{"title":"Linear response theory with finite-range interactions","authors":"D. Davesne , A. Pastore , J. Navarro","doi":"10.1016/j.ppnp.2021.103870","DOIUrl":null,"url":null,"abstract":"<div><p>This review focuses on the calculation of infinite nuclear matter response functions using phenomenological finite-range interactions, equipped or not with tensor terms. These include Gogny and Nakada families, which are commonly used in the literature. Because of the finite-range, the main technical difficulty stems from the exchange terms of the particle–hole interaction. We first present results based on the so-called Landau and Landau-like approximations of the particle–hole interaction. Then, we review two methods which in principle provide numerically exact response functions. The first one is based on a multipolar expansion of both the particle–hole interaction and the particle–hole propagator and the second one consists in a continued fraction expansion of the response function. The numerical precision can be pushed to any degree of accuracy, but it is actually shown that two or three terms suffice to get converged results. Finally, we apply the formalism to the determination of possible finite-size instabilities induced by a finite-range interaction.</p></div>","PeriodicalId":412,"journal":{"name":"Progress in Particle and Nuclear Physics","volume":null,"pages":null},"PeriodicalIF":14.5000,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.ppnp.2021.103870","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Progress in Particle and Nuclear Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0146641021000247","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, NUCLEAR","Score":null,"Total":0}
引用次数: 9
Abstract
This review focuses on the calculation of infinite nuclear matter response functions using phenomenological finite-range interactions, equipped or not with tensor terms. These include Gogny and Nakada families, which are commonly used in the literature. Because of the finite-range, the main technical difficulty stems from the exchange terms of the particle–hole interaction. We first present results based on the so-called Landau and Landau-like approximations of the particle–hole interaction. Then, we review two methods which in principle provide numerically exact response functions. The first one is based on a multipolar expansion of both the particle–hole interaction and the particle–hole propagator and the second one consists in a continued fraction expansion of the response function. The numerical precision can be pushed to any degree of accuracy, but it is actually shown that two or three terms suffice to get converged results. Finally, we apply the formalism to the determination of possible finite-size instabilities induced by a finite-range interaction.
期刊介绍:
Taking the format of four issues per year, the journal Progress in Particle and Nuclear Physics aims to discuss new developments in the field at a level suitable for the general nuclear and particle physicist and, in greater technical depth, to explore the most important advances in these areas. Most of the articles will be in one of the fields of nuclear physics, hadron physics, heavy ion physics, particle physics, as well as astrophysics and cosmology. A particular effort is made to treat topics of an interface type for which both particle and nuclear physics are important. Related topics such as detector physics, accelerator physics or the application of nuclear physics in the medical and archaeological fields will also be treated from time to time.