Role of non-coplanarity in nuclear reactions using the Wong formula based on the proximity potential

Abstract

we assessed Wong's formula for its angular momentum $\ell$-summation and "barrier modification" effects at sub-barrier energies in the dominant fusion-evaporation and capture (equivalently, quasi-fission) reaction cross-sections. For use of the multipole deformations (up to ${\beta }_4$) and (in-plane, $\Phi$=0${}^0$) orientations-dependent proximity potential in fusion-evaporation cross-sections of ${}^{58}$Ni+${}^{58}$Ni, ${}^{64}$Ni+${}^{64}$Ni and ${}^{100}$Mo, known for fusion hindrance phenomenon in coupled-channels calculations, and the capture cross-sections of ${}^{48}$Ca+${}^{238}$U, ${}^{244}$Pu and ${}^{248}$Cm reactions, forming superheavy nuclei, though the simple $\ell$=0 barrier-based Wong formula is found inadequate, its extended version, the $\ell$-summed Wong expression fits very well the above noted capture cross-sections at all center-of-mass energies $E_{c.m.}$'s, but require (additional) modifications of the barriers to fit the fusion-evaporation cross-sections in the Ni-based reactions at below-barrier energies. Some barrier modification effects are shown \cite{kumar09} to be already present in Wong expression due to its inbuilt $\ell$-dependence via $\ell$-summation.

Comments: DAE 2010, Pilani, Rajasthan