ELECTRON AND POSITRON SCATTERING FROM ATOMIC AND MOLECULAR SYSTEMS

Abstract

The studies involving collisions of electrons and positrons with atomic and molecular systems are not only of fundamental importance but also play key role in understanding the chemical and physical processes occurring in the laboratory and in the astrophysical environments, atomic processes in plasmas, laser physics, material and semiconductor industries. The basic parameter to describe such collision processes is their cross sections which vary with incident projectile energy and need to be obtained in very practical and reliable manner using suitable quantum mechanical approaches. The theories to describe the interaction of electron/positron with atoms, molecules and ions are subcategorized into different energy-dependent elastic and inelastic scattering processes. The study of electron (positron) colliding with atomic species has received considerable attention and is still an active field for research. However, the electron (positron) impact studies on molecular systems, being complex in nature still need special efforts or attention to be able to describe such processes in a more simplified and practical way. Besides the scattering with isolated atomic and molecular systems, the collisional study of electrons with the confined systems is also an active area of research. Basically, an atom or molecule (A) can be caged inside a bigger molecule, for example, in C60 fullerenes, known as endohedral fullerenes (A@C60). These confined atoms are also of interest due to their several applications in science and technologies. Such systems are very different from the natural isolated atoms or molecules as compared to when they are confined in some external environment. These confined systems often exhibit unusual behavior regarding their structure, stability, reactivity, bonding, interactions, and dynamics. Consequently, considering the electron/positron scattering from the confined atoms would be interesting to understand their fundamental behavior. In view of such importance and applications, the present thesis contains a detailed study of electron/positron elastic scattering from various molecules, molecular ions, atomic ions and confined atoms. The whole work of the thesis covers four main aspects. In the first aspect, we deal with the electron and positron scattering from molecules. The molecular targets having multi-centered atoms are difficult to describe in a unified single-center frame of reference due to having many atomic electrons along with the incident projectile. Thus, describing the electron-molecule collision process and to find out the related accurate scattering cross sections is a very challenging problem. Several theoretical methods have been introduced and applied to describe the low and high-energy electron scattering from molecules and these methods are important in some aspects but also have limitations. We mainly focused on the incident electrons/positrons having the intermediate and high energies. Our method considers to first obtain the spherically-averaged molecular static potential using the suitable Gaussian form of the analytical molecular wavefunction. This potential is mostly analytic except for the inclusion of the well-known error function for which very efficient algorithms exist for their numerical evaluation. Thereafter, we make a complex optical potential and consider the scattering from such potential. This can be applied to molecules of arbitrary complexity. In the second aspect, we applied a similar approach to study the scattering of electrons from the molecular ions for the first time and described the characteristic behavior of their cross sections with interesting discussions. This scattering is different from neutral molecules in the respect that molecular ions have the residual ionic charges on them which make the scattering process further complicated due to the long range Coulomb potential. In the third aspect, we have studied the scattering of electrons from multi-charged atomic ions where spin-orbit and exchange effects have dominant contributions. In fact, one must use a fully relativistic approach to solve this scattering problem. Thus, for the electron impact scattering from such atomic ions, we have used the multi-configuration Dirac Fock (MCDF) theory to obtain the wave functions to find the charge density and then modified the static potential by adding Coulomb interaction due to residual ionic charge. Thereafter, we solve the scattering problem by using the optical potential in the Dirac equation. Finally, in the fourth and last aspect, we consider the scattering of electrons from confined atoms. Here again, the wave functions of the confined atoms are obtained using the Dirac-Fock approximation and the charge density along with static potential are calculated. Using this confining potential the scattering problem is solved through the Dirac equations. Considering these four aspects, the whole work of the thesis is presented through eight Chapters as described below in a brief manner. Chapter 1 provides introductory information about the electron/positron scattering from atoms, molecules, ions and confined atoms and their applications in different fields of science. It also presents the non-relativistic and relativistic partial wave phase shift analyses methods that have been used to in the thesis to study the electron/positron scattering from the atomic and molecular potentials and obtain cross sections. In Chapter 2 (first aspect), we used an analytical approach to obtain the static potentials of methane (CH4) and silane (SiH4) molecules using Gaussian wave functions. To describe the electron/positron scattering from these molecules, the partial wave phase shift analysis method is used with complex optical potential consisting of static, exchange, polarization and imaginary absorption potentials. We have calculated the differential, integrated and momentum transfer cross sections in a wide range of incident electron and positron energies up to 500 eV. A detailed comparison of our results for CH4 and SiH4 with the available measurements and theoretical results is presented. In Chapter 3 (first aspect), with a similar analytic approach, we obtain the static potential, and then the detailed studies of the elastic scattering of electrons and positrons from ammonia (NH3) and phosphine (PH3) molecules are presented with a complex optical potential method. The differential, integrated, momentum transfer, absorption and total cross sections are calculated and reported in the incident electron and positron energy range of 10-500 eV. In order to test the applicability of our approach, the present results are compared with the available previous measurements and theoretical calculations. In Chapter 4 (first aspect), similar to the earlier two Chapters, the studies on electron and positron scattering from acetylene (C2H2) and hydrogen surphide (H2S) are presented and the cross sections are obtained for electron and positron using the optical potential method with their analytically obtained static potentials. The differential, integral, momentum transfer, absorption and total cross sections have been calculated for the incident projectile energies in the range 10-500 eV. The obtained results are compared with the previous available theoretical and experimental results, which show good agreement and thus, demonstrate the applicability of our method. Chapter 5 (second aspect), deals with our study of the electron impact elastic scattering from molecular ions and reports the cross section results for CH4+, NH3+, H2O+, NH4+ and H3O+ molecular ions for the first time. The Dirac equations are solved using an optical potential with the partial wave phase shift analysis method to obtain the scattering amplitudes. The differential cross section results are reported for 10–500 eV incident electron energy range. The cross sections for the different molecular ions and their corresponding neutral molecules are also compared.that have been used to in the thesis to study the electron/positron scattering from the atomic and molecular potentials and obtain cross sections. In Chapter 2 (first aspect), we used an analytical approach to obtain the static potentials of methane (CH4) and silane (SiH4) molecules using Gaussian wave functions. To describe the electron/positron scattering from these molecules, the partial wave phase shift analysis method is used with complex optical potential consisting of static, exchange, polarization and imaginary absorption potentials. We have calculated the differential, integrated and momentum transfer cross sections in a wide range of incident electron and positron energies up to 500 eV. A detailed comparison of our results for CH4 and SiH4 with the available measurements and theoretical results is presented. In Chapter 3 (first aspect), with a similar analytic approach, we obtain the static potential, and then the detailed studies of the elastic scattering of electrons and positrons from ammonia (NH3) and phosphine (PH3) molecules are presented with a complex optical potential method. The differential, integrated, momentum transfer, absorption and total cross sections are calculated and reported in the incident electron and positron energy range of 10-500 eV. In order to test the applicability of our approach, the present results are compared with the available previous measurements and theoretical calculations. In Chapter 4 (first aspect), similar to the earlier two Chapters, the studies on electron and positron scattering from acetylene (C2H2) and hydrogen surphide (H2S) are presented and the cross sections are obtained for electron and positron using the optical potential method with their analytically obtained static potentials. The differential, integral, momentum transfer, absorption and total cross sections have been calculated for the incident projectile energies in the range 10-500 eV. The obtained results are compared with the previous available theoretical and experimental results, which show good agreement and thus, demonstrate the applicability of our method. Chapter 5 (second aspect), deals with our study of the electron impact elastic scattering from molecular ions and reports the cross section results for CH4+, NH3+, H2O+, NH4+ and H3O+ molecular ions for the first time. The Dirac equations are solved using an optical potential with the partial wave phase shift analysis method to obtain the scattering amplitudes. The differential cross section results are reported for 10–500 eV incident electron energy range. The cross sections for the different molecular ions and their corresponding neutral molecules are also compared.