Optical Potential Folding Model

A method of calculating the one body density matrix(OBDM) of a nucleus on the basis of the mean field shell model is proposed, and its validation is also checked. The nucleon density and momentum distributions are calculated and compared with those of Hatree-Fock-Bogolubov theory and experimental data, respectively.The folding model is an important theory not only for calculating and analyzing the scattering data, but also for the study of nuclear structure. The exchange term of the folding potential is the main resource of the energy dependence, and the accuracy of the calculated exchange term dependents on the accuracy of the OBDM. So calculating the OBDM accurately is very important for the folding model.At first, the OBDM calculated in the shell model with Woods-Saxon potential is introduced into the single folding model. Such the local approximation used in the previous calculations is eliminated. And the local approximation of the OBDM is checked using the OBDM of shell model as the exact value. The effect of the local approximation on the folding potential is also checked. By using the folding potential as the real part of the optical potential, and the imaginary part of the optical potential of Koning-Delaroche, the angular distribution of elastic scattering is calculated. And the effect of the local approximation on the angular distribution of elastic scattering is analyzed. The calculated results are compared with those of JLM model. The single folding model with the shell model OBDM is applied in analyzing p,n+²⁸Si,³²S,⁴⁰Ca, ⁵⁸Ni and ⁹⁰Zr elastic scattering data.The OBDM is also introduced into the double folding model to calculate and analyzeαparticle elastic scattering data. In the double folding model, the effects of the local approximation on the folding potentials and elastic scattering cross sections are analyzed not only for the light nuclei, but also for the heavier nuclei like ⁵⁸Ni and ⁹⁰Zr. With the OBDM of the shell model introduced into the folding model, the exchange part of the folding potential is calculated accurately, and the folding model has a better physical foundation.