Theoretical Formalism To Estimate the Positron Scattering Cross Section

Abstract

A theoretical formalism is introduced in this article to calculate the total cross sections for positron scattering. This method incorporates positron-target interaction in the spherical complex optical potential formalism. The study of positron collision has been quite subtle until now. However, recently, it has emerged as an interesting area due to its role in atomic and molecular structure physics, astrophysics, and medicine. With the present method, the total cross sections for simple atoms C, N, and O and their diatomic molecules C2, N2, and O2 are obtained and compared with existing data. The total cross section obtained in the present work gives a more consistent shape and magnitude than existing theories. The characteristic dip below 10 eV is identified due to the positronium formation. The deviation of the present cross section with measurements at energies below 10 eV is attributed to the neglect of forward angle-discrimination effects in experiments, the inefficiency of additivity rule for molecules, empirical treatment of positronium formation, and the neglect of annihilation reactions. In spite of these deficiencies, the present results show consistent behavior and reasonable agreement with previous data, wherever available. Besides, this is the first computational model to report positron scattering cross sections over the energy range from 1 to 5000 eV.

Positron interactions with nitrogen and oxygen molecules: elastic, inelastic and total cross sections

“…In the mid to high energy range (100-10000 eV) it is seen in Figures 3 and 4 that the data we present fit well to the existing experimental and calculation work, save for that of Singh et al [10], which appears to diverge above 300 eV for the oxygen and nitrogen total cross section datasets. This fit is of primary importance when assessing the validity of cross sections at high energies and can be more easily shown in the Fano plots of Figures 7 and 8, where we also include data from the Livermore database for electron scattering of O 2 and N 2 using the additivity rule.…”

“…4. O2 molecule total cross sections from a variety of experimental and calculated methods to compare to our IAM-SCAR+I results for the positron impact energy range 0.1 to 10000 eV [10,24,46,47,[49][50][51] including previous IAM-SCAR results from 2012 utilising the dipole or dipole plus quadrupole formalism of the atomic polarization potentials (Eq. (1)), but without interference effects.…”

“…As Singh et al [10] also use the optical potential method to compute their TCS, the reason for this discrepancy at high energy and the unexpected angular dependence with respect to the Born-Bethe theory Fano plots in Figures 7 and 8 may arise from their treatment of the molecule geometry. They state that "the charge density and static potential is obtained by expanding the respective functions from the center of mass of the molecule.".…”

“…Recently headway has been made in approximate calculations on atomic and molecular cross sections for positron scattering. In a 2016 paper by Singh et al [10] a modified version of the spherical complex optical potential (SCOP) formalism has been used to provide positron total cross sections from 1 to 5000 eV, and these follow the low energy phenomena quite well. As the field grows towards accuracy and consistency, it is imperative to compare the different methods used for achieving these results.…”

“…In this article we produce new positron elastic, inelastic, differential and integral scattering cross sections for the N 2 molecule, and updated results for the O 2 molecule, using our IAM-SCAR+I method for molecular cross sections. These are compared to literature, including those more recently calculated by Singh [10]. First we introduce our method, IAM-SCAR+I, explained in detail in other publications [11][12][13] -an advancement on the IAM-SCAR method pioneered by Garcia and Blanco [14,15] in the early 2000s.…”