Sr-20 instructor pilot reported an near midair collision during initial approach with an unreported ...

Narrative:

While flying on an IFR flight plan were being vectored for the RNAV 31 at ZZZ. After receiving and turning to a vector to intercept the approach course; upon leveling the aircraft we saw a bonanza at our same altitude; within 50 meters of our nose crossing in front of us from left to right. The bonanza was close enough I could see the pilot and clear aircraft detail. Immediately the student and I pitched and banked away from the aircraft to maneuver away. Right afterward; ATC asked us if that aircraft was at our same altitude. I then stated that he was and reported a 'near miss'. The rest of the flight resumed and we completed an approach at ZZZ. Enroute back to ZZZ1; ATC provided us with a phone number and instructed me to contact them after landing. I promptly called after landing and gave them my oral narrative of what happened.I think that perhaps ATC is being overworked. Throughout the flight we did receive many traffic advisories. However there was none for this event. Neither the student or I would have been able to see the bonanza during the vector turn because we were busy setting up for the approach; and turning. To my knowledge the bonanza was VFR and not talking on frequency.

Original NASA ASRS Text

Title: SR-20 Instructor Pilot reported an NMAC during initial approach with an unreported aircraft.

Narrative: While flying on an IFR flight plan were being vectored for the RNAV 31 at ZZZ. After receiving and turning to a vector to intercept the approach course; upon leveling the aircraft we saw a Bonanza at our same altitude; within 50 meters of our nose crossing in front of us from left to right. The Bonanza was close enough I could see the pilot and clear aircraft detail. Immediately the student and I pitched and banked away from the aircraft to maneuver away. Right afterward; ATC asked us if that aircraft was at our same altitude. I then stated that he was and reported a 'near miss'. The rest of the flight resumed and we completed an approach at ZZZ. Enroute back to ZZZ1; ATC provided us with a phone number and instructed me to contact them after landing. I promptly called after landing and gave them my oral narrative of what happened.I think that perhaps ATC is being overworked. Throughout the flight we did receive many traffic advisories. However there was none for this event. Neither the student or I would have been able to see the Bonanza during the vector turn because we were busy setting up for the approach; and turning. To my knowledge the Bonanza was VFR and not talking on frequency.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.

Attributes
ACN	1739790
Time
Date	202004
Local Time Of Day	1201-1800
Place
Locale Reference	ZZZ.Airport
State Reference	US
Environment
Flight Conditions	VMC
Light	Daylight
Aircraft 1
Make Model Name	SR20
Operating Under FAR Part	Part 91
Flight Phase	Initial Approach
Flight Plan	IFR
Aircraft 2
Make Model Name	Beechcraft Single Piston Undifferentiated or Other Model
Operating Under FAR Part	Part 91
Flight Phase	Cruise
Flight Plan	None
Person 1
Function	Instructor Pilot Not Flying
Qualification	Flight Crew Multiengine
Events
Anomaly	Conflict NMAC

Sr-20 instructor pilot reported an near midair collision during initial approach with an unreported aircraft.