ZBW ARTCC CTLR ISSUES A VISUAL SEPARATION CLB TO A CITATION JET BELOW A B737 FLT THAT IS ON A CONVERGING COURSE.

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CONDITIONS: VMC GOOD VISIBILITY. FLT WAS CLRED DIRECT TO MANTA INTXN WITH BLM AS DEST. WE WERE ADVISED BY ZBW OF AN ACR Y ACFT AND CLRED TO CLB AFTER IDENTING ACFT WITH OUR OWN VISUAL SEPARATION. PIC PLT BEGAN CLB WITH VISUAL SEPARATION FROM CONVERGING ANGLES (ACR Y WITH ACR Y). THE CONVERGING ANGLES APPEARED SAFE FOR A CLB FROM 15000 FT TO FL230. PIC BEGAN CLB TO ABOUT 200 FT ABOVE ORIGINAL ALT THEN RECEIVED TCASI RESOLUTION TO STOP CLB AND DSNDED BACK TO ORIGINAL ALT 15000 FT; IMMEDIATELY THUS RESOLVING THE RA WITH ACR Y WITH THE ORIGINAL 1000 FT CLRNC. 1) PROB: CONVERGING ANGLES OF FAST MOVING ACFT. 2) BRIGHT SUNSHINE (DIFFICULT TO SEE IN GLARE). 3) TCASII ALERTED PROB. 4) TCASII ADVISED DSCNT FOR ACTION. SUPPLEMENTAL INFO FROM ACN 539823: THE ERROR I FEEL WAS CAUSED BY MY INACCURATE ASSESSMENT OF THE CONVERGENCE RATE AND SPD OF THE ACFT Y ACFT. AS A SAFETY ISSUE; I FEEL THAT TO HAVE GIVEN ME A VISUAL SEPARATION RESTR CLB; ON CONVERGING ACFT WAS ILL-ADVISED. SUPPLEMENTAL INFO FROM ACN 539660: WHILE IN CRUISE ON AIRWAYS INBOUND TO BDL AT 16000 FT MSL; ZBW ADVISED US OF CITATION TFC AT 2 O'CLOCK POS AND 10 MI CONVERGING AT 15000 FT. WE HAD THE TARGET ON TCASII AND FINALLY PICKED UP THE TFC AT APPROX 5 MI AND RPTED THE TFC IN SIGHT TO CTR. CTR THEN ASKED THE CITATION TO RPT US IN SIGHT. THE CITATION RPTED US IN SIGHT AND WAS GIVEN A CLRNC TO MAINTAIN VISUAL SEPARATION AND CLB TO FL280. THE CITATION ACKNOWLEDGED AND MAINTAINED 15000 FT UNTIL APPROX 2-3 MI AT OUR 1 O'CLOCK POS. HE THEN COMMENCED A CLB; WHICH SET OFF AT TCASII TA WHICH WAS IMMEDIATELY FOLLOWED BY AN RA COMMANDING US TO CLB. WE COMMENCED AN IMMEDIATE CLB AS THE COCKPIT TCASII DISPLAY ON OUR MAS SCREEN SHOWED THE CITATION CLOSING TO WITHIN 500 FT. AT THIS POINT A R TURN WAS ALSO INITIATED WITH TCASII SHOWING US CLOSING TO 300 FT OR LESS OF VERT SEPARATION AND OUR ESTIMATING LESS THAN 1 MI OF HORIZ SEPARATION. TCASII FINALLY HAD US MONITOR VERT SPD; AND CLRED OF CONFLICT AT APPROX 16800 FT MSL. CALLBACK CONVERSATION WITH RPTR ACN 539659 REVEALED THE FOLLOWING INFO: RPTR SAID HE WAS NOT COMFORTABLE WITH THE CLRNC AND ADVISED THE CAPT THAT HE DIDN'T THINK IT WAS A GOOD IDEA. HE SAID THEY WERE AT MACH .72 AT THE TIME. THE FO SAID THE CAPT HAD A BRIEF CONVERSATION WITH THE CTR LATER AND DISCUSSED THE TCASII EVENT.