The WKB Method for a Complex Potential

Abstract

The extension of the WKB method to a complex potential, as used in the optical "model of the nucleus, is discussed. The formula for the complex phase shifts is formally deduced, and its accuracy tested against exact calculations for a square potential well and a well with sloping sides. At low energies there occur large discrepancies; the WKB phases vary regularly with energy, whereas the exact values oscillate violently about the WKB values in a characteristic way and marked resonances occur. The factors affecting the accuracy of the method are discussed.