Influence of dimensionality on deep tunneling rates: A study based on the hydrogen-nickel system

The tunneling of subsurface hydrogen into a surface site of a nickel crystal is used to investigate deep tunneling phenomena. A method to calculate tunneling lifetimes based on an energy and time filter is developed, enabling converged lifetimes differing by 14 orders of magnitude. It is found that the reduced dimensional approximation always overestimates the tunneling rate. The vibrational adiabatic correction improves dramatically the one-dimensional calculation but nevertheless overestimates the cases of deep tunneling. The isotope effect is studied, pointing to experimental implications.