The quasirelativistic contact interaction and effective electron and spin densities at the nucleus: A model based on weighting the electron density with the finite Gaussian nucleus model

•Alternative approach for effective electron density of the Gaussian nucleus.•Weighted electron density with normalized distribution of the Gaussian nucleus.•Effective spin density for the Gaussian nucleus can also be obtained.•Consistent with the effective density obtained via derivative of the total energy.•Effective density evaluated using finite-field differentiation of nuclear potential.