PA28 PLT TAKES EVASIVE ACTION TO AVOID CLBING TFC IN PSP AIRSPACE.

Narrative

I WAS CAPT OF ACFT #1; A PA32R; ON THE FLT BEING DISCUSSED. THE FLT DEPARTED EMT ENRTE TO UDD. I PICKED UP FLT FOLLOWING AFTER DEP FROM EMT. I WAS PASSED TO PSP APCH UPON REACHING BANNING ARPT AT A CRUISING ALT OF 5500 FT. PSP TOLD ME TO STAY N OR OVER INTERSTATE 10 ABOVE 3500 FT ON MY TRANSITION TO UDD. I ACKNOWLEDGED. SHORTER AFTER; I WAS TOLD THAT THERE WOULD BE A B737 DEPARTING PSP CLBING NBOUND. I REPLIED; 'LOOKING.' WHEN THE ACFT WAS AIRBORNE; APPROX 2 MI AWAY; I ACKNOWLEDGED THAT THE ACFT WAS IN SIGHT. I WAS TOLD TO MAINTAIN VISUAL WITH THE TFC; WHICH WAS CLBING. THE B737 WAS ADVISED OF MY POS AND ALT BUT DID NOT HAVE ME IN SIGHT. THE DAY WAS QUITE HAZY AND IT WAS DIFFICULT TO APPROXIMATE HIS RATE OF CLB. HOWEVER; SEVERAL TIMES I HAVE BEEN NOTIFIED OF THE SAME TFC DEPARTING IN SIMILAR SITS AND THE TFC HAS ALWAYS BEEN SEVERAL THOUSAND FT ABOVE US AND NO FACTOR; EVEN FOR WAKE TURB. AS THE ACFT APCHED; I REALIZED THAT WE WERE ON A COLLISION COURSE. TO AVOID THE ACFT I MADE A SHARP R TURN AND DSNDED TO 2500 FT. THE B737 APPEARED TO MAINTAIN AT 3500 FT AND CONTINUE STRAIGHT AHEAD. AFTER CLR OF TFC; I RETURNED TO 3500 FT AND RESUMED MY INITIAL FLT PATH. IMMEDIATELY; THE B737 RPTED A TCASII 500 FT WARNING. APCH REPLIED BY SAYING THAT MY ACFT HAD THE B737 IN SIGHT. I TRIED TO EXPLAIN THAT EVEN THOUGH I HAD THEM IN SIGHT IT WAS DIFFICULT TO JUDGE DISTANCE BECAUSE OF THE HAZE. I ALSO EXPLAINED THAT I WAS UNDER THE IMPRESSION THAT THE B737 WAS CLBING AND FIGURED HE WOULD BE WELL ABOVE US PRIOR TO XING MY PATH. THE APCH CTLR REPLIED 'ROGER' AND NOTHING ELSE WAS SAID ABOUT THE SIT. I BELIEVE THAT THE CAUSE OF THIS NEAR MISS WAS A MISCOM ON THE PART OF ALL PARTIES INVOLVED. A POSSIBLE SOLUTION TO THE PROB MIGHT BE AN ALT RESTR PLACED ON THE DEPARTING TFC WHEN 2 ACFT WILL BE XING IN SUCH CLOSE PROX. ANOTHER SOLUTION MIGHT BE A CHANGE OF HDG FOR THE CRUISING ACFT TO KEEP CLR OF THE TFC. THIS SIT MADE ME REALIZE HOW DIFFICULT IT CAN BE TO DETERMINE RATE OF CLB AND FLT PATH ON A HAZY DAY; EVEN WHEN YOU HAVE TFC IN SIGHT. I BELIEVE THE SIT BECOMES MORE DANGEROUS WHEN YOU HAVE 2 ACFT OF SUCH DIFFERENT PERFORMANCE CAPABILITIES.