Center Controller reported an aircraft on an instrument approach took evasive action in response to a TCAS/RA for a VFR aircraft not in communication with ATC.

Narrative

Aircraft X arrival from ZZZ cleared for RNAV Y XX via ZZZZZ. Normal operation from south until turning on procedure from ZZZZZ1. Aircraft X received several timely traffic calls and eventually reported traffic in sight. Aircraft X responded with descent from RA. Large range since I had multiple sectors but I am sure they are less than safe distance despite the pilots taking the actions. Less than 500 ft. with a SR22 and jet ? Calls were made into blind and glad we at least had ADSB. It appears that the SR22 never made a move from the jet. Hope that was a good thing in this case.Add this to the Sector XX unsafe sector folder please. We call the traffic and do what we can when we can. It is extremely difficult to predict VFR traffic movements with many uncontrolled VFR approaches that meander within this area along with holds and transient aircraft that are not in communication. With the 25 to 30 aircraft routinely within 20 miles of the VOR and this normal approach configuration so many times we thread our IFR traffic through dangerous situations.