%0 Journal Article %T Study of Differential Cross-Section and S-Matrix Using Volkov Function and Taylor Series Expansion for Elastic Scattering %A Bhishma Karki %A Saddam Husain Dhob %A Kishori Yadav %A Jeevan Jyoti Nakarmi %A Kiran Khadka %J Open Journal of Microphysics %P 105-117 %@ 2162-2469 %D 2022 %I Scientific Research Publishing %R 10.4236/ojm.2022.124006 %X This paper deals with S-matrix, born first approximation, amplitude, and differential cross-section (DCS), using Volkov function and Taylor series expansion in laser field, scattering. Equation (30) copes-with DCS and Equation (36) deals with S-matrix, with different parameters, moreover, both equations contain real and imaginary parts. The DCS increases with increasing angle and polarizabilities, constant with dipole distance for both emission and absorption of single-photon. The DCS for both emission and absorption is responded to low incidence energy (30 eV - 60 eV) and photon energy (15 eV) while at high energy only emission and absorption are responded for DCS. The DCS between absorption and emission of a photon with angle variation, dipole distance, and atomic polarizabilities was found 1.098 a.u.2 and at high incidence, energies were found 0.1 a.u.2. %K S-Matrix %K Born First Approximation %K DCS %K Emission and Absorption of Photon %K Incidence Energy %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=121417