COMPARISON OF WKB AND EXACT PENETRABILITIES THROUGH 2-PEAKED FISSION-BARRIERS

The penetrability is computed exactly through two-peaked fission barri ers consisting of three smoothly joined parabolic segments by evaluati ng accurately the Weber's cylinder functions appearing in the exact fo rmulation of Cramer and Nix. When this is compared with the penetrabil ity obtained in the WKB approximation for an identical potential barri er, it is found that the WKB transmission resonances within the interm ediate well exhibit variable amounts of energy shifts from the exact r esonances as large as 150 keV for narrow wells, for incident energies between the top and the bottom of the well. To illustrate the overall performance of the WKB method as an approximation to fission penetrabi lity calculations, the ratio of penetrabilities by the WKB and the exa ct methods is graphically presented for all the allowed incident energ ies. The influence of curvature of the intermediate well, and of adjac ent barriers on energy shifts is examined in detail. It is found that the use of accurate values of Weber's function yields spontaneous fiss ion half-lives which are about 10% higher than the values reported by Cramer and Nix.