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Hyperspherical functions and quantum-mechanical three-body problem with application to carbon 12

Гиперсферическне функции и квантовомеханическая проблема трех тел в случае12C

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Il Nuovo Cimento B (1971-1996)

Summary

In this work we discuss a system of three identical particles (bosons) interacting by a particular two-body force. Using the complete set of the hyperspherical functions (K-harmonics) we find analytical expressions for eigenvalues and wave functions of the stationary states. The numerical evaluation gives a level sequence for a definite pair of potential parameters similar to that of the nucleus carbon 12.

Riassunto

In questo articolo si discute un sistema di tre particelle identiche (bosoni) che interagiscono per mezzo di una particolare forza di due corpi. Facendo uso dell’insieme completo di funzioni ipersferiche (armonicheK) si trovano espressioni analitiche per gli autovalori e le funzioni d’onda degli stati stazionari. La valutazione numerica dà per una coppia definita di parametri del potenziale una sequenza di livelli analoga a quella del nucleo del carbonio 12.

Резюме

В этой работе мы рассматриваем систему трех тождественных частиц (бозонов), взаимодействующих через двухчастичную силу. Используя полную систему гиперсферических функций (K-гармоник), мы находим аналитические выражения для собственных значений и собственных функций стационарных состояний. Численный расчет дает последовательность уровней для потенциала, описывающего ядро12C.

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Author notes

  1. H. Letz

    Present address: Institut für Angewandte Mathematik I, Martensstr. 1, D-852, Erlangen

Authors and Affiliations

  1. Institut für Theoretische Physik der Universität, Erlangen/Nürnberg

    H. Letz

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Letz, H. Hyperspherical functions and quantum-mechanical three-body problem with application to carbon 12. Nuov Cim B 30, 348–363 (1975). https://doi.org/10.1007/BF02725708

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