  In this study, we have investigated the inter-sublevel optical properties of
a core/shell/well/shell spherical quantum dot with the form of quantum
dot-quantum well heterostructure. In order to determine the energy eigenvalues
and corresponding wave functions, the Schr\"{o}dinger equation has been solved
full numerically by using shooting method in the effective mass approximation
for a finite confining potential. The inter-sublevel optical absorption and the
oscillator strength between ground ($1s$) and excited ($1p$) states have been
examined based on the computed energies and wave functions. Also, the effect of
a hydrogenic donor impurity, located at the center of the multi-shell spherical
quantum dot (MSQD), has been researched for different core radii ($R_1$), shell
thicknesses ($T_s$) and well widths ($T_w$) in certain potential. It is
observed that the oscillator strengths and the absorption coefficients are
strongly depend on the core radii and layer thicknesses of the MSQD.
