What was found
CRW - AIRCRAFT FUELED TO 3,950 POUNDS FUEL. EN ROUTE FROM CRW TO MEM, CREW OBSERVED AN IMBALANCE OF FUEL. CROSSFEED PROCEDURES SELECTED UNTIL IMBALANCE CORRECTED. ON DESCENT INTO MEM (VFR MODERATE TURBULENCE), CROSSFEED LIGHT CAME ON, CROSSFEED WAS VERIFIED CLOSED. ON FINAL, RT ENGINE BEGAN TO SURGE, CREW ELECTED TO SHUT DOWN RT ENG AND NOTIFIED MEM THEY WERE SINGLE ENGINE AND THERE WAS NO EMERGENCY. ONCE ON THE GROUND, FUEL TANKS WERE DIP STICKED FINDING THE AFT TANKS NEAR EMPTY. RT ENG RESTARTED AND RAN NORMAL. FUEL GAUGE DEFERRED PER MEL. ACFT RETURNED TO SERVICE WITHOUT FURTHER PROBLEMS. MX CHECKED FUEL QTY INDICATING SYS CALIBRATION AND FUEL SYS AFT FUEL TANK INDICATING CORRECTED AND MEL CLEARED.