论文标题
弱结合的两中子晕核的通用特性
Universal Properties of Weakly Bound Two-Neutron Halo Nuclei
论文作者
论文摘要
我们构建了一个有效的现场理论，即在限制的极限中，在两个中性分离能量$ b $和中子中子内部的两体虚拟能量$ε_n$比问题中的任何其他能量尺度都小，但是核心和单个中子之间的散射不是细调的，并且efimov效果不可能运行。该理论具有一个无量纲的耦合，可正式运行到紫外线中的兰道极。我们表明，该系统的许多属性在双重调整限制中是通用的。发现均方根半径和电荷半径的比率为$ \ langle r^2_m \ rangle/\ langle r^2_c \ rangle = a f（ε_n/b）$，其中$ a $ a $是core的质量和$ f $是该比率$ $ $ $ε_n/b $的功能，我们可以找到我们的比例。特别是，当$ b \ggε_n$，$ \ langle r^2_m \ rangle/\ langle r^2_c \ rangle = \ frac23 a $。 $ e1 $偶极强度函数的形状也仅取决于比率$ε_n/b $，并以显式分析形式得出。我们估计，对于$^{22} $ c核对我们理论的核心校正额度为20％或更少，如果两次中子分离能量小于100 keV，而$^{20} $ c核之间的$ s $ wave散射长度小于2.8 fm。
We construct an effective field theory of a two-neutron halo nucleus in the limit where the two-neutron separation energy $B$ and the neutron-neutron two-body virtual energy $ε_n$ are smaller than any other energy scale in the problem, but the scattering between the core and a single neutron is not fine-tuned, and the Efimov effect does not operate. The theory has one dimensionless coupling which formally runs to a Landau pole in the ultraviolet. We show that many properties of the system are universal in the double fine-tuning limit. The ratio of the mean-square matter radius and charge radius is found to be $\langle r^2_m \rangle/\langle r^2_c\rangle = A f(ε_n/B)$, where $A$ is the mass number of the core and $f$ is a function of the ratio $ε_n/B$ which we find explicitly. In particular, when $B\ggε_n$, $\langle r^2_m\rangle/\langle r^2_c\rangle = \frac23 A$. The shape of the the $E1$ dipole strength function also depends only on the ratio $ε_n/B$ and is derived in explicit analytic form. We estimate that for the $^{22}$C nucleus higher-order corrections to our theory are of order 20% or less if the two-neutron separation energy is less than 100 keV and the $s$-wave scattering length between a neutron and a $^{20}$C nucleus is less than 2.8 fm.
