Air carrier Captain reported an NMAC during descent requiring the copilot's abrupt action to avoid a non transponder GA aircraft.

Narrative

On the arrival the copilot abruptly pushed the plane over in a descent. I knew we had to start down but I thought it was a little aggressive. When I looked up he was calling out traffic 12 O'Clock high. All I saw was a windscreen full of color X and color Y aircraft; close enough to easy read the numbers on the side of the aircraft. I felt we missed that plane by 50 to 60 ft. I thought he was going to hit our tail. But no noise. The Copilot stated that he had a hard time calling out the traffic because he was responding to the threat. We were both very startled by the appearance of the plane. The other aircraft did not have a transponder on; there was no TCAS alert and ATC did not have them on radar. I reported the issue over the radio when I got my heart out of my mouth.The only factor was that other aircraft was not using a transponder. Had the Copilot been looking down or had not caught it; there could have been two aircraft down this evening.The copilot was flying and as a former military instructor pilot he kept his head on a swivel during the descent. Thank God for that and he saw Aircraft X and reacted very quickly before we smashed into the side of the plane. Today he saved two planes and people on our aircraft. Suggestion: All light GA aircraft should have a transponder on when flying across an arrival corridor and the exact altitude that is published for the arrival fixes.