Scaling Relation For The Energy Levels Of A Hydrogen Atom At High Pressures

Abstract

The effect of high pressure on a hydrogen atom has frequently been simulated by enclosing the atom in an impenetrable spherical box. It is shown that for such a confined hydrogen atom placed at the centre of a spherical box a simple scaling relation exists between the energy and the radius of the confining box for 1s, 2p, 3d, and 4f levels, and another similar relation exists for 2s, 3p, and 4d levels.

Study of a confined hydrogen‐like atom by the asymptotic iteration method

“…Such cage radii were first noted by Sommerfeld and Welker [5] in their detailed study on the variation of the binding energy of the 1s state of the hydrogen atom, as a function of the sphere radius, R. Assuming that the surface of the spherical box is impenetrable, they showed that, as R decreases, the binding energy diminishes, and there is a critical value of the sphere radius at which the binding energy becomes zero. More systematic studies were later carried by Varshni [30] where the critical cage radius was first recorded; see also [31]. In this section we shall use AIM to calculate the cage radius at which the eigenvalues are zero.…”

Oscillator strengths of the transitions in a spherically confined hydrogen atom

“…The coefficients a k and b k for a particular state are energy dependent, as the recurrence relations ( 14) and (15) show. On the other hand, energy is dependent on the ratio r c /r 0 and is of the form [29]…”

Spherical confinement of coulombic systems inside an impenetrable box: H atom and the Hulthén potential

“…Shannon and Fisher information entropies in position and momentum space of CHA in soft as well as hard spherical cavities have been investigated [49,50]. Various scaling relations are proposed [51]. Another interesting aspect of this problem is that as the confining radius decreases, binding energy decreases and there exists a critical value of this radius (r c ), at which latter becomes zero.…”