Dipole and quadrupole oscillator strengths have been calculated for the series of transitions nl → n l (n 5) in a hydrogen atom confined in the centre of a sphere with impenetrable walls. The non-monotonic dependence of the oscillator strengths on the radius of confinement has been discussed through their general forms obtained with a properly chosen radial wavefunction. It was qualitatively ascribed to variation of the radial electron density distributions of the states involved in the transitions. The effect of the confinement on the use of the dipole approximation has been studied, introducing a correction through the octupole term as well as performing the calculation with the full form of the interaction term.

Articles you may be interested inAccurate ab initio ro-vibronic spectroscopy of the X ̃ 2 Π CCN radical using explicitly correlated methods An ab initio study of the vibronic, spin-orbit, and magnetic hyperfine structure in the X Π 2 electronic state of NCO An ab initio study of the hyperfine structure in the X 2 Π electronic state of CCCH Ab initio study of the vibronic and spin-orbit structure in the X 2 Π electronic state of CCCH Potential energy surfaces for the electronic states of the HCCS radical correlating at linear nuclear arrangement with the A 2 ⌸ state are calculated by means of an extensive ab initio approach. They are used to compute the vibronic and spin-orbit structure of the A 2 ⌸ -X 2 ⌸ electronic transition. These calculations are carried out by means of a new variational approach based on the use of normal bending coordinates. The results of calculations question various interpretations of the available experimental data; on the other hand they do not offer reliable explanation of all features observed, pointing in this way at the shortages of the present, as well as of previous theoretical handling of the problem in question.

Using the Numerov–Cooley numerical method, we report several interesting characteristics of the eigenspectrum of 2D hydrogen atom confined inside an impenetrable circular boundary of radius ρc. At the confinement radius, ρc, exactly equal to the location of the only radial node of the unconfined atom state (l + 2, l), the successive pairs of the confined atom states (nl) and (n + 1, l + 2), where n ⩾ l + 2, are found to become degenerate. Accurate calculations of static dipole polarizability are reported for several confining radii using the standard second-order perturbation theory.

An isotropic 3D harmonic oscillator centrally enclosed in a spherical box with impenetrable walls is treated by analytical methods. It is explicitly shown how imposing the Dirichlet boundary condition on the wavefunctions results in (a) the complete removal of any systematic degeneracy of levels, and (b) the constant energy difference of exactly two harmonic oscillator units between all successive pairs of the confined excited states defined by the orbital quantum numbers l and l + 2, specifically when the radius of the spherical box is chosen to be the position of the only radial node in the first excited-state wavefunction of the unconfined harmonic oscillator for a given l. The lowest confined state of the given l is excluded in defining the successive pairs of excited confined states.

The eigenspectral properties of the 2D isotropic harmonic oscillator, centrally enclosed in the symmetric box with impenetrable walls, are studied for the first time using the annihilation and creation operators and the infinitesimal operators of the SU(2) group. It is shown explicitly how the imposition of the Dirichlet boundary condition at a certain uniquely prescribed confinement radius leads to the energy difference of two harmonic oscillator units between all successive pairs of the confined states, defined by the projection angular momentum quantum numbers [m, m ± 2] such that the lowest energy state corresponding to the chosen m is excluded in the first pair.