Study of the electronic structure and electron impact excitation cross section of helium impurities in spherical quantum dots

This manuscript is devoted to explore the atomic structure and electron impact excitation process of atom impurities in quantum dots. To achieve this goal, a method that solves the fully relativistic Dirac equation within the framework of relativistic configuration interaction is proposed. The Gaussian potential is used, which can accurately describe the location of impurities in quantum dots and their local effects on the surrounding electron cloud. The coupled Dirac equation is modified to include a new central potential, providing solutions that include both the continuous and bound state wave functions. The process of electron impact excitation is elucidated using the distorted wave method, all within the framework of relativistic Dirac theory. For illustrative purposes, a detailed investigation of the excitation energies, transition rates, wave functions, and excitation cross sections is carried out for a wide range of confinement strengths of the potential and quantum dot radii, using the helium impurities in spherical quantum dots as an example. Our results reveal that for a given confinement strength of the potential, the bound state wave functions are initially pulled into the inner region by the attractive Gaussian potential well, but eventually reflect the free atom scenario at large quantum dot radii. In contrast, the continuous electron wave functions exhibit monotonic variations as a function of the quantum dot radii. Such behavior of the wave functions gives rise to distinctive phenomena in the variation of excitation energies, transition rates, and excitation cross sections in relation to the potential parameters. Good agreement between the present results and existing data, where available, is obtained. This work holds importance not only for basic research in atomic physics but also for the optical and electronic applications of quantum dots. I.e., in the design and optimization of quantum dot lasers and quantum dot sensors.