SCATTERING OF ELECTRONS AND PHOTONS BY MOLECULAR SYSTEMS

Abstract

The work reported in the thesis is author's attempt to study the scattering of electrons and photons by molecular system using various quantum mechanical approaches. This work is divided broadly into two main categories. Under the first category, we have studied the elastic collisions of electrons from low to high energies with silane (SiH4), water (H20) and ammonia (NH3) molecules using a parameter - free optical potential model approach . In addition, we have also calculated the cross sections for the elastic and in-elastic scattering of fast electron and X-ray from carbondioxide (CO2) and SiH4 molecules using various basis sets in the first Born approximation. Under the second category, we aim at investigating the electronic structure of the alkaline earth oxide ED (E = Be, Mg, Ca and Sr) molecules and helium atom using a momentum density approach. During the last decade, the Compton scattering has emerged as one of the powerful experimental probe for studying the electronic momentum distributions in atoms , molecules and condensed matter. The spectral analysis of Compton scattered radiation, which is Doppler broadened because of the intrinsic momentum of the target electron, unveils a line profile called the Compton profile (J(q) ) which under the impulse approximation is the projection of the momentum density (Tr()) along the scattering vector. In addition to the Compton scattering the developments of other new experimental probes such as the high-energy-electron-impact-spectroscopy (HEEIS ) , the so called (e, 2e) reactions and the positron annihi-lation have further given a great promise of access to the electron momentum distribution , Tr( and the Compton profile , J(C) . Any test of the quality of target wave-functions and models , requires calculations of the Tr (P) and -+ 3( q ) . Once we know the Tf (p) , we can get very reliable information about many related quantities such as the incoherent scattering function, the cohesive energy, the chemical bond, the internally folded density (auto correlation function ) etc . All these quantities give a better understanding of the electronic structure of matter. The thesis has been divided into seven chapters. In the first chapter, we give the general introduction of the work. We briefly review the various theoretical and experimental developments relevant to the present study . The chapter forms the basis to the work reported in the subsequent chapters. In the second chapter, we have reported low-energy (0.1-30 eV) electron-SiH4 scattering by employing a parameter-free spherical optical potential which is a sum of three spherical terms namely the static, exchange and polarization forces. The total optical potential is then treated exactly in a partial-wave-analysis using the variable-phase approach to yield the scatt-ering phase shifts . We employ several version of parameter-free polarization and exchange potentials . We demonstrate that the qualitative features of the scattering parameters ( such as a Ramsauer-Townsend (RT ) minimum below 1 eV and a shape resonance structure around 2-3 eV) observed in recent experiments , can very well be reproduced in the present simple model . Quanti-tatively , our results (below 10 eV) are very close to the recent close-coupling calculations using a similar kind of (including non-spherical terms also) model optical potential. Above 10 eV, the present results are in very good agreement with experiment and are better than the earlier calculations. The third chapter is an extension of the e-SiH4 (c hapter-II) work to other non-linear polyatomic molecules having permanent dipole moment (H2O and NH3) . Elastic differential, integral and momentum transfer cross sections are reported for the scattering of electrons by water and ammonia molecules in the energy range 100-1000 eV. A parameter - free model optical potential which is again a sum of three spherical terms, namely the static, exchange and polarization forces, is constructed from near Hartree-Fock one-centre-expansion polyatomic wavefunctions. We find that the present calculated differential cross sections reproduce all the important features (such as forward peaking, dip at middle angles, and enhanced backward scattering) observed in the recent experiments. Quantitatively, the present results are in very good agreement with the available experimental data . The fourth chapter is devoted to the calculations of cross sections for elastic and inelastic scattering of fast electrons and photons (X-rays) from CO2 and SiH4 molecules. The self-consistent-field (SCF) molecular wave-functions for CO2 and SiH4 molecules are obtained through the standard Gaussian-80 and -82 versions of the programm respectively. The effects of basis set choice and free rotation on these cross sections are also investigated. The utility of an approximate scheme to correct SCF inelastic cross sections for the effects of electron correlation for CO2 molecule is examined. The probability density for the interelectronic distance, or radial intracule density, is obtained as a by-product . The fifth chapter of the thesis contains the work on the partial wave analysis of momentum density (71 (p) ) Compton profile (J ( ) and internally folded density or auto correlation function (B(r)-function) for the linear molecular systems such as the alkaline earth oxides EO (E = Be, Mg, Ca and Sr) . We have used SCF wavefunctions with Slater type basis . It is found that the partial wave decomposition provides a useful partitioning of the momentum densities, Compton profiles and BM-functions into isotropic and anisotropic terms of different symmetry. The similar but different bonding situations in this homologous series and the anisotropic components relating (iv) to momentum density, Compton profile and B(P)-function have been examined with the help of difference functions computed with respect to an ionic reference. We have also correlated our gas phase study with the recent Augumented Plane Wave (APW) band-structure calculations, and experimental measurements for the insulating compound Mg0 in crystalline phase.