离散尺度不变性和长程相互作用的模型研究
A Model Study of Discrete Scale Invariance and Long-Range Interactions
摘要：
我们研究了长程相互作用对束缚态谱离散标度不变性的影响。这个问题与核团簇态的有效场论描述和核中Efimov效应的表现有关。作为一个模型系统，我们选择了一个一维平方反比势补充了长程库仑相互作用。我们研究了系统的重整化和束缚态谱随库仑相互作用强度的变化。我们的结果表明，所需的反项重整化的平方反比潜力单独是足够的重整化的整个问题。然而，通过库仑相互作用的离散尺度不变性的破坏导致修改的束缚态谱。浅束缚态受库仑相互作用的影响很大，而深束缚态受平方反比势的影响很大。
英文摘要：
We investigate the modification of discrete scale invariance in the bound state spectrum by long-range interactions. This problem is relevant for effective field theory descriptions of nuclear cluster states and manifestations of the Efimov effect in nuclei. As a model system, we choose a one dimensional inverse square potential supplemented with a long-range Coulomb interaction. We study the renormalization and bound-state spectrum of the system as a function of the Coulomb interaction strength. Our results indicate, that the counterterm required to renormalize the inverse square potential alone is sufficient to renormalize the full problem. However, the breaking of the discrete scale invariance through the Coulomb interaction leads to a modified bound state spectrum. The shallow bound states are strongly influenced by the Coulomb interaction while the deep bound states are dominated by the inverse square potential.
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