The static and dynamic polarizabilities and the tune-out wavelengths of the ground state of Rb and the hyperfine ground states of
87,85Rb have been calculated by using the relativistic configuration interaction plus core polarization (RCICP) approach. It is found that the first primary tune-out wavelengths of the
5s1/2,F=1,2 states of
87Rb are 790.018187(193) and 790.032602(193) nm, respectively, where the calculated result for the
5s1/2,F=2 state is in good agreement with the latest high-precision measurement 790.032388(32) nm [R. H. Leonard et al., Phys. Rev. A 92, 052501 (2015)]. Similarly, the first primary tune-out wavelengths of the
5s1/2,F=2,3 states of
85Rb are 790.023515(218) and 790.029918(218) nm, respectively. Furthermore, the tune-out wavelengths for the different magnetic sublevels
MF of each hyperfine level
F are also determined by considering the contributions of tensor polarizabilities.
The electric dipole polarizabilities and the tune-out wavelengths for the n3S1 (n = 2, 3) states of Be2+ are determined through the application of the relativistic full-configuration-interaction approach. Our calculations directly integrate the mass shift operator into the Dirac-Coulomb-Breit Hamiltonian and further assess the quantum electrodynamics (QED) correction to the dynamic dipole polarizabilities using perturbation theory. The results reveal that the static electric dipole polarizability of the 23S1 and 33S1 states, as well as the 93 nm tune-out wavelength of the 23S1 state and the 238 nm tune-out wavelength of the 33S1 state, exhibits a high sensitivity to QED correction, which exceeds 80 ppm, providing a sensitive test for atomic structure theory.
The influence of hyperfine interactions on the tune-out wavelengths of the
39K,
40K, and
41K isotopes of the potassium atom was investigated. The hyperfine interaction of the
4s1/2 ground state results in a shift and splitting of the primary tune-out wavelength near 769 nm. The
4s1/2 state hyperfine splittings of the primary tune-out wavelength were almost equal to the hyperfine splittings of the ground states. The splittings in the wavelengths were 0.0009, 0.0026, and 0.0005 nm for
39K,
40K, and
41K, respectively. The hyperfine splitting of the
npJ levels leads to the creation of additional tune-out wavelengths. The additional tune-out wavelengths could be difficult to detect due to very small differences from the transition wavelengths to the
4pJ,F states. The hyperfine Stark shift for the ground states of all three isotopes was also computed, and the value for
39K was found to be compatible with the previous experiments and the most recent calculation using relativistic many-body perturbation theory.
Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the
6p,
7s,
7p,
8s,
8p, and
6d states and the dynamic dipole polarizabilities of the
6p and
7s states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the
7s1/2,
7p1/2,
8p1/2, and
8p3/2 states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the
6p1/2--
7s and
6p3/2--
7s transitions in the range of 488--1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the
7s1/2--
7p1/2 and
7s1/2--
7p3/2 transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the
6p1/2--
7p1/2 transition, are also evaluated and compared with available theoretical and experimental values.
Configuration interaction calculations are performed to determine the dipole polarizabilities and tune-out wavelengths for the
23S1 state in
Li+ ion. The finite nuclear mass correction is given by including the mass shift operator in the Dirac-Coulomb-Breit Hamiltonian directly, while the QED correction to dynamic dipole polarizabilities is evaluated by using the perturbation theory. The tune-out wavelengths for the
23S1(MJ=0) and $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}\phantom{\rule{0.28em}{0ex}}({M}_{J}=\ifmmode\pm\else\textpm\fi{}1)$ states are 159.620 55(6) nm and 159.631 14(6) nm, respectively. And the QED correction for 159 nm tune-out wavelength is 43 ppm. In addition, we obtain the static dipole polarizability for the $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}\phantom{\rule{0.28em}{0ex}}({M}_{J}=\ifmmode\pm\else\textpm\fi{}1)$ state to be 46.857 03(4) a.u., in which the contribution from QED is 70 ppm. The 159 nm tune-out wavelength and the static dipole polarizability of
23S1 state might provide a test of atomic structure theory.