The non-relativistic static and dynamic dipole polarizabilities of a hydrogen atom experiencing a cylindrical confinement are investigated. Two methods based on B-splines are used for computations of energies and wavefunctions. The first method is a variational-based method while the second one proceeds by a fit of the non-separable Coulomb potential in the product form. The computed energies compare very well with previous computations. They converge, as well as the dipole polarizability, to the exact unconfined free atom values with increasing basis size. The fit approach is found to be advantageous, as it helps to reduce the computational time without loss of accuracy.
The non-relativistic static and dynamic dipole polarizabilities of the ground and lowest excited states of the hydrogen atom, off-center in a spherical cavity, were investigated using B-Splines. For this purpose, the off-center Coulomb interaction, commonly evaluated by a multipole expansion was obtained in a different and faster approach. In the nearly centered case, the results obtained with a spherically symmetric description were recovered. The convergence tests performed showed the robustness of the numerical code used for these new calculations, and enabled us to carry out computations of the polarizabilities of the ground and lowest excited states of the off-center Hydrogen atom, as as function of the cavity radius and the distance from the center.
The energy levels, electric dipole polarizabilities of helium/helium-like quantum dots and endohedrally confined helium/helium-like atoms are studied via a configuration interaction method coupled with a B-spline based variational approach. The systems are characterized by their energies and the results compared with those reported in literature. The electric dipole polarizability sensitivity is observed to be tailored by the parameters characterizing the electronic confinement which as well quenches the nuclear effects on the behavior of the system when it is subjected to an external electric field. For the quantum dots, the polarizability decreases with the confinement strengthening while the endohedral confinement strengthening is observed to enhance the dipole polarizability.
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.
The energy levels, ground state binding energies, and electric dipole polarizabilities of hydrogenic impurities in quantum dots and quantum nanowires have been investigated using a non-relativistic B-spline based variational method. Firstly, we have worked on the characterization of those impurities (donor/electron) in quantum dots and quantum nanowires, considering the two cases where the impurity is centered or off-centered in the nanostructure. Secondly, the electric dipole polarizabilities have been computed and their sensitivity with confinement parameters investigated. So the energies, binding energies, and dipole polarizabilities were reported for the centered and the off-centered donor and electron impurities as a function of the cavity radius and the off-center displacement. We found that the polarization of the studied system greatly depends on the model potential form, the off-center displacement, and the cavity radius. In the case of quantum dots and for the parabolic potential, the convergence of the polarizability for large values of the quantum size is shown. For the quantum nanowire case, we have shown that the polarizability is greater in the case of the z axis displacement than that of the transversal one. This leads to the fact that the system is more polarizable when the impurity is moved along the z axis than the transversal one.
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