Shape and quantum size effects on the electronic structure, oscillator strengths and state lifetimes of helium-like quantum dots

Transition energies, electric static polarizability, oscillator strengths and state lifetimes of helium-like quantum dots are determined as a function of their shape and size. A configuration interaction approach based on B-spline functions is used. We found that, the oscillator strengths present an extremum around a low value of the dot radius whatever the shape of the confining potential. This extremum is due to the pressure on the energy levels in such a way that for a particular value of the dot radius, the second electron in the excited one-electron state reaches the borders of the confinement potential. The extremum position depends on the impurity charge and the oscillator strength value at this point changes with the potential well shape. As well, the increase of the effective mass involves the shift of the position of the oscillator strength extremum towards weak radius values. The first excited state lifetime globally increases with the dot radius and the reduction of the nuclear charge but presents a shoulder for a certain low value of the dot radius mostly marked for a triangular form of the confining potential.