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A theoretical comparison has been made for some calcium isotopes (${}_{20}$Ca) which are even–even nuclei and have the atomic mass (Z = 20) with its previous experimental data. Theoretical calculations of some ${}_{20}$Ca isotopes (A = 42, 44, 46, 48, 50, 52) adopted by the shell model theory were performed to calculate the transition rate B(E2), theoretical intrinsic quadruple moments ($Q_{0\mathrm{\text{Th}}})$ and theoretical deformation parameters (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$ were calculated by two methods by using different effective interactions for each isotope such as, su3fp, fpbm, fprkb, fpd6, kb3. Through code NuShellX@MSU, the single-body density matrix was calculated. The effects of the core polarization were neglected by adopting various effective charges that were employed, effective charges of conventional (Con-E), effective charges of standard (St-E) and effective charges of Bohr and Mottelson (B-M-E) which were calculated. The theoretical values of the B(E2)_Th, the $Q_{0\mathrm{\text{Th}}}$ and the (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$ were then compared with the previous experimental data where values of the transition rate B(E2)_Th, theoretical intrinsic quadrupole moments $Q_{0\mathrm{\text{Th}}}$ and theoretical deformation parameter (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$, using the fpbm, the fpd6 and the kb3 interactions were the best.

Beyond the second row of elements in the Mendeleev periodic table, the consideration of the relativistic effect is important in determining proper configurations of atoms and ions, in many cases. Many important quantities of interest in determining physical and chemical properties of matter, such as the effective charge, root mean square radii, and higher moments of radii used in many calculations, e.g. in the determinations of legend stabilization bond energies depend on whether the treatment is relativistic or not. In general, these quantities for a given l-orbital having two different j-values, e.g. and , differ from each other, hence, making it necessary to treat them as separate orbitals. This also necessitates characterizing bands with their j-values in many instants and not l-values, particularly for “d” and f-orbitals. For example, in Au, and are to be dealt with as two distinct bands. The observed enhancement of laser induced field emission in W, which is not understood in terms of non-relativistic band-structures, can be explained in terms of the expected relativistic band structure. Spin-orbit coupling, which is the manifestation of the relativistic effect, is a prime factor in facilitating intersystem crossing in bio-molecules.

Beyond the second row of elements in the Mendeleev periodic table, the consideration of the relativistic effect is important in determining proper configurations of atoms and ions, in many cases. Many important quantities of interest in determining physical and chemical properties of matter, such as the effective charge, root mean square radii, and higher moments of radii used in many calculations, e.g. in the determinations of legend stabilization bond energies depend on whether the treatment is relativistic or not. In general, these quantities for a given l-orbital having two different j-values, e.g. and , differ from each other, hence, making it necessary to treat them as separate orbitals. This also necessitates characterizing bands with their j-values in many instants and not l-values, particularly for “d” and f-orbitals. For example, in Au, and are to be dealt with as two distinct bands. The observed enhancement of laser induced field emission in W, which is not understood in terms of non-relativistic band-structures, can be explained in terms of the expected relativistic band structure. Spin-orbit coupling, which is the manifestation of the relativistic effect, is a prime factor in facilitating intersystem crossing in bio-molecules.