Instability of Pre-Existing Resonances Under a Small Constant Electric Field

Two simple model operators are considered which have pre-existing resonances. A potential corresponding to a small  electric field, f, is then introduced and the resonances of the resulting operator are considered as<tex> <tex>f\to 0</tex>. </tex>

It is shown that these resonances are not continuous in this limit. It is conjectured that a similar behavior will appear in more complicated models of atoms and molecules. Numerical results are presented.