团簇有效场论中的${}^{\ \ \ 6}_{ΛΛ} He$
${}^{\ \ \ 6}_{ΛΛ} He$ in cluster effective field theory
摘要：
用团簇有效场论对超核$ΛΛα$作为三体团簇系统进行了研究。我们发现，当积分方程中的截止值达到渐近极限时，三体接触相互作用存在极限环，因此应将其提升到首阶。我们还导出了一个确定方程的极限环再现数值得到的极限环。研究了$\nuclide[6][ΛΛ]{He}$的$Λ$双分离能$B_{ΛΛ}^{}$与$S$波$ΛΛ$散射长度$a_{ΛΛ}^{}$之间的相关性.在这种方法中的规模的作用进行了讨论。
英文摘要：
The hypernucleus $\nuclide[6][ΛΛ]{He}$ is studied as a three-body ($ΛΛα$) cluster system in cluster effective field theory at leading order. We find that the three-body contact interaction exhibits the limit cycle when the cutoff in the integral equations is sent to the asymptotic limit, and thus it should be promoted to leading order. We also derive a determination equation of the limit cycle which reproduces the numerically obtained limit cycle. We then study the correlations between the double $Λ$ separation energy $B_{ΛΛ}^{}$ of $\nuclide[6][ΛΛ]{He}$ and the scattering length $a_{ΛΛ}^{}$ of the $S$-wave $ΛΛ$ scattering. The role of the scale in this approach is also discussed.
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