Hi there, Dennis,
The view of the interior of the cap looks to have tsomething similar to the eccentric or off-centre feature that takes hold of an ER family collet but that may be a trick of the light.
I suggest that you add yet another photograph, a side view of the male thread. If you have the appropriate measuring apparatus, it would also help if you give us the overall diameter of the male thread and its pitch (turns per inch).
It may throw some light on your problem if we could compare the male thread parameters with those of various members of the ER collet chuck family.
Just my two penneth.