Improvements of traditional optical model and its applications in heavy-ion collision reaction

To describe the projectile-target interaction in heavy-ion collision, the traditional optical model is improved and a corresponding optical model for heavy-ion collisions is established in this work The program APOMHI is developed accordingly. In heavy-ion collisions, the mass of the projectile is comparable to the mass of target nucleus. Therefore, the projectile and target nucleus must be treated equally. The potential field for their relative motion must arise from an equivalent contribution of both nuclei, not just from the target nucleus. Consequently, the angular momentum coupling scheme must adopt <i> <b>L</b> - <b>S</b> </i> coupling, instead of <i> <b>j</b> - <b>j</b> </i> coupling. The projectile spin <i>i</i> and target spin <i>I</i> first couple to form the projectile-target system spin <i>S</i> (which varies between <inline-formula><tex-math id="M1">\begin{document}$ \left| {I - i} \right| $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ i + I $\end{document}</tex-math></inline-formula>). Then, the spin <i>S</i> of this system couples with the orbital angular momentum <i>L</i> of relative motion, forming a total angular momentum <i> <b>J</b> </i>. Thus, the radial wave function <i>U</i><sub><i>lSJ</i></sub> (<i>r</i>) involves three quantum numbers: <i> <b>l</b> </i>, <i> <b>S</b> </i>, and <i> <b>J</b> </i>, while traditional optical model only involves <i> <b>l</b> </i> and <i> <b>j</b> </i>. Furthermore, since the mass of projectile is similar the mass of target, the form of the optical model potential is symmetrical relative to the projectile and target. The projectile nucleus and the target nucleus are still assumed to be spherical, and their excited states are not considered. The projectile may be lighter or heavier than the target, but they cannot be identical particles. By using this optical model program APOMHI, the elastic scattering angular distributions and compound nucleus absorption cross sections for heavy-ion collisions can be calculated. Taking for example a series of heavy-ion collision reactions with <sup>18</sup>O as the projectile nucleus, a corresponding set of universal optical potential parameters is obtained by fitting experimental data. The comparisons show that the theoretical calculations generally accord well with the available experimental data. Here, the results for fusion cross-sections and elastic scattering angular distributions using several representative target nuclei (lighter, comparable in mass, heavier, and heavy compared to the projectile nucleus) are taken for example. Specifically, the fusion cross-section results correspond to targets <sup>9</sup>Be, <sup>27</sup>Al, <sup>63</sup>Cu and <sup>150</sup>Sm, while the elastic scattering angular distributions correspond to targets <sup>16</sup>O, <sup>24</sup>Mg, <sup>58</sup>Ni, and <sup>120</sup>Sn.