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arXiv 1211.2103nucl-thnucl-ex
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缺中子铅区偶偶核低激发态的超平均场计算

Systematics of low-lying states of even-even nuclei in the neutron-deficient lead region from a beyond-mean-field calculation

J. M. Yao, M. Bender, P. -H. Heenen

摘要:

位于缺中子铅区的原子核具有复杂的结构,随着中子和质子数的变化而迅速演化。最著名的例子是$^{186}$ Pb,其中三个最低能级是$0^+$态,两个受激的$0^+$态位于600 keV左右的低激发能。在相邻核中发现了具有不同性质的共存结构。在过去的几年中,已经进行了许多实验,其中带内和带外$γ$跃迁概率已经被测量。实验数据的详细解释需要使用一种超越平均场方法的方法,该方法允许确定光谱和跃迁概率。这种方法已经应用于这个质量区域的选定同位素。我们的目的是提供一个系统的调查,这个质量区,以确定如何以及实验数据可以理解使用国家的最先进的方法原子核结构。我们的方法的出发点是一组平均场波函数产生的轴向四极矩的约束,并使用Skyrme能量密度功能。通过将平均场波函数投影到角动量和粒子数上,并将对称性恢复的波函数作为轴向四极矩的函数混合,引入了超出平均场的相关性。与现有的数据进行了详细的比较,能量,电荷半径,光谱四极矩,$E0$和$E2$的中子缺Hg,Pb,Po和Rn同位素链的跃迁几率。我们的结果和基本的平均场之间的联系进行了分析。虽然我们的研究结果表明,实际的能量密度泛函必须进一步提高,以实现定量协议的数据得到定性协议。

英文摘要:

Nuclei located in the neutron-deficient Pb region have a complex structure, rapidly evolving as a function of neutron and proton numbers. The most famous example is $^{186}$Pb where the three lowest levels are $0^+$ states, the two excited $0^+$ ones being located at low excitation energy around 600 keV. Coexisting structures with different properties are found in the neighboring nuclei. Many experiments have been performed over the last few years in which in-band and out-of-band $γ$ transition probabilities have been measured. A detailed interpretation of experimental data requires the use of a method going beyond a mean-field approach that permits to determine spectra and transition probabilities. Such methods have already been applied to selected isotopes in this mass region. Our aim is to provide a systematic investigation of this mass region in order to determine how well experimental data can be understood using a state-of-the-art method for nuclear structure. The starting point of our method is a set of mean-field wave functions generated with a constraint on the axial quadrupole moment and using a Skyrme energy density functional. Correlations beyond the mean field are introduced by projecting mean-field wave functions on angular-momentum and particle number and by mixing the symmetry restored wave functions as a function of the axial quadrupole moment. A detailed comparison with the available data is performed for energies, charge radii, spectroscopic quadrupole moments, $E0$ and $E2$ transition probabilities for the isotopic chains of neutron deficient Hg, Pb, Po and Rn. The connection between our results and the underlying mean field is also analyzed. Qualitative agreement with the data is obtained although our results indicate that the actual energy density functionals have to be improved further to achieve a quantitative agreement.

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