Optical Model Analysis for Fusion Excitation Functions and Elastic Scatterings

Abstract

In heavy-ion fusion reaction, a short range imaginary potential Ws is explicitly introduced as the effect of the compound nucleus formation. The parameters of Ws obtained are found to be independent of scattering systems by analyzing experimental fusion excitation functions. For the elastic scattering, we add to the complex potential V +i Ws a long range imaginary potential WL due to direct reactions and find the resulting optical potential to be able to reproduce the experimental data of the angular distributions and excitation functions. The analysis for the fusion excitation functions has been carried out for the systems: 12C+12C, 14N + 12 C, l'O+ 12 C, 1'0+ 1 '0, l'O+ 24 Mg, l'O+ 27 AI, l'O+40Ca, 28Si+28Si and 40Ca+40Ca. For the two systems: 14N + 12C and 1'0 + 40Ca, the analysis for the elastic scattering has also been carried out. Considerable amount of the experimental data for the fusion excitation functions have been accumulated for many years. 1 l-1 2 ) For the light heavy-ions, the fusion excitation function is almost equal to the total reaction cross section in the low energy region. 13 ) In this energy region, the fusion or the total reaction cross sections are determined mainly by the penetration of the outer potential barrier. Above the certain energy (hereafter denoted as E bend ), however, the fusion excitation function becomes smaller than the total reaction cross section due to the significant contribution to the direct reactions. These behaviors for the fusion excitation functions are qualitatively inter­ preted by using the critical angular momentum Ie 14) which is a function of incident energy. In the energy region above E bend, contribution from the incident partial wave to the fusion reaction is limited up to Ie less than lmax, where lmax is associated with the maximum partial wave contributing to the total reaction cross section. In the energy region below Ebend, Ie becomes larger than lmax. Since any reactions do not occur beyond lmax, limitation on the incident partial wave is not Ie, but lmax in this energy region. 15 ) There are two different ways to determine Ie. The one is the way describing it in terms of the entrance channel quantities. A typical model is the Glas-Mosel model,15) in which the energy dependence of Ie is determined by introducing the energy independent critical radius Re~ 1.0(Ai /3 + A~/3) for fusion. 14 ) The other way relates Ie to the quantities concerning the compound nuclear states. In the