  Tunnel ionization rates of triplet Rydberg states in helium with principal
quantum numbers close to 37 have been measured in electric fields at the
classical ionization threshold of $\sim197$ V/cm. The measurements were
performed in the time domain by combining high-resolution continuous-wave laser
photoexcitation and pulsed electric field ionization. The observed tunnel
ionization rates range from $10^5$ s$^{-1}$ to $10^7$ s$^{-1}$ and have,
together with the measured atomic energy-level structure in the corresponding
electric fields, been compared to the results of calculations of the
eigenvalues of the Hamiltonian matrix describing the atoms in the presence of
the fields to which complex absorbing potentials have been introduced. The
comparison of the measured tunnel ionization rates with the results of these,
and additional calculations for hydrogen-like Rydberg states performed using
semi-empirical methods, have allowed the accuracy of these methods of
calculation to be tested. For the particular eigenstates studied the measured
ionization rates are $\sim~5$ times larger than those obtained from
semi-empirical expressions.
