ZOA Center Controller reported they vectored a descending air carrier off the STAR to avoid a VFR Corporate jet not in communication and on a conflicting course with the air carrier.

Narrative

Aircraft X was descending via the SLMMR5 arrival. Shortly before conflict alert initiated; I noticed a fast moving mode C intruder (MCI) opposite direction pointed right at SLMMR at 15500. The [unidentified VFR target] was still in NCT airspace when I noticed the confliction and when CA started; which showed me the ADS-B call sign of Aircraft Y; a frequent aircraft we work in this area. I quoted the traffic to Aircraft X; who said they were looking. At this point Aircraft X was in a fast descent below 17000; and I realized I could not stop Aircraft X above the [unidentified VFR target]. I then instructed Aircraft X to turn 30 degrees right and amended their altitude to 12000 since I took them off the STAR and wanted to get them to try to descend below traffic. Either right before or right after I issued the turn (I don't recall which); I issued a Traffic Alert to Aircraft X. I also attempted to reach out to Aircraft Y in the blind to see if they were on my frequency. Aircraft X then stated they were responding to an RA. The next update showed Aircraft Y turning right and descending. When Aircraft X stated they were clear of conflict; I cleared them direct POZUR and descended them to 12000. While the pilot did not report a NMAC; this is the closest call I've ever worked and I felt fairly shaken up after. I feel like had I not turned Aircraft X; this likely could have been a collision.After I noticed the [unidentified VFR target] was setting up to land at XXX; I called XXX ATCT to confirm the call sign; which they confirmed was Aircraft Y. While Aircraft Y didn't violate any CFRs or regulations to my knowledge; fast moving jets flying in the middle of arrival corridors VFR without receiving flight following is certainly a safety issue. While I fault myself for not noticing the conflict sooner; I know this situation would have been avoided if Aircraft Y was receiving flight following. After I got off position; I called a friend who works at XXX ATCT. Since he knows this aircraft and it frequently flies in/out of XXX; he said he would speak to the pilots just as an unofficial awareness discussion that it's advisable to get flight following when flying fast and through areas where there is likely to be other fast moving jets; like along the SLMMR arrival corridor; even though it's not required. I believe it's important that pilots are aware of the benefits to receiving flight following; especially in instances like these.