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 γ. The tunneling limit, γ→0, applies to ionization by quasistatic electric fields, but not by laser fields. For lasers, the γ→0 limit requires a relativistic treatment. Bounds on the applicability of tunneling theories depend on parameters other than γ, confirming the rule that strong-field phenomena require more than one dimensionless parameter for scaling.