Oscillator strengths, transition probabilities and state lifetimes of hydrogen atom confined in spherical cavity: off-center displacement effects

Abstract

The non-relativistic dipole transition matrix elements, oscillator strengths, transition probabilities and lifetimes of the ground and lowest excited states of the centered and off-centered confined Hydrogen atom in a spherical cavity, were investigated via a variational method using B-splines as basis functions. These atomic parameters, obtained with a high accuracy, were found to be strongly affected by the off-center displacement which induces the increase of the splitting between initially m's degenerate states. Due to the displacement of the atom from the center, some transitions that were initially forbidden have non-zero probabilities. The results obtained for the 2sσ, 2pσ, 2pπ, 3dσ, 3dπ, and 3dδ states have shown that, with the increase of the displacement, the state lifetimes exhibit one or several extrema depending on the confinement radius and the magnetic quantum number.

Binding energies, oscillator strengths of core/shell spherical quantum dots with or without on- or off-center donor impurities under an external magnetic field

“…The system considered was subjected to an external magnetic field in order to analyze the potential influence of the strength of the magnetic field on it. The approach adopted, which is derived from the one followed in our previous works [43,45], lies on a B-splines-based variational method. In the limit of a near zero displacement, we recover the values associated with the on-center case.…”

“…The effects of dielectric mismatch as well as the polarization charge effects are considered. The calculations are performed via the implementation of a variational method based on B-splines which has already demonstrated its accuracy and reliability in former works [40][41][42][43][44][45]. Finally, new interesting results have been obtained, thus enriching our understanding of the systems of interest in our study.…”

“…In equation (2.10), the vector a represents the off-center displacement, naturally because in this study, we consider also the case where the impurity is located out of the geometric center of the dot. To solve this equation, we proceed by the transformation used by Melingui et al [43,45]. In practice, we replace -…”

Effects of the magnetic field and the off-center displacement on the third-order nonlinear optical susceptibility of inverted core/shell spherical one-electron quantum dots

“…^where τ is the relaxation lifetime. M , i j k k represents the dipole transition matrix elements which depends on the polarization direction [46][47][48]. In case of parallel polarization [46],…”

Effects of size on the spectrum and stability of a confined on-center Hydrogen atom

“…Different models of confinement have been proposed to study the properties of confined atoms and molecules, most of which use a potential barrier to model the confinement. Among the models proposed are the infinite [55][56][57][58] or finite [59][60][61] spherical barrier, the harmonic potential [51], a parabolic confinement [62], the gaussian potential [63][64][65][66][67], the square-well potential [32,[68][69][70][71], a combination of Woods-Saxon potentials [60,72,73], and Lorenztian functions [74]. In the case of fullerenes, the use of the square-well potential or a combination of Woods-Saxon potentials provides suitable results in agreement with experiment [75].…”