  The longitudinal Coulomb C0, C2 and C4 form factors with core-polarization
effects have been studied using shell model calculations for 3/2$^+_1$ state
with excitation energy of 1.069 MeV, 5/2$^+_2$ state with excitation energy of
2.706 MeV and 7/2$^+_1$ state with excitation energy of 2.304 MeV state in
$^{27}$Al nucleus and 1/2 state in $^{31}$P nucleus. The two-body effective
interaction Wildenthal and universal sd-shell interaction A (USDA) are used for
sd-shell orbits. The Coulomb valance Tassie model (CVTM) and Bohr-Mottelson
(BM) collective model have been used to calculated the Core-polarization
effects. Three potentials are Harmonic Oscillator (HO) potential, Wood-Saxon
(WS) and SKX potential,which have been used to calculated the wave functions of
radial single particle matrix elements. The results for these potentials are
compared with final update experimental data. The calculations with inclusions
of core-polarization effects give a good agreements of experimental data.
