ECCPA: Calculation of classical and quantum cross sections for elastic collisions of charged particles with atoms

The Fortran program eccpa calculates differential and integrated cross sections for elastic collisions of charged particles with atoms by using the classical-trajectory method several quantum methods approximations. are described within framework static-field approximation, interaction between projectile target atom represented Coulomb potential atomic nucleus screened electrons. To allow use fast robust calculation methods, is assumed to be same in center-of-mass frame laboratory frame. Although this assumption neglects effect relativity on interaction, it allows strict relativistic kinematics. equation relative motion shown have form as non-relativistic theory, a reduced mass an effective potential. wave motion, obtained from correspondence principle, formally identical Schrödinger potential, reduces familiar Klein-Gordon when much larger than that projectile. Collisions spin 1/2 projectiles also solving Dirac equation. Various approximate solution applied generic sum Yukawa terms, which good part calculations performed analytically. useful assessing validity accuracy various approximations, pedagogical tool. Program Title: CPC Library link files: https://doi.org/10.17632/c3tn9hyfvb.1 Licensing provisions: CC NC 3.0 Programming language: 90/95 Nature problem: computes (DCSs) (electrons, positrons, muons, antimuons, protons, antiprotons, alphas) neutral atoms. Calculations approximation potentials expressed terms their parameters fitted electrostatic resulting Thomas–Fermi model self-consistent Dirac–Hartree–Fock–Slater calculations. provides DCSs computed four different approaches: classical trajectory method, Born partial-wave expansion phase shifts, eikonal approximation. user allowed select number atom, model, kind its kinetic energy. Calculation results written output files formats suited visualization plotting program. A Java graphical interface running visualizing interactively. Solution method: extension formulated central, fundamental requirement adopted schemes; DCS then (Lorentz) transform calculated This scheme qualifies semi-relativistic, because accounts kinematics rigorous way, but disregards differences interactions observed frames. We consider elementary formulation based (or Klein–Gordon) principle. Accurate scattering can at expense considerable numerical work. avoid difficult shifts radial equation, we adopt simplified strategy combines (first) both amplitude Wentzel–Kramers–Brillouin (WKB) shifts. describe semi-classical known yield reliable small angles. case electrons positrons considered similar grounds, amplitudes work approximating performing Integrals functions given analytical formulas means adaptive algorithm 20-point Gauss-Legendre quadrature formula bisection scheme; control errors gives better about 10 ? well-behaved integrands. whole energy takes no longer few seconds modern personal computer, quite irrespectively atom. Additional comments including restrictions unusual features: correspond point nuclei. parameterization instead tables (obtained, e.g. , structure calculations) has minor DCSs. limited large angles, where actual does differ due finite size nucleus, disregarded here. provide fairly accurate description moderate deflection They used, Monte Carlo simulations transport matter. information generated approaches, permits identifying ranges