  The modeling of non-local-thermodynamic-equilibrium plasmas is crucial for
many aspects of high-energy-density physics. It often requires
collisional-radiative models coupled with radiative-hydrodynamics simulations.
Therefore, there is a strong need for fast and as accurate as possible
calculations of the cross-sections and rates of the different collisional and
radiative processes. We present an analytical approach for the computation of
the electron-impact excitation (EIE) cross-sections in the Plane Wave Born
(PWB) approximation. The formalism relies on the screened hydrogenic model. The
EIE cross-section is expressed in terms of integrals, involving spherical
Bessel functions, which can be calculated analytically. In order to remedy the
fact that the PWB approximation is not correct at low energy (near threshold),
we consider different correcting factors (Elwert-Sommerfeld, Cowan-Robb,
Kilcrease-Brookes). We also investigate the role of plasma density effects such
as Coulomb screening and quantum degeneracy on the EIE rate. This requires to
integrate the collision strength multiplied by the Fermi-Dirac distribution and
the Pauli blocking factor. We show that, using an analytical fit often used in
collisional-radiative models, the EIE rate can be calculated accurately without
any numerical integration, and compare our expression with a correction factor
presented in a recent work.
