| Abstract: | The dynamic polarizabilities of ${\rm 3s}^2\,^1{\rm S}_0$ and ${\rm 3s}{\rm 3p}\,^3{\rm P}_0^{\rm o}$ states of Al$^+$ are calculated using the hybrid configuration interaction and many-body perturbation theory method, and multiconfiguration Dirac-Hartree-Fock method in this work. Five ultraviolet magic wavelengths for the Al$^+$ clock transition ${\rm 3s}^2\,^1{\rm S}_0$-${\rm 3s3p}\,^3{\rm P}_0^{\rm o}$ are predicted. Although the suitable lasers are not available presently, the potential precision measurement on these magic wavelengths for the Al$^+$ clock transition would be used to extract the ratios of several certain transition matrix elements with high accuracy, and then help to improve the precision and reliability of the estimate of the BBR shift of the Al$^+$ clock transition. The differential dynamic polarizabilities at certain wavelengths are evaluated, which are useful to assess the ac Stark shift of the Al$^+$ clock transition frequency and helpful in the clock experiments to suppress the ac Stark shift of the clock transition as possible as it can. |
