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Microscopic Cluster Models

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Book cover Clusters in Nuclei, Vol.2

Part of the book series: Lecture Notes in Physics ((LNP,volume 848))

Abstract

We present an overview of microscopic cluster models, by focusing on the Resonating Group Method (RGM) and on the Generator Coordinate Method (GCM). The wave functions of a nuclear system are defined from cluster wave functions, with an exact account of antisymmetrization between all nucleons. For the sake of pedagogy, the formalism is mostly presented in simple conditions, i.e. we essentially assume spinless clusters, and single-channel calculations. Generalizations going beyond these limitations are outlined. We present the GCM in more detail, and show how to compute matrix elements between Slater determinants. Specific examples dealing with \(\alpha\)+nucleus systems are presented. We also discuss some approximations of the RGM, and in particular, the renormalized RGM which has been recently developed. We show that the GCM can be complemented by the microscopic variant of the R-matrix method, which provides a microscopic description of unbound states. Finally, extensions of the GCM to multicluster and multichannel calculations are discussed, and illustrated by typical examples. In particular we compare different three-\(\alpha\) descriptions of \(^{12}\hbox{C}.\)

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Acknowledgments

This text presents research results of the IAP program P6/23 initiated by the Belgian-state Federal Services for Scientific, Technical and Cultural Affairs.

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  1. Physique Nucléaire Théorique et Physique Mathématique, C.P. 229, Université Libre de Bruxelles (ULB), 1050, Brussels, Belgium

    P. Descouvemont

  2. IPHC Bat27, IN2P3-CNRS/Université de Strasbourg,BP28, 67037, Strasbourg Cedex 2, France

    M. Dufour

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    Christian Beck

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Descouvemont, P., Dufour, M. (2012). Microscopic Cluster Models. In: Beck, C. (eds) Clusters in Nuclei, Vol.2. Lecture Notes in Physics, vol 848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24707-1_1

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