Modification of The Transition Rate in The Hydrogen Atom placed in Finite Space

When a hydrogen atom trapped in finite space formed by two parallel perfectly conducting plates, the transition rates can be modified. Life-time of the hydrogen $2P_{1/2}$-state is estimated to be shorter as much as $56.3ps$ with a separation distance of $b = 1.2 \mu m$ between two plates. Although the modification is dependent on position of the atom, the life-time can be shorten or lengthen by adjusting the separation distance even for the case that the atom is placed at the center between two plates.