We discuss the spectrum of very high Rydberg states as detected via io
nization in weak external electric fields. For the conditions of inter
est, namely, states just below the ionization continuum and weak field
s, the classical barrier to dissociation is extremely far out from the
core. About the saddle point the potential is very shallow. It is con
cluded that ionization by tunneling is far too slow. Only electrons wh
ose energy is above the classical barrier can be detected via ionizati
on. However, not all electrons which energetically can ionize will nec
essarily do so. Electrons may fail to ionize if the fraction of their
energy which is in the direction perpendicular to the field is high. T
he computed fraction of electrons which fails to ionize does depend, i
n a sensitive way, on the diabatic vs adiabatic switching on of the ex
ternal field. More experiments and theoretical work is needed on this
point. A classical procedure based on the adiabatic invariance of the
volume in phase space is developed for the computation of the fraction
of electrons that can surmount the classical barrier for a given fiel
d. Analytically exact results are obtained for adiabatic switching and
for the sudden limit where the rise time of the field is shorter than
the period of the orbit. For the case of diabatic switching (which is
appropriate for very high n values), the exact classical computations
on the yield of ionization show that the onset of ionization is at an
energy of 4.25 F1/2 cm-1 below the ionization potential and the 50% p
oint it as 3.7 F1/2 cm-1 for a field F in V/cm.