study of the spin-orbit interaction effects on energy levels and the absorption coefficients of spherical quantum dot and quantum anti-dot under the magnetic field

In this study, the energy levels of spherical quantum dot (qd) and spherical quantum anti-dot (qad) with hydrogenic impurity in the center, in the presence of spinorbit interaction (soi) and weak external magnetic field have been studied. to this aim, solving the schrodinger equation for the discussed systems by using the finite difference method, the wave functions and energies of these systems are calculated. then the effect of the external magnetic field, system radius size and height of potential barrier on the energy levels and also the linear, nonlinear and total absorption coefficients, (acs), of the mentioned systems are studied. numerical results show that the soi in both models causes a split of 2𝑝 level into two sub-levels of 2𝑝1/2and 2𝑝3/2 where the low index indicates the total angular momentum j. also, considering the electron spin, under an applied magnetic field, the 1𝑠 and 2𝑝 levels split into two sub-levels and six sub-levels, respectively. furthermore, in this research, it is proved that energy changes are significantly different as a function of radius size and height of the potential barrier in qd and qad models and the acs of these systems behave differently according to the incident photon energy at the same condition.