| In this paper, theα-cluster structures of the even-even lighter nuclei with the same numbers of proton and neutron were studied by applying the Glauber theory and the optical model respectively, combined with the independentα-cluster model,to the particle-nucleus and nucleus-nucleus elastic scattering reactions. Both theα-cluster structures in these nuclei and the effectiveness of the models were verified.By fitting the parameter formula to the observedπ--αelastic scattering data, we obtained a set of parameters, which can be used to calculateπ+-αelastic scattering in the intermediate energy range, with fitting the experimental data ofπ+-αelastic scattering differential cross sections. With the parameter formula ofπ+, the consideration of angular distribution of differential cross sections can be separated toπ+ andπ-, then the results was compared with the experimental data to analysis the difference betweenπ+ andπ-. According to the similarity of theory and experiment, the applicability ofα-cluster model and Glauber theory was discussed, and a set of reliable parameters will be useful for future work.According to the adjustable parameters figure, the function curve, which was drawn fitting the parameter formula ofπ--αelastic scattering, ofπ+ as the incident particle can be satisfactory with the experimental data. To test the reliability of this set of parameters and the applicability of parameter formula, in this paper, the experimental data ofπ±-28Si elastic scattering which cover a wider range of energy was used for comparison, it was still a good match. Meanwhile, the Coulomb correction and isospin correction can be included into theα-cluster model, and the difficulty of calculation can be simplified. Also, even in such a nucleus 28Si, which has more nucleons, the trend of nucleus in the form ofα-cluster is still clear.In order to applyα-cluster model of dealing with the nuclei with valence nucleons outside the filled shells, wave functions of shell model were taken into account, specifically, the angular distribution of differential cross sections ofπ±-14C,π±-26Mg,π±-34S,π±-42Ca elastic scattering were discussed. As mentioned earlier, the characteristics of this type of nuclei is seen as an integer number ofαparticles and two valence nucleons outside the filled shells, for example, 14C is composed of 3αparticles and two neutrons. Scattering process can be regarded as the combination of two kinds of sub-processes,π±-αandπ±-n. For the former, all the advantages ofα-cluster model was kept, and the parameters obtained above can still be used. For the latter, the neutron wave function is given by the shell model. Although the scattering process ofπ±toα-cluster part is similar, theoretically, the same with the above, to neutron, which in different states, is distinguishing. It can be seen from the derivation of this article, theoretically, to distinguish between different states of isospin, and this is a great improvement.Comparison with experimental data showed that, in the calculations ofπ±-14C,π±-42Ca scattering can be satisfactory with the it better thanπ±-26Mg andπ±-34S. Considering that our deduction is rigorous, the deviation between the theories and the experiments may be generated by the physical model used is too simplified. For example, if we consider it more carefully, the two valence nucleons was not only fill in a single particle level, rather should be a few single particle near the Fermi level are taken into account.To solve this problem, adjustable parameters can be given as the probability in each state to disposal of nuclear reaction with the mixed states. However, we have to add three adjustable parameters for a mixture of three single-states. Even if there is a good accordance, strong persuasion does not exist, unless adequate experimental data verify the theory. Due to very little experimental data is available that if an experiment corresponding to a set of parameters, there is no universality, and the verification will be meaningless. Look forward to more experiments to enrich the verification. As the third task of this article, the independentα-cluster model was used to study nucleus-nucleus scattering. As both the incident nucleus and target nucleus have theα-cluster structures, the double folding method can be used toα-αinteraction potential between them and density distribution ofα-cluster in nucleus, to construct the real part of the nucleus-nucleus interaction potential. On the other hand, the Woods-Saxon potential was used as the imaginary part of the interaction potential to simulate the process of absorption. Typical of the interaction potential with imaginary part is the optical potential.To deal with the optical potential, the distorted wave Born approximation was used. Taking into account that it is elastic scattering process and the nuclear force is short range one, so the optical potential can be regarded as a perturbation, and then, the Born approximation could be used. As for the distorted wave, Coulomb interaction exists between the incident nucleus and the target nucleus, and the Coulomb force is a long-range one, thus the plane wave distorted by the Coulomb force field, in other words, the incident wave function is the Coulomb distorted wave function.After comparing with the experiments, the calculated results are not consistent with the experiment data. Taking into account that, the process of derivation is rigorous expect the Born approximation was used in the theoretical analysis, it seems to indicate that the optical potential can not simply be regarded as a perturbation, and separated from the wave function of nucleus. In other words, optical potential has impact on the internal structure of the nucleus. This issue needs further study.
|
PDF Full Text Request