Calculation of fusion reaction cross-section and angular momentum window of 6 li , 16 o , 56 fe and 86 kr on fusion reaction with 208 pb at e lab = 500 mev

Fusion reaction cross-section and angular momentum values help in identifying the possibility of occurrence of a fusion reaction. Fusion cross-sections of heavy ion reactions have been calculated using the semi-classical approach with heavy ions as projectiles. In this model of calculation of fusion reaction cross section, three potentials have been used namely: Coulomb potential, nuclear potential and centrifugal potential. Fusion reactions between the pairs of heavy ions have been studied and their crosssection calculated in semi classical formulation using one-dimensional barrier penetration model, taking scattering potential as the sum of Coulomb, centrifugal and proximity potential. Ion-ion interaction potentials have been calculated and various quantities of interest obtained from their potential curves. The quantities of interest are then used in the calculation of fusion reaction cross-section and angular momentum window. The calculated theoretical values of interest have been found to agree with the experimental values with a small variation of less than ten percent. The calculated V1B values of 6 Li+ 208 Pb, 16 O+ 208 Pb and 56 Fe+ 208 Pb reactions were found to be 32.92MeV, 80.49MeV and 234.99MeV respectively, while the experimental values are 30.10MeV, 74.90MeV and 233.0MeV respectively. The calculated fusion cross-sections are found to be 292.88mb for 6 Li+ 208 Pb, 314.00mb for 16 O+ 208 Pb and 182.60mb for 56 Fe+ 208 Pb reactions. It has also been found out from the results that heavy ions can undergo fusion reaction even though there is an enormous Coulomb repulsive force associated with the heavy ions. INTRODUCTION Due to the short deBroglie wavelength of heavy-ions compared to the size of the ions, classical approximations for low energy collisions are expected to be good at least for the macroscopic features of heavy-ion reactions such as fusion and deep inelastic collision. Therefore, classical macroscopic approaches have been widely used in which one chooses the relevant collective degrees of freedom and then invokes suitable mechanisms for transfer of energy from the collective degrees to the frozen internal degrees of freedom (Godre et al., 1989; Bucham, 1988 and Zetili, 2007). The knowledge of a variety of accelerators in the last few decades has made it possible to accelerate not only protons, deuterons and alpha-particles, but also heavy ions like carbon, nitrogen and oxygen among others. During the last forty years very heavy-ion beams like those of krypton, xenon and uranium have been used as projectiles to study a variety of nuclear reactions between complex heavy ions. A new field of heavy ions physics has, therefore, opened up with a number of promising applications (Flerov and Barashenkov, 1975). The study of fusion of complex heavy nuclei and the structure of nuclei at high excitation energy and angular momentum has become the centre of attraction for theoretical as well as experimental nuclear physicists worldwide in recent years. The most interesting aspect of heavy ion physics lies in the fact that the classical and semi classical theories are capable of explaining many features of heavy ion elastic, inelastic scattering fusion and other reactions. International Journal of Physics and Mathematical Sciences ISSN: 2277-2111 (Online) An Online International Journal Available at http://www.cibtech.org/jpms.htm 2012 Vol. 2 (4) October-December pp.72-87/Bitok et al. Research Article 73 It has been shown (Burcham, 1988 and Marmier and Sheldon, 1970) that under appropriate conditions, heavy-ion reactions may clearly show a classical character. The criterion for heavy-ion reactions which qualify to be treated classically can be expressed as v e Z Z  2 2 1   > unity ..............................................................................................(1) A condition satisfied for most of the cases in heavy-ion reactions (Burcham 1988). Here  is known as Sommerfeld parameter and is the ratio of distance of closest approach “dmin” and deBroglie wavelength 2  associated with the projectile. The total ion-ion interaction potential,   r Vtotal for the heavy-ion pairs is written as; (Dutt and Puri, 2010 and Santhoshi et al., 2008).         r V r V r V r V l centrifuga nuclear Coulomb total   