text: Tunneling ionization from the ground state of a hydrogen atom in an electrostatic (DC) field was solved schematically by Lev Landau, using parabolic coordinates. This provides a simplified physical system that given it proper exponential dependence of the ionization rate on the applied external field. When , the ionization rate for this system is given by:
  Landau expressed this in atomic units, where . In SI units the previous parameters can be expressed as:
  The ionization rate is the total probability current through the outer classical turning point. This rate is found using the WKB approximation to match the ground state hydrogen wavefunction through the suppressed coulomb potential barrier.
  A more physically meaningful form for the ionization rate above can be obtained by noting that the Bohr radius and hydrogen atom ionization energy are given by
  where  is the Rydberg energy. Then, the parameters  and  can be written as
  so that the total ionization rate can be rewritten
  This form for the ionization rate  emphasizes that the characteristic electric field needed for ionization  is proportional to the ratio of the ionization energy   to the characteristic size of the electron's orbital . Thus, atoms with low ionization energy (such as alkali metals) with electrons occupying orbitals with high principal quantum number  (i.e. far down the periodic table) ionize most easily under a DC field. Furthermore, for a hydrogenic atom, the scaling of this characteristic ionization field goes as , where  is the nuclear charge. This scaling arises because the ionization energy scales as  and the orbital radius as . More accurate and general formulas for the tunneling from Hydrogen orbitals can also be obtained.
  As an empirical point of reference, the characteristic electric field   for the ordinary hydrogen atom is about  (or ) and the characteristic frequency  is .