费米子介质梯形图的全阶恢复
Resummation of fermionic in-medium ladder diagrams to all orders
摘要：
在有限密度下研究了短程相互作用正比于散射长度$a$的费米子系统。在任何顺序$a^n$，我们评估的完整贡献，每个粒子$\bar E(k_f)$的能量所产生的组合（多）粒子和空穴-空穴再散射介质中。通过简单地将粒子-空穴传播子分解为真空传播子加上介质插入，并在介质环路的$(n-1)$次幂中校正某些对称因子，可以实现这种新颖的结果。已知的低密度膨胀的结果，并包括顺序$a^4$准确地再现。$a k_f$中出现的级数可以以反正切函数上的二重积分的形式求和到所有阶。在该表示中，可以取酉极限$a\to \infty$，并且可以获得通用Bertsch参数的值$ξ= 0.5067$。我们还讨论了在低密度中子物质的状态方程的应用，并提到的再膨胀方法的进一步扩展。
英文摘要：
A system of fermions with a short-range interaction proportional to the scattering length $a$ is studied at finite density. At any order $a^n$, we evaluate the complete contributions to the energy per particle $\bar E(k_f)$ arising from combined (multiple) particle-particle and hole-hole rescatterings in the medium. This novel result is achieved by simply decomposing the particle-hole propagator into the vacuum propagator plus a medium-insertion and correcting for certain symmetry factors in the $(n-1)$-th power of the in-medium loop. Known results for the low-density expansion up to and including order $a^4$ are accurately reproduced. The emerging series in $a k_f$ can be summed to all orders in the form of a double-integral over an arctangent function. In that representation the unitary limit $a\to \infty$ can be taken and one obtains the value $ξ= 0.5067$ for the universal Bertsch parameter. We discuss also applications to the equation of state of neutron matter at low densities and mention further extensions of the resummation method.
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