Lower bounds to the ground-state energy ofN-body systems and conditions on the two-body potentials necessary for the existence ofN-body bound states
SummaryWe obtain simple lower bounds to the ground-state energy ofN-body systems, and conditions on the two-body forces which are necessary for the existence ofN-body bound states. The simpler version of these conditions reads (with an obvious meaning of the symbols)

$$ - 2h / - 2\int\limits_0^\infty {drr\sum\limits_{i > j}^N {m_i m_j } (m_i + m_j )^{ - 1} V_{ij} (r)\theta [ - V_{ij} (r)] \geqslant 1} $$

 thus it provides the directN-body generalization of the well-known Jost-Pais condition.RiassuntoSi ottengono semplici limiti inferiori per l’energia del livello fondamentale di un sistema diN corpi, e condizioni sulle forze a due corpi che sono necessarie per l’esistenza di stati legati aN corpi. La più semplice di tali condizioni recita (con ovvio significato dei simboli) —

$$ - 2h / - 2\int\limits_0^\infty {drr\sum\limits_{i > j}^N {m_i m_j } (m_i + m_j )^{ - 1} V_{ij} (r)\theta [ - V_{ij} (r)] \geqslant 1} $$

, sicché costituisce una diretta generalizzazione al caso diN corpi della ben nota condizione di Jost e Pais.РеэюмеМы получаем простые нижние границы для знергии основного состояния системN-частиц и условия на двух-частичные силы, которые необходимы для сушествования свяэанных состоянийN-частиц. Простейщий вариант зтих условий имеет вид (эначение символов очевидно)

$$ - 2h / - 2\int\limits_0^\infty {drr\sum\limits_{i > j}^N {m_i m_j } (m_i + m_j )^{ - 1} V_{ij} (r)\theta [ - V_{ij} (r)] \geqslant 1} $$

; что представляет непосредственноеN-частичное обобшение хорощо иэвестного условия йста-Пейса.

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