  The expression of the electron broadening operator including the effect of
penetrating collisions, i.e. for which the incoming electron enters the extent
of bound-electron wavefunctions, is rather complicated, even for hydrogen. It
involves integrals of special functions, which evaluation deserves scrutiny. We
present a simple approximate form of the electron collision operator for
hydrogen including penetration effects, both in direct and interference terms.
The new expression is accurate and easy to compute. In the Penetration Standard
Theory, the collision operator is convergent whatever the value of the maximum
impact parameter. However, when penetration theory is not valid anymore, it
should be questioned. We discuss the problem of strong collisions when
penetration effects are taken into account.
