Improved Approximated Solutions to the Nonlinear Debye Potential

The shielding effect of plasma on the electrostatic potential due to a central nucleus is studied. The potential is determined by the Poisson equation with Boltzmann factor for the charge density of ions. The aim of this work is to find approximated analytical solutions, without the usual linearization hypothesis, by means of the technique of quasifractional approximants in two points. In a previous work (Martín and Pérez, 1994) a quasifractional fractional approximation was obtained, but the coefficients were found by means of the numerical solution of the differential equation. Now we find a complete analytical expression. The approximant found is highly precise in the range of validity of the physical model used.