s-wave scattering for deep potentials with attractive tails falling off faster than -1/r{sup 2}
s-wave scattering for deep potentials with attractive tails falling off faster than -1/r{sup 2}
复制标题
深势的 s 波散射，吸引尾部脱落速度快于 -1/r{sup 2}
DOI：
10.1103/physreva.84.032701
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发表时间：
2011
影响因子：
2.9
通讯作者：
H. Friedrich
中科院分区：
文献类型：
--
作者：
T. Mueller;A. Kaiser;H. Friedrich
对于具有吸引尾部的势，如典型原子相互作用中所发生的那样，我们提出了一个简单的 s 波相移 {delta}{sub 0} 公式。它揭示了 {delta}{sub 0}(E) 对势尾的普遍依赖性以及特定于给定势的效应的影响，这些效应通过散射长度 a 进入，或者等效地，阈值量子数 n{sub th} 的非整数部分 {Delta}{sub th} 进入。该公式准确地再现了从阈值到半经典状态的{delta}{sub 0}(E)，远远超出了有效范围扩展的有效性。我们推导了 {delta}{sub 0}(E) 公式中出现的尾部函数，并证明了该公式对于与 1/r{sup 6} 或 1/r{sup 4} 成比例的有吸引力的潜在尾部以及由 1/r{sup 4} 项和不可忽略的 1/r{sup 6} 贡献组成的混合潜在尾部的有效性。
For potentials with attractive tails, as occur in typical atomic interactions, we present a simple formula for the s-wave phase shift {delta}{sub 0}. It exposes a universal dependence of {delta}{sub 0}(E) on the potential tail and the influence of effects specific to a given potential, which enter via the scattering length a, or equivalently, the noninteger part {Delta}{sub th} of the threshold quantum number n{sub th}. The formula accurately reproduces {delta}{sub 0}(E) from threshold up to the semiclassical regime, far beyond the validity of the effective-range expansion. We derive the tail functions occurring in the formula for {delta}{sub 0}(E) and demonstrate the validity of the formula for attractive potential tails proportional to 1/r{sup 6} or to 1/r{sup 4}, and also for a mixed potential tail consisting of a 1/r{sup 4} term together with a non-negligible 1/r{sup 6} contribution.