NMAC BTWN AN LTT AND A SMA SEL HOMEBUILT ACFT AT THE INTXN OF 2 RWYS DURING LNDG ROLL.

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WHILE LNDG AT JMS ARPT WE HAD A NEAR COLLISION WITH A HOMEBUILT ACFT. CONDITIONS ON THE FIELD WERE CLR SKIES; 20 PLUS MI VISIBILITY AND WINDS WERE LIGHT AND VARIABLE. WE WERE APCHING FROM THE SW AND DECIDED TO LAND ON RWY 4. WE MADE RADIO CALLS FOR A 20 MI FINAL RWY 4; 15 MI FINAL RWY 4; 10 MI FINAL RWY 4; 5 MI FINAL RWY 4 AND SHORT FINAL RWY 4 OVER THE ADVISORY FREQ. AS THE NOSE WHEEL WAS TOUCHING DOWN DURING OUR LNDG; I (THE CAPT) NOTICED A HOMEBUILT ACFT XING OUR RWY ABOUT 3500 FT IN FRONT OF US. BOTH THE FO AND I HIT THE BRAKES AND REVERSE PWR. WE SKIDDED OVER 2000 FT; WHILE THE HOMEBUILT CROSSED FROM OUR L TO R. WE MISSED HIM BY ABOUT 25 FT. WE BLEW OUT 2 TIRES AND ENDED UP REPLACING ALL 4 MAIN TIRES. THE HOMEBUILT PLT LANDED ON RWY 13 AND WAS TAXIING TO THE GENERAL AVIATION RAMP. HE SAID HE DIDN'T SEE US. THE HOMEBUILT HAD NO RADIOS NO ELECTRICAL SYS. WE BOTH LOOKED FOR TFC; THE FO AND MYSELF; WHILE ON APCH TO RWY 4 AND NEVER SAW THE HOMEBUILT. TO AVOID THIS IN THE FUTURE; AS FAR AS THE FLC GOES; WE COULDN'T HAVE LOOKED ANY HARDER FOR TFC. WE JUST DIDN'T SEE THE HOMEBUILT. AS FAR AS THE HOMEBUILT GOES; HAD HE HAD A HANDHELD RADIO THIS WOULD HAVE BEEN AVOIDED. ALSO; I FEEL; THE HOMEBUILT PLT COULD NOT HAVE LOOKED BEFORE XING THE RWY. IT'S HARD TO MISS A 16000 LB AIRPLANE WITH 3 LNDG LIGHTS.