Simultaneous description of elastic, fusion and total reaction cross sections for the $\pmb{^{6}He+^{209}Bi}$ system for energies around the coulomb barrier

Abstract

A systematic and simultaneous description of elastic scattering, reaction and fusion cross sections for the system $^{6}He+^{209}Bi$ at energies below the Coulomb barrier is given within the direct reaction theory. Woods-Saxon optical potentials are used in the calculations where a cut-off parameter $% R_{F}$ is defined to separate the fusion and direct reaction absorption processes. A $\chi ^{2}-$search for energy dependent forms for the diffuseness parameter $a_{I}$ and the radial parameter $R_{I}$ of the imaginary potential $W_{\alpha }$ that best fits the experimental data is carried out. Good fits to the data are found. A relationship between the large values found for $a_{I}$ and $R_{I}$ with the large spatial extension of the halo nucleus $^{6}He$ wave function is also looked for.