Ionization probability of the hydrogen atom suddenly released from confinement

Abstract

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. K E Y W O R D S confined atoms, ionization energy distribution function, ionization probability, sudden approximation Int J Quantum Chem. 2018;118:e25563.

Ionisation and excitation probabilities of a hydrogen atom suddenly released from penetrable confinement

“…As it could be expected, those orbitals with a larger spatial extension are affected by confinement at larger distances. Both, the oscillatory behaviour of the orbital energy with the sawtooth structure shown in Figure 1, and the fact that the energy is always negative, were not obtained for an infinite barrier [24]. This is because for a finite barrier the orbital may extend over the entire space while for the infinite barrier the orbital is confined between the nucleus and the barrier.…”

“…In the inset, we show the ionization probability only for the 4s, 5s and 6s orbitals for r 0 between 20 and 32. For r 0 values different from those where tunnelling takes place, the ionization probability shows an oscillatory behaviour, as it was the case of the infinite barrier [24]. A significant rise in the ionization probability of the 4s state is observed as r 0 is reduced from r 0 = 35 to r 0 = 26.2.…”

“…As in our previous work [24], the analytic continuation method [29][30][31] has been used to obtain all the radial functions involved in the calculation. The radial Schrödinger equation is written as…”

“…Ref. [23] for an extensive compilation of results, less information is available in the literature on the stability of the atomic or molecular species when confinement is removed [24].…”

“…A spherical confining cavity of finite barrier height v 0 with inner radius r 0 and thickness ∆ with the nuclear position at its center has been considered. This is a model of penetrable confining environments [25][26][27][28] which will introduce new effects not described by impenetrable walls [24]. In this work we shall study the s states of the hydrogen atom.…”