Positron Impact Elastic Scattering by Calcium Atom Using First Order Distorted Wave Born Approximation with a Complex Potential
Wakhu, Wechuli Benard
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The concept of elastic scattering of projectiles by atomic targets has the fundamental importance in understanding the complex projectile-target interaction and the dynamics of the collision process. Compared to electrons, positron scattering is considered as the alternative way to acquire knowledge about atomic structures and to examine phenomena such as the Fermi surface of metal and nano-precipitates in solids. Further, positron scattering cross section data is essential for the development of various technological fields; for example astrophysics, plasma sciences, material sciences and bio-medicine. Additionally, positron cross sections are used as input data in some modeling software. Accurate cross section data is required in these applications. Thus, lack of complete agreement among the available theoretical data, unavailability of experimental data and the DWBA method with a complex potential at impact energy range 10-200 eV not having been utilized in such a study; are the reasons that informed this investigation. Consequently, this research sought to establish whether the second term of the DWBA T-matrix element significantly affect the cross sections and how the cross sections obtained herein compare with other calculations when the distorting potential is varied. After formulating the complex potential with positronium formation channel proficiently incorporated, the radial Schrödinger equation was solved numerically for low values of orbital angular momentum quantum number using the Numerov’s method. The associated integral equation was solved iteratively for high values of orbital angular momentum quantum number. The extracted phase shifts were used to compute the T-matrix which was then used to determine DCS while the optical theorem was applied to calculate TCS. With only static potential, the DWBA and OP methods yield same DCSs. The polarization potential increases the DCS at small scattering angles and further introduces a local minimum whose position shifts toward forward scattering angles with increasing projectile-target impact energy. With a real potential that incorporates static-polarization potentials, the structure of the present TECS for OP and DWBA is consistent with those of the available data. With a complex potential, the agreement between the present OP and DWBA DCS results is excellent. In conclusion, with a complex potential that incorporates positronium formation effect, the exact agreement between the DWBA and OP results implies insignificant effect of the second term of the direct T-matrix element on DCS as well as TCS while the effect of positronium on the cross sections does not extend beyond 150 eV. From these findings, it is recommended that at intermediate energies, a complex potential inclusive of positronium formation channel should be applied and the procedure of accounting for inelastic cross section suggested herein this study be comprehensively tested on positron-alkaline earth atoms to clearly establish its suitability.