  The polaron binding energy and effective mass in a degenerate polar gas is
calculated in the fractional-dimensional approach under plasmon pole
approximation.The effect of carrier densities on the static and dynamic
screening correction of the electron-phonon interaction and electron-electron
interaction to the polaronic propertis is calculated from electron
self-energies within the second-order perturbation method. The Hubbard local
field factor has been used for the static screening correction in the polaronic
properties. We found that polaronic properties decrease with increase with
carrier density and dimensionality of the system.
