Accurate Calculations Of Tune-out And Magic Wavelengths For Low-lying States Of He

Helium is the most simple many-electron atomic system, and is also an important research object in precision measurement physics. Theoretical calculations of atomic structure and experimental measurements of transition spectrum for helium play important roles in developing many-electron atomic structure theory, determining physical constants and extracting nuclear structure information. The polarizabilities of helium, which describe the respond of an atom to an external field, have an important application in analyzing Ac/Dc Stark shift of precision spectrum measurements. The tune-out or magic wavelength is the wavelength at which the Ac Stark shift of a quantum state or transition vanishes. Tune-out and magic wavelengths have novel and important applications in cooling and trapping atoms, accurate estimations of transition matrix elements and test of quantum electrodynamic theory. For example, the combination of theoretical calculation and experimental measurement of the 413 nm tune-out wavelength for helium 23 S state, can provide a nonenergy test of QED theory. And in order to improve the precision for the measurement of nuclear charge radius of helium, the accurate magic wavelength of 319.8 nm for the 21 S → 23 S transition is used to design the optical dipole trap.In this thesis, we develop independently the configuration interaction(CI) program based on B-spline functions and perform large-scale parallel calculations, which improve the precision of theoretical calculations for energies, wavefunctions and transition matrix elements, and provide reliable theoretical results of polarizabilities, tune-out and magic wavelengths. The specific contents are as follows,(1) In the frame of nonrelativity, the static dipole polarizabilities in the length, velocity and acceleration gauges for helium 23 S, 33 S, 23 P and 33 P states are calculated, and the agreements between values in the length and velocity gauges are at the level of 10-7accuracy. Also a series of tune-out and magic wavelengths in the visible and infrared region are determined. The 413 nm tune-out magic wavelength of 23 S state for∞He,4He, and3 He are respectively 413.038 28(3), 413.139 19(2) and 413.172 22(2) nm, which improve the hybrid value of Mitroy and Tang. Moreover, the magic wavelength of 1066 nm for the23 S → 33 P transition can be expected to determine the ratio of transition matrix elements(23S → 23P)/(33P → 63S), which provides a unique way to obtain accurate transition matrix element involved in highly excited states.(2) Under the frame of relativity, the value of 413.084 5(4) nm for the tune-out wavelength of helium 23S1 state, which includes finite nuclear mass and relativistic corrections,is obtained. The present value for the MJ= 1 sublevel reduces the discrepancy between the previous theoretical calculation and experimental measurement from 134 ppm to 19 ppm.Magic wavelengths in the visible region for the doubly forbidden transition of 21 S → 23 S are obtained, which improve the semi empirical results and providing more reliable magic wavelengths.(3) The finite nuclear mass and relativistic corrections to energies, polarizabilities, tuneout and magic wavelengths have been considered, and also QED effect is must be included.First, the term called Bethe logarithm, which is in the leading QED correction to energies,is calculated by using present NRCI method. Bethe logarithms for n3S(n = 2- 9) states of helium are calculated, and the relative uncertainties for n3S(n = 2- 5) states have reached to about 10-7to 10-8.(4) The NRCI program is extended to the calculations of the Li+ions. Dynamic polarizabilities and tune-out wavelengths for 23 S, 33 S, 23 P and 33 P states, and magic wavelengths for the 23 S → 33 S, 23 S → 23 P, and 23 S → 33 P transitions are obtained. The finite nuclear mass corrections to energies, oscillator strengths, dynamic polarizabilities,tune-out and magic wavelengths are considered as well. Present calculations will provide reliable theoretical input data for cooling and trapping Li+, and analyzing Ac/Dc Stark shift in experiments.