Elastic scattering of electrons by Sr atom: a study of critical minima and spin polarization

Abstract

Within the framework of the complex optical potential, the critical minima (CM) in the differential cross sections and the spin polarization in the elastic scattering of electrons by the Sr atom are studied in the energy range E i =1-1000 eV using the Dirac and Schrödinger partial wave methods. The two methods are, respectively, termed as the optical potential method of Dirac (OPMD) and optical potential method of Schrödinger (OPMS). The differential cross sections (DCSs), total cross sections (TCSs), momentum transfer cross sections (MTCSs), integral elastic cross sections (IECSs), viscosity cross sections (VCSs) and inelastic cross sections (INCSs) for e-Sr scattering are also calculated for the same energy range. In OPMD, the complex optical potential is composed of the static, exchange, polarization and absorption potentials. The OPMS potential, on the other hand, comprises the static, local exchange, polarization, spin-orbit, and absorption components. The number of CM points has been found to be respectively 7 and 5 with OPMD and OPMS methods in the DCSs of e-Sr scattering. The number of maximum spin polarization points observed is 13 and 10 for the OPMD and OPMS respectively. The energy dependence of TCS, MTCS, IECS, VCS, and INCS, studied in this work, show a non-monotonous pattern for energies beyond about 50 eV. So far as we are concerned, this is the first work for the study of CM in the DCSs of the e-Sr scattering as there are neither experimental nor theoretical studies published in the literature for the same.The strontium (Sr), with Z=38 , is one of the six alkaline earth metals with electron valence configuration 5s 2 . The scattering of electrons from Sr atom has drawn considerable interest due to the presence of low-lying shape resonance (SR) structures and the existence of its negative ion Sr − [7]. To the best of our knowledge, there is no extensive experimental or theoretical study on DCS and other cross sections for e-Sr scattering in the literature. However, we found two experimental works on the total cross section (TCS) by Romanyuk et al [8] and Kazakov et al [9] for a narrow electron energy interval 1-10 eV that agree with the two-state close-coupling (CC2) theoretical calculations of Fabrikant [10]. In their work, Romanyuk et al [8] observed a sharp increase of TCS as the scattering energy decreases to 0.1 eV. Kazakov et al [9] found a d-wave shape resonance at 1.2 eV by studying the structure of electron spectra for the scattering of electrons by the Sr atom, but they also attributed a minimum structure in 0.3-0.4 eV.Szmytkowski and Sienkiewicz [11] have done theoretical calculations on TCS using the relativistic polarized orbital approximation for the elastic electron scattering by Sr in the energy range 0.2-10 eV. They calculated the static part of their interaction potential by solving the Dirac-Hartree-Fock (DHF) equations for the isolated target while the polarization potential was obtained by solving the coupled DHF equations for the target perturbed by an electric field prod...