DiracSolver: A tool for solving the Dirac equation

Abstract

Advantageous numerical methods for solving the Dirac equations are derived. They are based on different stochastic optimization techniques, namely the Genetic algorithms, the Particle Swarm Optimization and the Simulated Annealing method, their use of which is favored fromintuitive, practical, and theoretical arguments. Towards this end, we optimize appropriate parametric expressions representing the radial Dirac wave functions by employing methods that minimize multi parametric expressions in several physical applications. As a concrete application, we calculate the small (bottom) and large (top) components of the Dirac wave function for a bound muon orbiting around a very heavy (complex) nuclear system (the 208Pb nucleus), but the new approach may effectively be applied in other complex atomic, nuclear and molecular systems. Program summaryProgram Title: DiracSolverProgram Files doi: http://dx.doi.org/10.17632/7hv9mtdvmp.1Licensing provisions: GPLv3Programming language: GNU-C++Nature of problem: The software tackles the problem of solving the Dirac equation using stochastic optimization methods.Solution method: The software utilizes three stochastic optimization methods for the solution of Dirac equation in the form of neural networks. The used methods are: genetic algorithm, particle swarm optimization and simulated annealing.