels. The studies of such processes require fully relativistic treatment where the projectile and target electrons are described through Dirac equations. We have considered a number of excitations which are important and having applications to plasma modeling in the frame work of relativistic distorted wave theory. We have focused on those transitions for which either new experimental results have been recently reported or earlier theoretical calculations did not exist. In addition, we have also considered the elastic scattering from atoms and molecules using suitable optical model potential method and explored the suitability of such method. Since the scattering amplitude cannot be evaluated exactly, different approximation methods have been adopted to study electron-atom collisions. The available methods for electron-atom collisions can be broadly divided into two categories i.e., non-perturbative and perturbative approaches. Among the non-perturbative approaches, the convergent close coupling (CCC), R-matrix and variational methods have been successful in their non-relativistic form in the recent past. Such methods have been found suitable and extensively used in the low incident electron energy region. In the high energy region more channels open up requiring heavy computational efforts which makes the calculation impractical. Though, there have been recent efforts to develop techniques to extend the low energy methods to intermediate energy region as well as to incorporate the relativistic effects. Among the perturbative approaches, distorted wave theory has been found very successful at intermediate as well as higher incident electron energies in predicting the experimentally measured various scattering parameters. As compared to non-perturbative approaches the distorted wave method is relatively less expensive and has been used in its v non-relativistic and relativistic forms. However, in the present work the fully relativistic distorted wave approximation theory is used to describe accurately the electron scattering from heavy atoms and ions where electron spin-orbit interaction is relatively large for both the projectile and target electrons. The relativistic effects can be included ideally through the use of the Dirac equations for describing both the atomic and continuum electrons involved in the collision process. In this way electron spin is automatically incorporated in a natural way. For studying elastic electron-atom and electron-molecule scattering, optical model potential approach has been found very successful and still being widely used recently. However, elastic scattering of electron from heavier atoms should be studied using relativistic approach where the optical model potential is used and the scattering is described through Dirac equations. Further, the electron elastic scattering from molecules using optical model potential is complicated by the fact that molecules are a multi-centered target with the nuclei of the constituent atoms being a center of charge. Thus one of the most important parts of a scattering calculation is to obtain the static potential which represents the interaction of the incident electron with the unperturbed charge distribution of the molecule. Calculating this potential is a difficult challenge if multi-center wave functions are used for the target. A method is developed to address this problem. In the light of above mentioned aims the whole work carried out in the present thesis has been described through 1-7 Chapters systematically. These are outline below. Chapter –1 gives an introduction on the subject of the work presented in the thesis. It describes various recent theoretical models available to study the electron–atom/ion and electron-molecule collision processes. A general description of the relativistic distorted wave theory as applied to electron-atom/ion collision is introduced which has been utilized in detail in the present thesis. Chapter–2 describes relativistic distorted wave calculations carried out to study the electron-impact excitation of Zn and Yb atoms from their ground 1S0 state which have outer shell configurations 3d104s2 and 4f 146s2, respectively. Excitations to the excited singlet P vi states viz. (4s4p, 4s5p) 1P1 in Zn and (6s6p, 6s7p) 1P1 in Yb along with the (6s5d) 1D2 state in Yb have been considered. Differential and integrated cross section results have been obtained and compared with recent experimental results and theoretical convergent close coupling calculations. Using the same theory, electron impact excitation of cadmium atom from its first excited metastable states have also been considered in view of new experiment results reported and no previous calculations are available. Theoretical results of Stokes parameters and electron-impact coherence parameters for excitation of 41P1 state of zinc atoms are presented in the light of recent measurement from the group of Toruń in Poland. The electron-photon coincidence method in the coherence-analysis version was applied to obtain data for scattering angles in the range from 50 to 400 for incident electron energy 100 eV. Our relativistic distorted wave calculations are presented together with experimental results and convergent close coupling calculation. In Chapter–3, relativistic distorted-wave calculations are carried out for the electron impact excitation of the (6s) 2S1/2 state in indium from the ground (5p) 2P1/2 state. Differential cross sections are obtained at incident electron energies of 10, 20, 40, 60, 80 and 100 eV and scattering angles up to 100. The results are compared with recently reported experimental data from the Belgrade group. This comparison suggests that the relative measurements at the smallest scattering angles are too low resulting in an incorrect normalization. Chapter–4 presents a detailed study using fully relativistic distorted wave theory for electron impact excitation of Zn-like through Co-like tungsten ions in a wide range of incident electron energies up to 50 keV. Electron impact excitations, viz., 3d–4p and 3d–nf (n = 4–8) transitions from the M-shell of the ground state in the Zn-like W44+, Cu-like W45+, Ni-like W46+ and Co-like W47+ ions have been considered. These transitions have been identified to be among the most intense lines in the M-shell x-ray spectra of Zn-like through Co-like W ions by the group of Lund in Sweden. Excitation cross sections have been reported for the dipole allowed transitions in all the four ions along with the linear polarization of the photon emissions due to the decay of the excited anisotropic states to the ground states for all the four ions. The analytic fits to the calculated cross sections for plasma application purposes have been provided. vii In Chapter–5, elastic scattering of electron from the ground and excited states of barium have been studied using relativistic optical-model potential approach. Results for the differential cross sections are obtained for the scattering from the ground and excited states of the barium atom in the range of 5-100 eV incident electron energy. The ground state results are compared with the available experimental and other theoretical results. From the Manitoba group in Canada relative differential cross section results are reported for elastic electron scattering from the laser-excited (6s6p) 1P1 and cascade-populated (6s5d) 1,3D1,2 levels of barium at 5, 10, and 20 eV impact energy. Comparisons of our calculated absolute and relative differential cross section results with the measurements are presented along with the CCC and relativistic CCC calculations. Chapter–6 presents a method for calculating the static potential of an arbitrary spherically-symmetrized molecule which is represented by the well-known Gaussian wavefunctions. This potential is given in analytic form which, in additions to elementary functions, contains the error function for which simple and accurate methods for its evaluation exist. We have used this potential, along with polarization-correlation and exchange potentials, to calculate the differential cross sections for the scattering of electrons from the water molecule in the energy range 30-100eV. Comparison with previous calculations and experimental measurements show that this method produces accurate results for the differential scattering cross sections. Finally, the Chapter–7 gives the summary of the whole work presented in the thesis along with some concluding remarks.