The intensity of the radiation having a maximum delay [...] and other articles having a value docume

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Value documents or other articles having authentication features, authentication apparatuses, and methods of authentication are provided that relate to the use of taggants that absorb radiation from an illumination source and emit radiation in a manner that has a maximum intensity occurring a duration of time after the illumination source has been switched off. The taggants include a crystalline composition comprising a host crystal lattice doped with a first rare earth active ion, and in some examples a second rare earth active ion.