  Energy-changing electron-hydrogen atom collisions are crucial to regulating
the energy balance in astrophysical and laboratory plasmas and relevant to the
formation of stellar atmospheres, recombination in H-II clouds, primordial
recombination, three-body recombination and heating in ultracold and fusion
plasmas. Computational modeling of electron-hydrogen collision has been
attempted through quantum mechanical scattering state-to-state calculations of
transitions involving low-lying energy levels in hydrogen (with principal
quantum number n < 7) and at large principal quantum numbers using classical
trajectory techniques. Analytical expressions are proposed which interpolates
the current quantum mechanical and classical trajectory results for
electron-hydrogen scattering in the entire range of energy levels, for nearly
all temperature range of interest in astrophysical environments. An asymptotic
expression for the Born cross-section is interpolated with a modified
expression derived previously for electron-hydrogen scattering in the Rydberg
regime using classical trajectory Monte Carlo simulations. The derived formula
is compared to existing numerical data for transitions involving low principal
quantum numbers, and the dependence of the deviations upon temperature is
discussed.
