A Systematic Study Of Nuclear Pairing Gaps And Deformation Energies

As one of the basic quantities in nuclear physics,the nuclear masses(nuclear binding energy)have always attracted a lot of attentions.At present,about 3000 nuclear masses have been measured experimentally,and the theoretical prediction of about 5000 nuclear masses are still not measured,so the theoretical calculation of nuclear masses and the analysis of prediction power are particularly important.Most of the stable nuclides in nature are even-even nuclei.It indicates that the binding energy is larger when the number of protons and neutrons in the nucleus exist in pairs.This pairing interaction(pairing correlation)causes an odd-even masses difference(oddeven effect)in the formula for atomic mass and affects nuclear deformation.One usually extracts the pairing gaps by using the odd-even masses difference between neighboring nuclei.However,the odd-even masses difference also includes the contribution of shell effects,deformation effects,isospin effect and other residual effects.Systematic analysis of the correlation between odd-even masses difference and these residual effects is helpful for the purification of pairing gaps and provides an alternative method for extracting shell correction energy,which is of great importance.The collective model of the nucleus proposes that there is deformation in the nucleus.The difference between the energy of the nucleus in the ground state and the energy in the spherical state,it is called nuclear deformation energy.Almost all nuclei have collective vibration motion,so it is necessary to analyze the relationship between deformation energy and shell correction energy,and as well as that between the pairing gaps and nuclear deformation parameters.On the one hand,based on the extracted pairing gaps from AME2016,using the Pearson's correlation coefficient,the correlation between pairing gaps and pair energy,shell correction and isospin asymmetry are analyzed.Four formulas are used to calculate the experimental pairing gaps,and the contribution of various residual effects in the odd-even masses difference are analyzed.It is found that the pairing gaps is highly correlated with the pair energy and it indicates that pairing correlation is the most important factor affecting the odd-even masses difference.Compared with the pairing gaps of the surrounding nuclei,the pairing gaps of the magic number nuclei calculated by each formula has a mutation,so it can be seen that the shell effect has a certain influence on the odd-even mass difference.The nucleus can be divided into four categories by the parity of the number of protons and neutrons,and then we have analyzed systematically the correlation between pairing gaps shell correction.The results basically show that there is a significant correlation between the two and the five-point formula has the strongest correlation.It indicates that the contribution of shell correction in the odd-even masses difference cannot be ignored.It provides an alternative method for calculating or testing shell correction energy by systematically analyzing the connection between the two.At the same time,we analyze the correlation between the pairing gaps and the isospin asymmetry degree through the isotope chain,and found that some of them showed highly correlated characteristics.Which provides a possible way to improve the nuclear mass model.On the other hand,based on the nuclear deformation parameters and deformation energy given by WS4 nuclear masses model,we study the correlation between nuclear deformation energy and nuclear deformation,shell correction and pairing gaps.The results show that there is a strong correlation between the nuclear deformation energy and the nuclear deformation parameters.For the region where the proton number Z is magic number and N is non-magic number,they have the strongest correlation,and the correlation coefficient equals 0.821.The correlation coefficient between the deformation parameters of the double magic nucleus and the shell correction equals 0.915,indicating that the ground state of the double magic nuclei also have a weak deformation state slightly deviating from the sphere,and the stronger the shell correction is,the more spherical the nucleus tends to be.For some large deformed nuclei,such as N=100,N=105,the deformation parameters are highly correlated with the shell correction.The strong correlation between deformation and shell correction may provide an indirect method for extracting shell correction.Finally,the correlation between the nuclear deformation energy and the pairing gaps is studied.The results show that the correlation coefficient between the nuclear deformation energy and pairing gaps is about 0.8 in the region of the double magic nuclei.