Confinement approach to pressure effects on the dipole and the generalized oscillator strength of atomic hydrogen

Abstract

Initial calculations to explore the role of pressure on generalized oscillator strengths (GOSs) for the hydrogen atom are presented. Our work is based on models of quantum confinement where the hydrogen atom is assumed to be spatially confined in a spherical cavity bounded by a barrier potential of finite height. For a given confinement radius and barrier height the energy spectrum for all available bound states and a number of continuum states (pseudocontinuum) is obtained by solving the Schr\"odinger equation using a finite-differences method. In contrast with the free atom case, the GOS momentum-transfer distribution for the $1s\ensuremath{\rightarrow}nl$ transitions is enhanced in amplitude and width as pressure increases. A turnover of this behavior takes place at a critical pressure, indicating the approach to the limit of confining capacity for the system to hold the $nl$ state. As a consequence of this behavior, the corresponding dipole oscillator strength (DOS) values provide a useful way to characterize the critical pressures for the fading and ultimate bleaching of the spectroscopic emission lines. It is also found that the height of the barrier---simulating different confining media---also affects these properties. These findings may be equally applicable to the study of inelastic energy loss from swift bare ions incident on matter under high pressures, photoabsorption, and photoionization cross sections of caged atoms as well as on optical properties of hydrogenic impurities trapped in spherical quantum dots.