In some special cases you can have huge effects. One example is bound ##\beta## decay, where the electron decays into a bound atomic state rather than a free (scattering) state. Of course it can do so only if the corresponding atomic state is not occupied by an electron since electrons are fermions. A famous example is Rh 187 which as a neutral atom decays with a half-life of about ##42 \cdot 10^9 \, \text{y}##, making it apparently to a perfect clock to measure the age of astrophysical objects by measuring the abundance ratio of Rh and Os (it's decay product). However, when the Rh is ionized, then bound-state ##\beta## decay can take place. Then the half-life becomes of the order of ##10 \; \text{y}##, i.e., a 9 orders of magnitude smaller value. In fact the half-life of ionized Rh 187 has been measured at GSI in Darmstadt (Germany) to be ##33 \;\text{y}##. For a very nice review by Fritz Bosch, one of the scientists involved in these measurements, see
http://www.euroschoolonexoticbeams.be/site/files/nlp/LNP651_contrib5.pdf