WKB approximation to subbarrier fusion

Summary

Fusion cross-sections for the astrophysically interesting reactions¹²C+¹²C,¹⁶O+¹²C and¹⁶O+¹⁶O at subbarrier energies are calculated using the Wentzel-Kramers-Brillouin (WKB) approximation. Comparison of the WKB results with those of the more commonly used Hill-Wheeler (HW) expression for transmission through a parabolic barrier indicates that the WKB approach provides a better description of fusion at subbarrier energies. The barrier for both the WKB and HW approaches is generated from the nuclear proximity, Coulomb and centrifugal potentials. The WKB approximation is then used to calculate the subbarrier fusion cross-sections for reactions involving^10,11B,^12,13C,¹⁴N and¹⁶O. The half-central-density radius parameter (C _i) of the proximity potential is determined by fitting the cross-section data of identical systems. Using the fitted values ofC _i fusion cross-sections for non-identical systems are predicted. The predicted cross-sections are found to agree well with the data.