Summary
Generalizing the leading ideas and the standard methods of modern approaches to theN-body problem, we devise direct procedures for describing the dynamics of clusteredN-body systems. We show that these procedures, leading tom-cluster integral equations, can be developed starting from any type of multiparticle coupling scheme. Cluster models are formulated in the framework of the Faddeev-Yakubovskii coupling scheme (both in the original sophisticated language and, more simply, in terms of variables with artificial indices) as well as in the context of any approach with highly-connected-kernel equations. Our general formulation reproduces all the existingN-particle equations in the limit casem =N.
Riassunto
In questo lavoro si generalizzano alcuni concetti di base e alcune metodologie proprie delle moderne formulazioni del problema aN corpi, cosí da individuare tecniche adatte alla descrizione di sistemi a molte particelle « clusterizzati ». Mostriamo che queste tecniche, che conducono ad equazioni integrali per sistemi conm « cluster », possono essere elaborate a partire da qualsiasi schema di accoppiamento fra i canali. Vengono proposti dei modelli a « cluster » nell’ambito dello schema di accoppiamento di Faddeev e Yakubovskii (sia nella sua sofisticata versione originale sia in termini di variabili con indici arbitrari), come pure nell’ambito dei vari formalismi ad equazioni integrali a « kernel » altamente connesso. Mostriamo che, nel caso limitem = N, il nostro formalismo riproduce tutte le equazioni finora proposte perN particelle.
Реэюме
Обобшая основные идеи и стандартные методы современных подходов кN-частичной проблеме, мы раэвиваем процедуры для описания динамики систем иэ сгруппированныхN-частиц. Мы покаэываем, что зти процедуры, проводяшие к m-кластерным интегральным уравнениям, могут быть раэвиты иэ любого типа схемы многочастичной свяэи. Кластерные модели формулируются в рамках схемы свяэи Фаддеева-Якубовского (с помошью первоначального усложненного яэыка и в терминах переменных с искусственными индексами), а также в рамках любого подхода с уравнениями, содержашими сильно свяэанные ядра. Наща обшая формулировка воспроиэводит все сушествуюшиеN-частичные уравнения в предельном случаеm=N.
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Form = N eqs. (5.7) reduce to eqs. (20) of ref. (10).
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Cattapan, G., Vanzani, V. A systematic treatment of cluster models in multiparticle dynamics. Nuov Cim A 58, 85–104 (1980). https://doi.org/10.1007/BF02730223
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DOI: https://doi.org/10.1007/BF02730223