Enhancement factor γ of a sharp emitting tip: A revisit with the aim of a simple formula for?

We have revisited the problem of the enhancement factor γ of a sharp tip. We have simulated the tip apex by an ellipsoid and by a proper solution in spheroidal coordinates we have found a simple formula for γ in terms of the corresponding γ of the hemisphere on a post (HOP) problem and of the sharpness S=R
₁
/R
₂
of the tip where R
₁
, R
₂
are the radii of the ellipsoid.