STUDY OF COLLISIONAL PROCESSES IN ATOMIC SYSTEMS

Abstract

Considerable attention has focused during the last many years in studying elastic and inelastic scattering of electrons from atoms, ions, molecules and various structures of materials. Studies of such electron induced processes are not only of fundamental importance to understand the basic nature of interaction involved with the different atomic systems but these have numerous applications in various branches of science and technology. The electron impact collision studies on atoms and ions have received a greater attention in the recent years because of the continuous growing demands of the reliable electron impact cross section data for the various fine structure transitions in plasma modeling and diagnostic, spectral analysis of various laboratory and astrophysical plasmas, laser physics and many more applications. The available experimental measurements are limited and often unresolved for the transitions, which are closely spaced in energy. Thus, there is a real need of appropriate and reliable theoretical calculations to meet this requirement. However, experimental techniques have become more advanced and sophisticated with the time and now deeper information of electron impact collision dynamics can be extracted. There are information which cannot be obtained through the traditionally measured differential and integrated cross sections. For example, with the electron-photon coincidence techniques one can measure the Stokes parameters of the emitted light with which one can gain knowledge about the shape and orientation of charge cloud electron excited atoms as well as the population of various magnetic sub-levels. Now it is also possible to perform such experiments with spin polarized electrons. The collisions from spin-polarized electrons provide information about spin dependent electron-exchange and spin-orbit interaction. Besides detecting the emitted photons by using spin polarized beam, one can also analyze the spin of the scattered electron and measure the different spin parameters. To analyze theoretically the results obtained from these sophisticated experiments one needs to utilize fully relativistic theoretical approaches. In the present thesis three main aspects have been addressed. The first aspect has been to report detailed electron impact fine structure excitation cross section data for some of the inert gases which are often used for plasma diagnostic purposes. Further, to utilize iii these reliable cross sections into a suitably developed plasma model and check the improvement in the plasma parameters so obtained. Most of the earlier calculations for plasma modeling used electron impact fine structure resolved excitation cross sections in approximate manner. The success of optical-based plasma diagnostic techniques depends on using accurate cross section data as these plasma models require a large number electron impact collision cross section data over a wide range of impact energies. The second aspect has been to study relativistic effects such as spin-orbit and exchange in the electron excitation of heavier atoms. For this purpose, fully relativistic calculations have been taken up for the excitation of Hg by spin polarized electrons and the results are compared with the recently measured Stokes parameters through electron-photon coincidence techniques. Finally, the third aspect is to study the relativistic effects in the electron impact elastic scattering from heavier alkalis and lead atoms and report cross sections and spin parameters. The presently available and suitable quantum mechanical theoretical approaches to study electron atom collisions can be categorized broadly as perturbative and non-perturbative methods. The recently used non-perturbative methods are convergent close-coupling (CCC) and R-matrix. These theoretical calculations involve heavy computational work and their applicability is limited to low impact energies. Also in these methods, the incorporation of relativistic effects is only recently explored. However, among the perturbative approaches the distorted wave approximation theory has been the most successful and widely applied. This approach produces quite reliable results which are mostly found to provide good comparison with the experimental measurements. In the present thesis a fully relativistic distorted wave (RDW) approximation theory for studying various electron-atom collision processes has been used. The relativistic treatment in RDW method is based on obtaining the solutions of Dirac equations to describe projectile and target electrons and using them to evaluate T-matrices. This is a natural way to incorporate the relativistic effects to all orders. The whole work of the thesis is presented through 1-8 Chapters and has been briefly described below iv Chapter – 1 is an introductory Chapter which gives the review of the relevant experimental and theoretical work reported on the studies of electron – atom collision and their application. It outlines and discusses the various theoretical approaches used to study electron impact excitation of atoms which is the main process considered in this thesis. A detailed description of distorted wave approximation theory in its relativistic form is also given as this has been mainly used in the present thesis for studying the electron impact excitations of different atoms. Chapter – 2 describes the study of electron impact excitation of Ar from its ground 3p6 configuration to the higher lying fine-structure levels of the 3p53d, 3p55s, and 3p55p manifolds using relativistic distorted-wave approximation theory. Results for the differential and integrated cross sections are obtained at energies in the range up to 100 eV. These are compared with available experimental measurements and earlier theoretical non-relativistic distorted-wave and R-matrix calculations. Analytic fits to our integrated cross sections are also provided. Chapter – 3 deals with the further extension of the electron-impact excitation study of Ar reported in Chapter 2 to fine-structure excitations in Krypton atoms. In this chapter the RDW cross sections are calculated and reported for the electron-impact excitation of Kr from its ground 4p6 state to the fine-structure levels of the 4p54d, 4p55p and 4p56s manifolds. The results are compared with available measurements and other calculations. There have been no previous theoretical calculations for the 4p54d or 4p56s manifolds. In order to provide integrated cross sections over a wide range of energies the cross sections are fitted to the analytic formulae. Chapter – 4 addresses the application of the calculated detailed fine-structure RDW cross section data for Ar reported in Chapter 2. In this chapter a collisonal radiative model has been developed for low temperature Ar plasma which incorporates the calculated RDW cross sections in order to test the effectiveness of including these in the plasma modeling. Excitation cross sections from the two 3p54s J=1 resonance levels, 1s2 and 1s4, to the higher lying 2p fine-structure manifold as well as for transitions among individual levels of the 1s and 2p manifolds are also calculated and included in the present model which v were not fully considered in any earlier model. The calculations have been performed for the population densities of the 1s and 2p levels and these are compared with recent optical emission spectroscopic measurements. The variation of population densities of all the 1s and 2p levels with electron temperature and density are presented. Also the calculations of the intensities for the 750.38 nm (2p11s2) and 696.54 nm (2p21s5) lines are performed and compared with recently reported experimental results. The present work suggests that the inclusion of a complete fine-structure description of the electronic processes occurring in the plasma is important for the success of a collisional radiative model. Chapter – 5 considers the study of the excitation of mercury atoms by the impact of spin-polarized electrons in the light of recently reported experimental results from the group of Münster in Germany. RDW calculations are presented for the differential stokes parameters P1, P2, P3 and P4 for the excitation of Hg atoms from the ground 6s2 1S0 state to the triplet 6s6p 3P1state at scattering energy of 25 eV. Further, all the angle integrated four Stokes parameter P1, P2, P3 and P4 for the excitation of 61P1 and 63P1 states of mercury atom from its ground 61S0 state are also reported in the incident electron impact energy range up to 100 eV using the same RDW approximation theory. The comparison of our calculated Stokes parameters shows good agreement with experimental measurements. In Chapter – 6, study of the elastic scattering of electrons from the heavier alkali atoms viz. Rb, Cs and Fr are presented using a relativistic optical model potential approach. In this chapter the results are reported for the differential cross-section, angular variation of spin polarization parameters S, T, U as well as angle integrated elastic, total and momentum-transfer cross sections. For e-Rb elastic scattering both the differential cross section and asymmetry parameter results, agree very well with the available experimental data while for e-Cs scattering, our results are in reasonable agreement with available experimental measurements as well as other theoretical calculations. There are no other theoretical or experimental results to compare with our new results for e-Fr scattering. vi Chapter – 7 further considers the elastic scattering of electron but with Pb atoms using spin polarized electrons. This study has been taken up in the light of recent measurements from the group of Münster in Germany which are reported for the spin-asymmetry function SA in elastic scattering of spin-polarized electrons from lead atoms in their 6s26p2 3P0 ground state in the incident electron energy range 11-14eV. The calculations have been performed utilizing the same relativistic optical model potential approach as described in Chapter 6. Our calculation show reasonable agreement with the recent measurements. The last Chapter – 8 gives the summary of the entire work presented in the thesis as well as the concluding remarks, comments and suggestions.