Thanks everybody for the help, and Happy New Year!
I agree the use of a collect chuck seems to be the best solution,
Howewer, I did a ring in delrin, of the same diameter of the ring groove in the cap, and same width.
I cutted in 2 half rings the first one i did, but it was difficult to keep in the right position the pen ring and the 2 half plastic rings.
I machined a new ring of the same size, and I cutted it only once. Then I shrincked it with a plyier more times, from gently to stronger, and turning the plyiers in order to apply the pressure in different points.
It worked not perfectly but quite well, even if the pen I tested has a very loose ring.
I think this could be a reasonable solution for this issue, in particular if the ring is not so loose.
See the picture here below: