  The drastically expanded use of the Woods-Saxon potential in modern day
nuclear physics and the availability of new nuclear data motivated us to review
and optimize the parameters of this potential to the experimental
single-nucleon spectra around the doubly-magic nuclei between $^{16}$O and
$^{208}$Pb. We obtain a parameterization which is applicable over the whole
nuclear chart for nuclides between $^{16}$O and the heaviest elements. Apart
from Coulomb components the obtained parameter set is isospin symmetric. We
demonstrate that the potential provides a good description of the nuclear mean
field leading to quality single-particle spectra, nuclear radii, prediction of
drip-lines, shell closures and other properties. Thus presented Woods-Saxon fit
provides adequate single-particle basis for shell model calculations bridging
over into the continuum.
