Folding model analysis for 240 MeV

In order to study giant resonance induced by Li scattering, optical model (OM) analysis of Li elastic scattering is necessary to get the optical parameters. OM has been widely used to analyze the heavy ion scattering data in term of empirical Woods-Saxon (W-S) parameterizations of the nuclear potential. However, it was found that a satisfactory microscopic understanding of heavy ion scattering can be obtained if one relates the optical potential to a fundamental nucleonnucleon (NN) interaction through the double folding (DF) approach by folding this interaction with the nuclear matter distributions of both the target and projectile nuclei [1]. Since Li is a loosely bound nucleus, breakup has a large contribution to the real part of the nuclear potential and is responsible for the substantial renormalization factor NR for the real folded potential [2]. Li elastic scattering itself is very interesting. Li is in the mass number range A=4-12, where the elastic scattering show a transition between characteristics of light ions (A≤4) and characteristics of heavy ion (A≥12). Such data could provide a stronger test of the validity of any model for heavy ion potentials [3,4]. A beam of 240MeV Li ions from the Texas A&M University K500 superconducting cyclotron bombarded self-supporting Si and Mg target foil in the target chamber of the multipole-dipole-multipole spectrometer. Elastic scattering and inelastic scattering to the lowlying states were measured from 5°-35°. The calibration procedures were described in details in Refs. [5,6]. The experimental cross sections were obtained from the charge collected, target thickness, dead time and known solid angle. The cumulative uncertainties in target thickness, solid angle, etc., result in about a ±10% uncertainty in absolute cross section. Two different NN effective interactions (M3Y[7] and JLM[8]) were used to get the folded potential. Folding calculation I (FCI) used density dependent M3Y NN interaction and was described in detail by D.T. Khoa [9], while folding calculation II (FCII) with JLM effective interaction was described and discussed by F. Carstoiu et al. [10], L. Trache [11] and the references in these two papers. Two different density forms, Fermi distribution and Hartree Fork (HF) density [12], were used for target ground density during the folding procedures and are listed in Table I. The cluster-orbital shell-model approximation [13] form was used for Li ground density with FCI. FCI was carried out with code DFPD4 [14] and elastic scattering data were fitted with code ECIS[15]. The optical parameters obtained are listed in Table II. FCII and the elastic scattering fit were carried out with code OPTJLM1[16]. HF densities were used for both target and projectile. The optical parameters are listed in Table III. The angular distributions of the calculated cross-section are plotted along with data in Fig.1 for Mg and Fig.2 for Si. Both FCI and FCII give almost the same quality fits for each nucleus. The FCII fit has large oscillations at large angles than the FCI fit. A scaling factor on radius of the real optical potential is necessary to fit the elastic scattering for both Mg and Si when FCI is used. Different densities choices (as shown in Table I) will slightly change the value of the scaling factor (as shown in Table II.), but it can not