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 Schrödinger equation using a finite-differences method. In contrast with the free atom case, the GOS momentum-transfer distribution for the 1s → 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.

Information‐entropic measures in free and confined hydrogen atom

“…[1][2][3] In the last few decades, quantum confinement has emerged as a very fascinating and relevant research area from both theoretical and experimental perspectives. [2][3][4][5][6][7] Discovery and development of modern experimental techniques have given the required insight about responses of matter under confinement. Furthermore, advancement of nanoscience and nanotechnology has also stimulated extensive research activity to explore and study such systems.…”

Information-entropic measures for non-zero l states of confined hydrogen-like ions

“…Many interesting aspects such as rearrangement and redistribution of ground and excited energy states, simultaneous and incidental degeneracy, change in hyperfine splitting constant as well as dipole shielding factor, nuclear magnetic screening constant, pressure, variation of static and dynamic polarizability, hyperpolarizability, information entropy, etc., were probed with varying confining radius (r c ). A vast literature exists on the subject; here we refer to a selective set [13][14][15][16][17][18][19][20][21][22][23][24]. Eigenvalues and eigenfunctions of CHA can be solved exactly in terms of Kummer M-function (confluent hypergeometric) [17].In past twenty years, information measures were explored extensively for various quantum systems in both free and confinement situations.…”

The H, H2+, and HeH2+ systems confined by an impenetrable spheroidal cavity: Revisited study via the Lagrange‐mesh approach

“…If we consider the analytical expression for the generalized oscillator strength (GOS) for the transition of a free hydrogen‐like system: where q is the momentum transfer and Z the nuclear charge. In the optical limit ( ), corresponds to the DOS , which becomes Z ‐independent as: which, after considering the isotropy factor 1/3 as in Equation becomes as given by Bates .…”

“…If we consider the analytical expression for the generalized oscillator strength (GOS) for the 1s ! 2p transition of a free hydrogen-like system [47][48][49] :…”