A B737 CAPT RPTED THAT HE AND HIS FO STARTED TO DEBRIEF THEIR APCH DURING THE TAXI; WHICH CAUSED THEM TO FORGET IF THEY HAD RECEIVED CLRNC TO CROSS AN ACTIVE RWY.

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DURING LNDG ROLL AND BELOW 60 KIAS; CTL OF THE ACFT PASSED FROM THE FO TO THE CAPT ON HIGH SPD TXWY T. ILS APCH TO RWY 28R WAS IN USE DUE TO THE PRESENCE OF A MARINE LAYER OVER THE FIELD AND SOUTH BAY. BECAUSE OF THIS CONDITION; RWY 28L WAS BEING USED ON A VERY LIMITED BASIS; AND PREVIOUS ARRS WERE BEING GIVEN CLRNCS TO CROSS RWY 28L DURING THEIR LNDG ROLL. I (THE CAPT) CHKED THE ARR AND DEP ENDS OF RWY 28L AND SAW NO TFC. I PROCEEDED TO CROSS RWY 28L. AFTER XING; THE FO CONTACTED GND AND WE WERE CLRED TO TAXI TO THE GATE. AFTER XING RWY 28L; NEITHER PLT COULD REMEMBER RECEIVING A SPECIFIC CLRNC TO CROSS THE RWY. AFTER PARKING AT THE GATE; THE FO AND I DEBRIEFED THE SIT. IT WAS DETERMINED THAT AFTER THE FO XFERRED CTL; HE BEGAN TO REVIEW THE APCH. I ACCEPTED CTL OF ACFT AND WAS ALSO THINKING BACK TO THE APCH. THIS LACK OF VIGILANCE AND TASK AT HAND CONTRIBUTED TO THE ERROR. AS DIFFICULT AS IT MAY BE AT THE TIME; SELF CRITIQUE AND REVIEW SHOULD BE DONE AFTER THE ACFT IS PARKED AND THE ENGS SHUT DOWN.