Ionization probability of the hydrogen atom suddenly released from confinement

The problem of the stability of a confined atom when it is extracted from the confining cavity has been investigated, modeled by a spherical hard wall potential. The ionization probability when the atom is released from confinement has been obtained. The dependence of the ionization probability on the confinement radius and on the quantum numbers of the initial confined state has been studied. The probability density function of the ionization energy of the ejected electron has been obtained for the different cases considered. The oscillatory structure of this distribution function, with a principal maximum located in the neighborhood of the energy of the initial state and minima very close to zero has been elucidated. The sudden approximation has been applied and the analytic continuation method has been used to calculate the different stationary states. An H atom inside a spherical hard wall potential is used to infer information on the stability of atoms when they are released from confinement. The ionization probability is calculated for different initial confined states and radii. Assuming ideal conditions for extraction, the time needed to remove confinement can be neglected, thus allowing to obtain exact solutions that can be adapted to match more realistic situations.