Quantum Effects In The Nuclear Mass And Elastic Scattering Between Identical Nuclei

The nucleus is a quantum mechanical many-body system.The quantum effect of nucleus mainly occur in two aspects:?1?For nuclear structure,the quantum effect is reflected as the shell effect since the state of each nucleon in the nucleus is quantized and the nucleon is in a series of discrete single particle energy levels;?2?For nucle-ar reaction,the quantum effect is reflected as interference or diffraction effect since the microscopic particles have wave-particle duality and the motion of microscopic particles is described by wave functions.In terms of the quantum shell effect in the nu-clear structure,some related studies have found that the traditional magic number may change dramatically depending on the N/Z ratio when we move towards the particle drip lines and found that there are great differences in the shell structure of the nucle-us obtained with different model parameters.Meanwhile,in the terms of the quantum interference effect in nuclear reactions,we find that the quantum interference effec-t of pure Coulomb scattering between two-identical-particle has a direct relationship with the closest distance between the projectile nucleus and the target nucleus.This relationship provide us with a method to directly extract the information of nucleus-nucleus interaction potential from measured data and reduce the model dependence.It is therefore of great significance to study the quantum effect in the nuclear structure and the elastic scattering between two-identical-particle.Firstly,by using the Weis???cker-Skyrme?WS4?nuclear mass model,the influence of the statistical uncertainties of model parameters on the shell effect is investigated.The statistical uncertainties in the 15 model parameters of the WS4 mass model are investigated considering the weak correlations between the parameters of the macro-scopic part and those of the microscopic part.The statistical uncertainties in the depth of the Woods-Saxon potential V₀and the strength of spin-orbital potential?₀are rela-tively large,both of which are related to the shell effect in the nuclear mass.In order to further study the influence of the statistical uncertainties of model parameters on the shell correction energy,the nuclear mass change caused by the statistical uncertainties of model parameters are investigated.We find that the nuclear mass near the magic number are sensitive to the model parameters which are related to the shell effect,e-specially the Woods-Saxon potential radius coefficient r₀.The statistical error in the predicted energy of a certain nucleus in its ground state is estimated by the maximal energy uncertainty due to the statistical uncertainties of model parameters.The dis-crepancies from the experimental data are almost all smaller than the statistical errors estimated with the proposed approach.In addition,the parameter uncertainties and sta-tistical errors of WS4 mass model and WS*mass model are compared.The statistical uncertainties of model parameter in the WS4 mass model is reduced by 10%?50%compared with the WS*mass model.Secondly,the relationship between the quantum interference effect of the pure Coulomb scattering of identical particles and the closest distance between the projec-tile nucleus and the target nucleus is proposed for the first time.Based on the assump-tion that the scattering angle of identical particles at head-on collision is around 90⁰,we derive the relationship between angle separation of pairs of Mott scattering valleys around 90⁰and the closest distance between the projectile nucleus and the target nucle-us,which is tested by the 4 different identical particle reaction partner.The extracted result are in good agreement with the empirical closest distance formula predictions.The Coulomb barrier for⁵⁸Ni+⁵⁸Ni are also extracted and compared simultaneously with some model predictions.We find that the extracted result is in good agreement with the three empirical nucleus-nucleus interaction potentials.The deflection function for the Coulomb scattering between identical particles is also studied.We find that quantum interference evidently affects the deflection function for scattering between two identical nuclei if the two nuclei approach to each other close enough,which veri-fies our assumption.In addition,the elastic scattering angular distributions for¹⁶O+¹⁶O at energies below and above the Coulomb barrier are studied with an optical potential model,and the Coulomb barrier position extracted from the quantum interference effect is in good agreement with the those from optical potential.