The five longest tune-out wavelengths for the potassium atom are determined using a relativistic structure model which treats the atom as consisting of a single valence electron moving outside a closed shell core. The importance of various terms in the dynamic polarizability in the vicinity of the 4pJ , 5pJ and 6pJ transitions are discussed.
The lowest 3 tune-out wavelengths of the four alkaline-earth atoms, Be, Mg, Ca and Sr are determined from tabulations of matrix elements produced from large first principles calculations. The tune-out wavelengths are located near the wavelengths for 3 P o 1 and 1 P o 1 excitations. The measurement of the tune-out wavelengths could be used to establish a quantitative relationship between the oscillator strength of the transition leading to existence of the tune-out wavelength and the dynamic polarizability of the atom at the tune-out frequency. The longest tune-out wavelengths for Be, Mg, Ca, Sr, Ba and Yb are 454.9813 nm, 457.2372 nm, 657.446 nm, 689.200 nm, 788.875 nm and 553.00 nm respectively.
A relativistic description of the structure of heavy alkali-metal atoms and alkali-like ions using S-spinors and L-spinors is developed. The core wave function is defined by a Dirac-Fock calculation using an S-spinor basis. The S-spinor basis is then supplemented with a large set of L-spinors for calculation of the valence wave function in a frozen-core model. The numerical stability of the L-spinor approach is demonstrated by computing the energies and decay rates of several low-lying hydrogen eigenstates, along with the polarizabilities of a Z = 60 hydrogenic ion. The approach is then applied to calculate the dynamic polarizabilities of the 5s, 4d, and 5p states of Sr +. The magic wavelengths at which the Stark shifts between different pairs of transitions are 0 are computed. Determination of the magic wavelengths for the 5s → 4d 3
High-precision multipole polarizabilities, α for 4 of the 1s ground state of the hydrogen isoelectronic series, are obtained from the Dirac equation using the B-spline method with Notre Dame boundary conditions. Compact analytic expressions for the polarizabilities as a function of Z with a relative accuracy of 10 −6 up to Z = 100 are determined by fitting to the calculated polarizabilities. The oscillator strengths satisfy the sum rules i f ( ) gi = 0 for all multipoles from = 1 to = 4. The dispersion coefficients for the long-range H-H and H-He + interactions are given.
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