I was wondering how the nucleus can influence the atomic properties (chemical and physical). I found that the mass number influences the boiling, melting and density of an atom. Also the electron wave functions depend on the number of protons. But are there also other properties of the nucleus like electric or magnetic spin which influence the atomic properties? Or do some atomic properties influence the nuclear properties?
The OP is basically searching for hyperfine interaction. Nuclei may have magnetic dipole ($I \geq) 1/2$, electric quadrupole ($I \geq) 1$) and higher moments. These moments interact with the electrons and may cause hyperfine splitting of electronic energy levels. A famous example is the 21 cm line resonance due to the hyperfine interaction of the proton (S=1/2) and electron (S=1/2) spins in neutral hydrogen atoms.
Heavy nuclei exert a strong Coulomb attraction on the inner shell electrons. This force is so strong the first, lowest energy level electrons may come very close to the nucleus. The electrons energy is also dependent on the electron-electron interactions that occur in an atom. For heavy nuclei, the lower shell electrons actually have a non-zero probability of spending time inside a nucleus. This time inside a nucleus actually screens the electrons and increases the electron-electron energy. The solution can be derived using quantum mechanics.