In the present work, the calculations have been performed for dispersion interaction between heavy elements $({\mathrm{Zn}}^{+},$ ${\mathrm{Cd}}^{+},$ ${\mathrm{Hg}}^{+},$ ${\mathrm{Pb}}^{+}, \mathrm{Zn}, \mathrm{Cd}, \mathrm{Hg}, \mathrm{and} \mathrm{Pb})$ with graphene and carbon nanotubes by evaluating van der Waals $C_3$ coefficients using the well-known Lifshitz theory. The dispersion coefficients are expressed in terms of reflection coefficients of graphene and carbon nanotubes which are calculated within the framework of the Dirac model. In addition, accurate values of dynamic dipole polarizabilities at imaginary frequencies of considered ions and atoms which are vital have been calculated using relativistic methods. The comparisons of our calculated static dipole polarizabilities for the considered elements with the values reported in the literature are also presented. The dispersion interactions of the considered heavy elements with the graphene and carbon nanotubes of different radii in a wide range of separation distances have been studied. The results have also been analyzed with another subtle variable, i.e., the gap parameter of the graphene wall. The interaction coefficients obtained for both the materials, i.e., for graphene and carbon nanotubes, are mutually compared and it is found that graphene can be said to be a preferable material for adsorption of these toxic heavy elements.

The scalar and tensor components of the electric quadrupole (E2) polarizabilities of the first two excited states of all the alkali-metal atoms are determined. To validate the calculations, we have evaluated the ground state E2 polarizabilities of these atoms and compared them with the literature values. We could not find the ground state E2 polarizability value for Fr in the literature to compare with our result. The dominant parts of these quantities are estimated by combining the precisely calculated E2 transition matrix elements of many low-lying transitions with the experimental energies, while the other contributions are estimated using lower-order methods. Our estimated values for the ground states of the above atoms are in good agreement with the literature values suggesting that our estimated E2 polarizabilities for the excited states of the alkali atoms, which were not known earlier except for the Li atom, are also quite accurate. These reported E2 polarizabilities could be useful in guiding many precision measurements in the alkali atoms.

In the present work, we determine the $C_5$ coefficients along with their uncertainties due to quadrupole polarization effects of all the alkali atoms interacting with a metal (Au), a semiconductor (Si), and four dielectric materials (${\mathrm{SiO}}_2, {\mathrm{SiN}}_x$, yttrium aluminum garnet, and sapphire). The required dynamic electric quadrupole ($E2$) polarizabilities are evaluated by calculating $E2$ matrix elements of a large number of transitions in the alkali atoms by employing a relativistic coupled-cluster method. A significant contribution towards the long-range van der Waals potential is made by the quadrupole polarization effects. Our finding shows that contributions from the $C_5$ coefficients to the atom-wall interaction potentials are pronounced at short distances (1–10 nm). The $C_3$ coefficients of a Fr atom interacting with the above material media are also reported. These results could be useful in understanding the interactions of alkali atoms trapped in different material bodies during high-precision measurements.

Light shift in a state due to the applied laser in an atomic system vanishes at tune-out wavelengths (${\lambda }_T$s). Similarly, differential light shift in a transition vanishes at the magic wavelengths (${\lambda }_{magic}$s). In many of the earlier studies, values of the electric dipole (E1) matrix elements were inferred precisely by combining measurements and calculations of ${\lambda }_{magic}$. Similarly, the ${\lambda }_T$ values of an atomic state can be used to infer the E1 matrix element, as it involves dynamic electric dipole ($\alpha$) values of only one state whereas the ${\lambda }_{magic}$ values require evaluation of $\alpha$ values for two states. However, both the ${\lambda }_{magic}$ and ${\lambda }_T$ values depend on angular momenta and their magnetic components (M) of states. Here, we report the ${\lambda }_{magic}$ and ${\lambda }_T$ values of many $S_{1/2}$ and $D_{3/2,5/2}$ states, and transitions among these states of the Mg${}^{+}$, Ca${}^{+}$, Sr${}^{+}$ and Ba${}^{+}$ ions that are independent of M values. It is possible to infer a large number of E1 matrix elements of the above ions accurately by measuring these values and combining with our calculations.