{"title":"Universality for Three Bosons with Large, Negative Effective Range: Aspects and Addenda","authors":"Harald W. Grießhammer","doi":"10.1007/s00601-024-01923-3","DOIUrl":null,"url":null,"abstract":"<div><p>Resummed-range Effective Field Theory is the consistent non-relativistic Effective Field Theory of point interactions in systems with large two-body scattering length <i>a</i> and an effective range <span>\\(r_0\\)</span> large in magnitude but negative. Its leading order is non-perturbative, and its observables depend only on the dimensionless ratio <span>\\(\\xi :=2r_0/a\\)</span> once <span>\\(|r_0|\\)</span> is chosen as base unit. This presentation highlights aspects for three identical spinless bosons and adds details to a previous discussion (Griesshammer and van Kolck in Eur Phys J A 59:289, 2023). At leading order, no three-body interaction is needed. A ground state exists only in the range <span>\\(0.366\\ldots \\ge \\xi \\ge -8.72\\ldots \\)</span>, and excited states display self-similarity and Discrete Scale Invariance, with small corrections for nonzero <span>\\(r_0\\)</span>.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"65 2","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Few-Body Systems","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s00601-024-01923-3","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Resummed-range Effective Field Theory is the consistent non-relativistic Effective Field Theory of point interactions in systems with large two-body scattering length a and an effective range \(r_0\) large in magnitude but negative. Its leading order is non-perturbative, and its observables depend only on the dimensionless ratio \(\xi :=2r_0/a\) once \(|r_0|\) is chosen as base unit. This presentation highlights aspects for three identical spinless bosons and adds details to a previous discussion (Griesshammer and van Kolck in Eur Phys J A 59:289, 2023). At leading order, no three-body interaction is needed. A ground state exists only in the range \(0.366\ldots \ge \xi \ge -8.72\ldots \), and excited states display self-similarity and Discrete Scale Invariance, with small corrections for nonzero \(r_0\).
期刊介绍：
The journal Few-Body Systems presents original research work – experimental, theoretical and computational – investigating the behavior of any classical or quantum system consisting of a small number of well-defined constituent structures. The focus is on the research methods, properties, and results characteristic of few-body systems. Examples of few-body systems range from few-quark states, light nuclear and hadronic systems; few-electron atomic systems and small molecules; and specific systems in condensed matter and surface physics (such as quantum dots and highly correlated trapped systems), up to and including large-scale celestial structures.
Systems for which an equivalent one-body description is available or can be designed, and large systems for which specific many-body methods are needed are outside the scope of the journal.
The journal is devoted to the publication of all aspects of few-body systems research and applications. While concentrating on few-body systems well-suited to rigorous solutions, the journal also encourages interdisciplinary contributions that foster common approaches and insights, introduce and benchmark the use of novel tools (e.g. machine learning) and develop relevant applications (e.g. few-body aspects in quantum technologies).
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