In this thesis, we investigate few-body physics and many-body physics of ultralong-range Rydberg molecules. Ultralong-range Rydberg molecules are formed through scattering processes between Rydberg electrons and ground state atoms. The huge size of the Rydberg electron's orbit makes the Rydberg electron able to interact with more than one ground state atom in cold atomic gases with atom number densities from 10
12 cm
−3 to 10
14 cm
−3. In cold atomic gases, the ground state atoms on average are far away from each other. They are weakly interacting. Depending on the angular momentum state of the Rydberg electron, two types of polyatomic Rydberg molecules have been studied. When the Rydberg electron is in an
ns state, the isotropic probability distribution of the Rydberg electron makes the Rydberg electron interact with different ground state atoms equally. The total binding energy is a summation of the binding energy from each scattering process. These additive interactions have been studied using Cs
6s+83s and
6s+90s polyatomic Rydberg molecules in this thesis. When the Rydberg electron is in an
l>0 angular momentum state, spatial correlations between different ground state atoms are established through the anisotropic probability distribution of the Rydberg electron. The total binding energy depends on the relative positions of different ground state atoms. These nonadditive interactions are studied using Cs
6s+6s+34d and
6s+6s+36d triatomic Rydberg molecules in this thesis.
Wolfang Pauli wrote that he had gone by train to pay a visit to Niels Bohr and at the very moment of the accident in James Frank’s laboratory his train stopped for a few minutes in Gottingen station. If, before Bohr, spectroscopy was an essentially empirical science that went little farther than to catalogue absorption and emission wavelengths, the new atomic theory offered a guide to the interpretation of the experimental results and, as often happens, theory and experiment cooperated with each other to yield the interpretation of various observed phenomena. Bohr then turned his attention to molecules, obtaining correct results for the hydrogen molecule but surprisingly not so for the helium atom which also has two electrons. Otto Stern and his collaborators investigated fundamental points concerning the kinetic theory of gases, verified spatial quantization, measured the magnetic moment of the proton, verified the de Broglie relation for waves made by helium atoms etc.
We apply our new method of approach to electronic states in correlated systems [for a brief review, Part I, see: Acta Phys. Pol. B31, 2879 (2000)] to the analysis of the states and electron localization in nanoscopic chains containing up to N = 12 atoms. The Mott and the Hubbard criteria of localization are explicitly evaluated and the importance of the former is stressed. We also define the many-particle wave function and calculate it explicitly for the hydrogen molecule. Further applications of our method are listed at the end.