Elastic Scattering Of Ultracold Atom And Theoretical Study Of Spectroscopic Properties Of Diatomic Molecule Or Ion

The study of atomic collision is always one of a classical subjects of atomic and molecular physics.With the rapid development of laser cooling,evaporative cooling,sympathetic cooling and trapping techniques in magnetic-optical trap,atomic collision properties in the cold and ultracold regimes have become applicable.Ultracold atom collisions play a crucial role in the achieving of Bose-Einstein condensation?BEC?and determining the properties of condensation,and also have important impact on the formation of Fermi Degeneracy gas?FDG?,ultracold molecule and dual-species BEC.Properties of cold atom collisions has become an important research field in atomic and molecular physics.Atomic gas is diluted at low temperature.Interaction of cold atoms is mainly two-body collision and only a few partial wave contribute to scattering processes.Scattering properties of atoms are characterized through an s-wave scattering length.For example,?1?this scattering length determines the low energy elastic scattering cross sections,which is proportional to the square of s-wave scattering length,and is crucial to the success of evaporative cooling;?2?The stability of a condensation is totally controlled by the sign of the s-wave scattering length.In particular,for bosonic atoms with a>0 the possible Bose condensate is stable,whereas for a<0 it is unstable,and only a small number of atoms can be found in the degenerate state in a trap.In contrast to cold atom collision,which only have thirty year time period,the field of studying ground and low-lying excited states of diatomic molecules and ions have a long history.Although researchers have obtained a large number of spectroscopic data for diatomic molecules and ions in the past,with the further development and improvement of theoretical method and computing technology,exponentially increasing computing power,and extensive use of business software,this provide the very good basis to more accurately calculate the spectroscopic parameters and transition properties.Owing to the application in molecular structures and spectroscopy,ultracold collisions,molecular reaction dynamics,plasma physics,evolution of interplanetary medium,atmosphere environmental protection,it has attracted extensive attention in the field to study low-lying states of diatomic molecules and ions.Thesis is mainly made up of the following four parts:1?Based on the accurate triplet least-bound state energy,we calculate the triplet s-wave scattering length for cold ²³Na-⁴⁰K collisions.The s-wave scattering length is-814.1_-31⁺²⁹.₃a₀,where a0 is the Bohr radius.By using the mass scaling method,those scattering lengths also obtain for ²³Na-⁴¹K and ²³Na-³⁹K.The degenerate internal states approximation is used to estimate the scattering data of atoms which collided in different spin state.2?The s-wave scattering lengths are obtained for all stable isotope combinations of Ca atoms(except ⁴⁰Ca-⁴⁴Ca combination)and those values are very sensitive to small changes of the reduced mass.The smaller scattering length for ⁴²Ca?417.5 a₀?,compared with ⁴⁰Ca?440a₀?,shows that ⁴²Ca will be a good candidate for realizing quantum degenerate.The large interisotope scattering length between ⁴³Ca and ⁴²Ca indicates that sympathetic cooling of⁴³Ca by ⁴²Ca atoms will be effective,and ⁴³Ca-⁴²Ca can also be used to study of isotopic Bose-Fermi mixtures.The existing a d-wave shape resonance between different spin component collisions of ⁴³Ca is consistent with the theoretical prediction.3?This paper investigates the spectroscopic parameters and transition probabilities of 25low-lying states,which come from the first five dissociation channels of AlC⁺cation.The potential energy curves are calculated with the complete active space self-consistent field method,which is followed by the valence internally contracted multireference configuration interaction approach with Davidson correction.Of these 25 states,only the 3⁵?^-state is repulsive;the c¹?⁺,f¹?,and 1⁵?states have the double well;the first well of c¹?⁺state and the second well of 1⁵?state are very weakly bound;the first well of c¹?⁺state has no vibrational levels;the 2⁵?state and the double well of f¹?state have only several vibrational states;the B³?^-,E³?⁺,D³?,1⁵?⁺,2⁵?^-and 1⁵?states are inverted when the spin-orbit coupling effect is included.The avoided crossings exist between the B³?^-and 3³?^-states,the c¹?⁺and d¹?⁺states,the f¹?and 3¹?states,the 1⁵?and 2⁵?states,as well as the 2⁵?and 3⁵?states.Core-valence correlation and scalar relativistic corrections are considered.The extrapolation of potential energies to the complete basis set limit is done.The spectroscopic parameters and vibrational levels are determined for all the?-S and?bound states.The transition dipole moments are calculated.Franck–Condon factors of a great number of electronic transitions are evaluated.On the whole,the spin-orbit coupling effect on the spectroscopic parameters and vibrational levels is small except for very few states.The results determined in this paper could provide some powerful guidelines to observe these states in a spectroscopy experiment.4?The diatomic molecule BeC has a complex electronic structure with a large number of low-lying electronic excited states.The potential energy curves of X³?^-,A³?,b¹?,c¹?and d¹?⁺states of BeC are calculated by using high level ab initio calculations,which included the use of a dynamically weighted complete active space self-consistent field?DW-CASSCF?procedure.The ro-vibrational energy levels are also obtained based on the ab initio PECs.The spectroscopic parameters are determined from the ro-vibrational levels with Dunham expansion.The dipole moment,transition dipole moment and radiative lifetime also are obtained in this part.Except the A³?state,which have double well,the PECs for other four states are fitted into analytical potential energy functions using the Extended-Rydberg potential function.