【作者】 李涛；

【导师】 王宁；

【作者基本信息】 广西师范大学 ， 理论物理， 2014， 硕士

【摘要】 本论文基于Weizsacker-Skyrme (WS*)原子核质量模型对原子核电荷半径及裂变位垒进行了系统的研究。一方面,考虑原子核同位旋效应和壳效应的影响,提出一个四参数的原子核电荷半径公式。该电荷半径公式引入了新的同位旋依赖项(1-I),与传统的IA1/3形式相比,新的同位旋依赖形式使均方根电荷半径相对实验值的均方根偏差降低15%。同时引入了壳修正能的依赖项△E/A描述壳效应对电荷半径的影响,其中△E是WS*质量模型计算得到的原子核基态壳修正能。该项的引入使均方根偏差降低了17%,显著地提高了电荷半径的计算精度。由该公式计算了885个实验已测量原子核的均方根电荷半径,其均方根偏差仅为0.022fm,比Hartree-Fock-Bogolyubov (HFB21)模型的结果减小了15%。对于343个偶偶核,计算得到的均方根偏差仅为0.016fm,明显小于相对论平均场的计算结果(0.026fmm)。同时,该电荷半径公式能较好地再现幻数核的测量结果,尤其是Ca同位素链的抛物线趋势。由于较全面地考虑了体积项、表面项、同位旋及壳效应对电荷半径的影响,将该公式外推到超重核区域具有一定的可靠性,可以预言超重核的电荷半径。利用提出的电荷半径公式,我们还研究了原子核的新幻数及原子核对称能。其一,通过计算Ne同位素链的电荷半径并与实验数据比较,我们发现在中子数Ⅳ=14,16处可能存在新幻数,这一结果与核质量模型的计算结果相一致。其二,通过计算30S和30Si这一对镜像核的均方根电荷半径,发现镜像核均方根电荷半径的偏差与核物质对称能斜率参数L之间存在明显的线性关联,并由此确定了L的范围L=54士19MeV,这一结果与其它方法研得结果基本一致。另一方面,基于WS*核质量模型及现有的裂变位垒实验数据给出一种计算原子核裂变位垒的方法。我们尝试性地研究了原子核裂变准鞍点的四极形变,发现准鞍点处的四极形变与基态的四极形变之差随质量数A的增加呈现出指数递减的规律。在对准鞍点与基态形变研究的基础上,利用WS*模型得到的势能曲面计算了长椭球和球形核的裂变位垒高度,比较好的再现了实验数据。对于112个实验上已测的裂变位垒均方根偏差为1.02MeV,与ETFSI方法的结果相比均方根偏差减小了40.7%。对于锕系核均方根偏差仅为0.46MeV,均方根偏差比ETFSI方法降低了37.8%。我们还系统的计算了电荷数98≤Z≤128,中子数Ⅳ≤200的超重区域基态为长椭球和球形核的裂变位垒高度,发现基于裂变位垒高度得到的超重稳定岛中心位置Ⅳ=176～178和Z=118～120与基于WS*模型给出的基态壳修正预言的位置非常接近。更多还原

【Abstract】 In this work, the nuclear charge radii and the fission barriers of heavy nuclei have been studied by using the Weisacker-Skyrme mass model. On one hand, a four-parameter nuclear charge radii formula was proposed by considering the shell and isospin effects. A new form I(1—I) for describing the isospin effect is introduced in the formula. We note that the rms deviation with respect to the885measured nuclear charge radii can be further reduced by about15%comparing with the result from the form IA1/3. To consider the shell effect, we introduce a correction termΔE A in the proposed formula, where ΔE is the shell correction of nuclei from the WS*mass model. With the microscopic shell correction, the rms deviation in the charge radii can be reduced by17%. Based on the proposed four-parameter nuclear charge radius formula, the known experimental datas are systematically investigated. The calculated rms deviation with respect to the885measured charge radii is only0.022fm with the proposed formula, which is smaller than the result of the HFB21model by15%. For the measured rms charge radii of343even-even nuclei, the rms deviation is0.016fm, which is significantly smaller than the result (0.026fm) of the RMF calculations. The results of magic nuclei, especially the parabolic charge radii trend in the Ca chain due to the shell effect is reasonably described with the formula. Furthermore, we predict the rms charge radii with the proposed formula for some super-heavy nuclei.The proposed nuclear charge radii formula is simultaneously applied for the study of shell evolution and nuclear symmetry energy. We find new magic number N=14,16based on the charge radii variation trend of Ne chain. On the other hand, the liner relationship between the slope parameter L of the nuclear symmetry energy and rms charge radius difference of the30S-30Si mirror pair is clearly observed. The estimated slope parameter is about L=54±19MeV from the coefficient of the isospin term in the proposed charge radius formula. In addition, we propose a method for calculating nuclear fission barriers based on the WS*nuclear mass model and existing experimental datas of fission barrier. We attempt to study the quadrupole deformation of nuclei at the quasi-saddle-point in the fission path. We find that the difference between quasi-saddle-point and ground state deformation decreases with the mass numbers A which can be reasonably well described by an analytical formula. Based on the formula for the deformation at the quasi-saddle-point, we calculate the fission barriers of prolate and spherical nuclei based on the potential energy surfaces from the WS*nuclear mass model. The rms deviation with respects to the112measured fission barriers falls to1.02MeV, which is smaller than the results of ETFSI model by40.7%. For the actinide nuclei, the rms deviation is only0.46MeV, which is smaller than the results of ETFSI model by37.8%. And we systematically calculated fission barrier heights for the prolate and spherical nuclei in the range of proton numbers98≤Z≤128and neutron numbers N≤200. The predicted central position of the super-heavy island could lie around N=176～178and Z=118～120according to the calculated fission barriers of nuclei, which is very close to the predicted position based on ground state shell corrections from the WS*nuclear mass model.更多还原