If the EM frequency $\omega$ is low enough so that the dipoles can track it then the latter behave roughly if they were in a static field, such "low" frequency can be all the way to optical. I do not thin for X-rays one can define permittivity meaningfully.

If the EM frequency $\omega$ is low enough so that the dipoles can track it then the latter behave roughly if they were in a static field, such "low" frequency can be all the way to optical. I do not think for X-rays one can define permittivity meaningfully.