Applications Of Relativistic Coupled-cluster Theory Based On B-spline Basis

A relativistic version of coupled-cluster theory and corresponding code are developed for atomic structure property calculations.We use the no-pair Dirac-Coulomb-Breit Hamiltonian,together with a finite B-spline basis set to expand the large and small components of the Dirac wave function.Our code has many modules including calculating the energy levels,transition matrix element,lifetimes,g-factors,hyperfine structure constants,static and dynamic polarizaribilities,and polarizability-related properties of monovalent or single-hole atomic systems.Fr is a very important candidate for the search of parity-nonconservation effects and of the permanent electric dipole moment of the electron,the analysis of these researches require accurate atomic parameters by theoretical calculations.Thus,we employ our method to calculate the atomic properties of Fr,in order to test our method and provide some useful atomic structure parameters.First,we used this method to calculate energies,reduced matrix elements and lifetimes of Fr.With these transition energies and transition matrix elements,the static and dynamic polarizabilities of many low-lying states are determined using states summation method.The tun-out wavelengths of the ground state in the range of 340-800 nm,the magic wavelengths for transition 7s-8s in the range of 800-1500 nm and the transition 7s-7p in the range of 7s,8s,and 7p states for a linearly polarized light are determined.These tun-out and magic wavelengths may be useful for laser cooling and trapping Fr atom,and for related high-precision trapping measurements.Then,we also calculate the magnetic dipole hyperfine structure constants for n(n=7-12)S,n(n=7-12)P,and n(n=6-11)D states of 212 Fr.Ignoring the influence of the field shift effect,the magnetic dipole moment m of isotope 207-213,220-228 Fr are determined by combining with experimental values for magnetic dipole hyperfine-structure constant of 7P state.These values are in good agreement with the existing measured values.However,there are a few available experimental values for Fr hyperfine-structure constants.To verify the accuracy of hyperfine-structure constants of excited states,we use the same method to evaluate hyperfine-structure constant A of the S,P and D state in Cs atom with the principal quantum number n?12,and investigate the role of electron correlation corrections.The importance of electron correlation effects,especially the nonlinear corrections of the cluster operators,is demonstrated by comparing the results of various approximations with available experimental values.Moreover,the correlation trends for individual electron correlation effects involving direct,core-polarization,and pair-correlation ones in members of Rydberg series are also investigated in the framework of the coupled-cluster theory.Some interesting features are observed.This may be useful for studying this kind short-range properties.The works of Fr and Cs demonstrate that our method can not only calculate accurately the long-range properties,but also predict reliably short-range property.In the future,we will optimize and expand this method.