2008/04/30 by H. -W. Hammer, R. Higa · 1 citation
Physics and Astronomy · #Nuclear physics research studies #Quantum Mechanics and Non-Hermitian Physics #Rare-earth and actinide compounds #cond-mat.other #nucl-th
paper · pdf · doi:10.1140/epja/i2008-10617-3
published as Eur.Phys.J.A37:193-200,2008 · 8 pages, 6 figures, EPJ style, published version
openalex publication_date 2008/07/18 · arxiv created 2008/11/18 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/31
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.