A B737-300 ON APCH AT 8000 FT DECLARED AN EMER AND DIVERTED DUE TO LOSS OF TRAILING EDGE FLAP CTL CAUSED BY R FLAP XMITTER.

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FLT WAS CONDUCTED WITHIN NORMAL PARAMETERS FROM DEP AT ZZZ UNTIL WE WERE APPROX 25 MI SW OF ZZZ1 AND ON APCH TO RWY 4R. THE ALT WAS APPROX 8000 FT MSL; AND THE INDICATED AIRSPD WAS APPROX 210 KTS. I CALLED FOR FLAPS 1 DEG; THEN FLAPS 2 DEGS; AND THEN FLAPS 5 DEGS. I HEARD THE FO MOVE THE FLAP HANDLE THROUGH THE DETENTS. HE THEN STATED WE HAD A FLAP PROB. I THEN LOOKED AT THE FLAP GAUGE AND AT THE LEADING EDGE INDICATOR LIGHTS. THE AMBER 'LEADING EDGE FLAPS TRANSIT' LIGHT WAS ILLUMINATED AND THE 2 FLAP NEEDLES WERE SPLIT. THE NEEDLE FOR THE L FLAP WAS JUST PRIOR TO THE #1 SETTING ON THE GAUGE AND THE NEEDLE FOR THE R FLAP WAS JUST OUT OF THE UP POS. I LOOKED AT THE LEADING EDGE DEVICES ANNUNCIATOR PANEL OVERHEAD AND OBSERVED THAT THE LEADING EDGE FLAPS INDICATOR LIGHTS WERE ALL GREEN AND THE LEADING EDGE SLATS INDICATOR LIGHTS WERE ALL ILLUMINATED IN THE 'EXT' POS. I DIRECTED THE FO TO REQUEST RADAR VECTORS. ATC GAVE US HEADINGS AND ASSIGNED US AN ALT. I THEN DIRECTED THE FO TO READ THE NON-NORMAL CHKLIST FOR ASYMMETRICAL TRAILING EDGE FLAPS. WHILE READING THE CHKLIST; THE FO READ THE 'CAUTION' THAT PERTAINS TO THE ALTERNATE FLAPS SWITCH. I CALLED FLT CTL. I EXPLAINED OUR SIT TO THE DISPATCHER. I TOLD HIM I PREFERRED TO DIVERT TO ZZZ2 INTL ARPT WHERE THE WX WAS BETTER THAN AT ZZZ1. HE CONCURRED; AND TOLD ME HE WOULD SEND FUEL BURN NUMBERS. WE THEN ASKED ZZZ1 CTR FOR A NEW CLRNC TO ZZZ2. THEY GAVE US A CLRNC AND ASSIGNED US AN ALT. ENRTE TO ZZZ2; I BRIEFED THE FLT ATTENDANTS AND I MADE A PA. WE ALSO DECLARED AN 'EMER' WITH ATC. WE ACCOMPLISHED THE 'TRAILING EDGE FLAPS UP LNDG' CHKLIST DURING THE APPLICABLE PHASES OF OUR DSCNT; APCH; AND LNDG. WHEN WE WERE ESTABLISHED ON AN APPROX 15 MI FINAL FOR RWY 4L AT ZZZ2; I CALLED FOR GEAR DOWN AND THE 'DEFERRED ITEMS -- BEFORE LNDG CHKLIST.' THE FO READ THE FIRST ITEM; WHICH SAYS 'ALTERNATE FLAPS MASTER SWITCH...ARM.' I CHOSE TO OMIT THIS STEP (AND THE SECOND STEP: 'ALTERNATE FLAPS POS SWITCH (230 KTS MAX...MOMENTARY DOWN)' OF THE 'DEFERRED ITEMS -- BEFORE LNDG' CHKLIST. THIS DECISION WAS BASED ON THE 'CAUTION' IN THE 'ASYMMETRICAL TRAILING EDGE FLAPS' CHKLIST WHICH WARNED AGAINST USING THE ALTERNATE FLAPS SWITCH WHEN ASYMMETRICAL FLAPS ARE PRESENT. I THEREFORE DETERMINED THAT THE SAFEST COURSE OF ACTION WAS TO DECLINE THE USE OF THE ALTERNATE FLAP SWITCH. CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THIS AIRPLANE HAD A LONG MAINT HISTORY OF TRAILING EDGE FLAP ASYMMETRICAL FAILURES. THE RPTR SAID THE LOGBOOK HAD A CHRONIC HISTORY OF ASYMMETRICAL TRAILING EDGE FLAP SHUTOFFS AND WORK ACCOMPLISHED FROM GND CHK OK'S TO FLAP POS INDICATOR REPLACEMENTS. THE RPTR STATED THE MOST RECENT WORK WAS REPLACEMENT AND CALIBRATION OF THE L TRAILING EDGE FLAP POS XMITTER. THE RPTR SAID THE CORRECTIVE ACTION WAS REPLACEMENT AND CALIBRATION OF THE R TRAILING EDGE FLAP POS XMITTER.