  A generic scheme to trap atoms at the magic wavelengths
($\lambda_{\rm{magic}}$s) that are independent of vector and tensor components
of the interactions of the atoms with the external electric field is presented.
The $\lambda_{\rm{magic}}$s for the laser cooling D2 lines in the Rb and Cs
atoms are demonstrated and their corresponding polarizability values without
vector and tensor contributions are given. Consequently, these
$\lambda_{\rm{magic}}$s are independent of magnetic sublevels and hyperfine
levels of the atomic states involved in the transition, thus, can offer unique
approaches to carry out many high precision measurements with minimal
systematics. Inevitably, the proposed technique can also be used for electronic
or hyperfine transitions in other atomic systems.
