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In this study, we have investigated the influence of an external electric field on the electronic properties of the ground and excited states and studied the linear and the third-order nonlinear optical properties (i.e., absorption coefficients and refractive indices) in a spherical semiconductor quantum dot of a parabolic confinement with an on-center shallow hydrogenic impurity. In the calculations, a variational procedure was employed within the effective-mass approximation. We found that the binding energies of the ground and excited states, the absorption coefficients, and the refractive index changes of 0s-1p and 1p-2d transitions depend on the applied electric field. The results show that the existence of the electric field has great influence on the optical absorption coefficients and the refractive index changes. Also, we have found that the magnitudes of the absorption coefficient and the refractive index change of the spherical quantum dot increase for transitions between higher levels.