Limits on tunneling theories of strong-field ionization.

It is shown that tunneling theories of ionization by lasers are subject to upper and lower bounds on the Keldysh parameter gamma. The tunneling limit, gamma-->0, applies to ionization by quasistatic electric fields, but not by laser fields. For lasers, the gamma-->0 limit requires a relativistic treatment. Bounds on the applicability of tunneling theories depend on parameters other than gamma, confirming the rule that strong-field phenomena require more than one dimensionless parameter for scaling.