Summary
The structural features of the leading and auxiliary equations obtained from a general multioluster reduction of the minimally connectedN-body scattering equations are deduced from the properties of the chains of partitions linked by the interaction potentials. We give a simple derivation of the connectivity properties of the original equations as well as of the structurally similar auxiliary equations. Finally, we show that the leading equations have the noteworthy property of being automatically connected without the need for iteration.
Riassunto
Si discutono le caratteristiche strutturali delle equazioni principali e ausiliarie ottenute mediante una riduzione generale a molti cluster delle equazioni dello scattering perN corpi minimamente connesse. Tali caratteristiche seguono dalle proprietà di catene di partizioni collegate per mezzo di potenziali d’interazione. Si presenta una derivazione nuova e semplice delle proprietà di connessione sia delle equazioni originali sia delle equazioni ausiliarie, che hanno la medesima struttura. Infine, si mostra che le equazioni principali possiedono l’importante proprietà di essere automaticamente connesse senza la necessità d’iterazione.
РЕжУМЕ
ОпРЕДЕльУтсь стРУкт УРНыЕ ОсОБЕННОстИ ОсНОВНых И ВспОМОгАт ЕльНых УРАВНЕНИИ, пОлУЧЕННы х Иж ОБЩЕгО МНОгОклАс тЕРНОгО пРИВЕДЕНИь УРАВНЕНИ И РАссЕьНИь МИНИМАльНО сВьжАННы х N-ЧАстИц. ЁтИ сВОИстВА ВыВОДьтсь Иж сВОИстВ цЕпОЧЕк клАстЕРОВ, сВьжАННых пОтЕНцИАлАМИ ВжАИМО ДЕИстВИь. пРЕДлАгАЕтсь пРОстО И ВыВОД сВОИстВ сВьжНОстИ Дл ь ИсхОДНых УРАВНЕНИИ, А тАкжЕ Дль стРУктУРНО пОДОБНых ВспОМОгАтЕльНых УРАВНЕНИИ. В жАклУЧЕН ИЕ, Мы пОкАжыВАЕМ, ЧтО О сНОВНыЕ УРАВНЕНИь ОБлАДАУт ВАжНыМ сВОИ стВОМ, ОНИ АВтОМАтИЧЕ скИ сВьжАНы БЕж НЕОБхОДИМОстИ Ит ЕРАцИИ.
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References
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G. Cattapan andV. Vanzani:Properties of chains of partitions and their applications to the N-particle problem, to be published.
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Cattapan, G., Lovitch, L. & Vanzani, V. Structural properties of effective multicluster equations derived fromN-body scattering theory. Nuov Cim A 77, 263–276 (1983). https://doi.org/10.1007/BF02816655
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DOI: https://doi.org/10.1007/BF02816655