FLC OF AN EMBRAER E120 LANDED WITHOUT CLRNC.

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ON APCH INTO RDU; WE WERE ASSIGNED OUR RWY AND CLRED FOR A VISUAL APCH AT ABOUT 7 NM OUT. WITH THE LATE RWY ASSIGNMENT; WE WERE RUSHED TO COMPLETE OUR APCH CHKLIST AND LNDG CHKLIST. ON 3-4 MI FINAL; WE HAD THE 'DOORS' WARNING LIGHT AND VOICE WARNING. WE TURNED OUR ATTN TO THE 'CARGO' DOOR LIGHT ON THE OVERHEAD PANEL. AFTER DECIDING THAT THE CARGO DOOR WOULD NOT BE A FACTOR; WE RETURNED OUR ATTN TO THE LNDG CHKLIST AND THE LNDG ITSELF. WITH THE RUSH TO COMPLETE CHKLISTS AND THE DISTR OF THE WARNING LIGHT; WE FAILED TO REALIZE THAT WE HAD NOT BEEN HANDED OFF TO THE TWR. UPON LNDG; WE CONTACTED GND; AND HE INQUIRED WHETHER WE HAD HEARD ANY TWR XMISSIONS. IT WAS THEN THAT WE REALIZED THAT WE HAD LANDED WITHOUT A CLRNC. THE CAPT SPOKE WITH THE TWR AND APCH CTLRS OVER THE PHONE AND WAS TOLD THAT NO CONFLICTS HAD OCCURRED. THIS CHAIN OF EVENTS PROVES THAT CRM CAN EASILY BREAK DOWN IN BUSY CONDITIONS DURING CRITICAL PHASES OF FLT. IN THE FUTURE WE WILL BOTH CERTAINLY BE MORE COGNIZANT OF MAINTAINING SITUATIONAL AWARENESS DURING ABNORMAL SITS. WE WILL ALSO BE TURNING ON THE TAXI LIGHT WHEN CLRED TO LAND AS A REMINDER.