ROLE OF THE SUPERSYMMETRIC SEMICLASSICAL APPROACH IN BARRIER PENETRATION AND HEAVY-ION FUSION

The problem of heavy-ion fusion reactions in the one-dimensional barri er penetration model (BPM) has been reexamined in light of supersymmet ry-inspired WKB (SWKB) method. Motivated by our recent work [Phys. Let t. A 184, 209 (1994)] describing the SWKB method for the computation o f the transmission coefficient T(E), we have performed similar calcula tions for a potential barrier that mimics the proximity potential obta ined by fitting experimentally measured fusion cross section sigma(F) (E) for the light-light and light-heavy systems. For illustration, we have first dealt with an analytically solvable potential which interpo lates between two well-known nuclear barriers such as the Morse and th e Eckart for two limiting values of the free parameter of the potentia l. Comparison of the predicted T(E) with the exact analytic ones revea ls that the present scheme yields consistently better results than tho se obtained from the WKB approximation. Furthermore, in contrast to th e WKB method, analytic continuation of our SWKB transmission coefficie nt for the corresponding potential well (obtained through the inversio n procedure) leads to exact energy eigenvalues. We have further studie d the energy dependence of the total fusion cross section for differen t processes such as O-18+C-12, F-19+C-12, O-16+Pb-208, and O-16 with e ven isotopes of Sm, using a parametrized potential barrier suggested b y Ahmed. The predicted cross sections are in agreement with values obt ained from the WKB method and with direct experimental measurements fo r the beam energy near and above the Coulomb barrier. In the case of s ub-barrier fusion, our results are substantially better than those giv en by the Hill-Wheeler parabolic approximation which overestimates sig ma(F)(E), especially for the light-ion systems.