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Use of the local harmonic approximation in the theory of radiationless transitions

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Il Nuovo Cimento D

Summary

The possibility of applying the «local harmonic approximation» to the calculation of the generating functions used in the theory of radiationless transitions has been investigated. The approximation attempts to «adapt» point by point the generating function to the curvature of the potential, varying the oscillator frequency in a suitable manner. In the simple case of two identical Morse oscillators separated by a constant energy gap ΔE, the radiationless transition probability has been computed for a wide range of ΔE values. The results are compared with those obtained by summing over the exact bound states of a Morse oscillator. It is found that the line shape is qualitatively correct although some spurious negative contribution is introduced by the approximation.

Riassunto

È stata esaminata la possibilità di applicare la cosiddetta «approssimazione armonica locale» al calcolo delle funzioni generatrici usate nella teoria delle transizioni non radiative. La suddetta approssimazione tenta di «adattare» punto per punto la funzione generatrice alla curvatura del potenziale, variando in modo opportuno la frequenza dell’oscillatore. Nel caso semplice di due oscillatori di Morse identici separati da un dislivello costante di energia ΔE, la probabilità di transizione non radiativa è stata calcolata per un vasto intervallo di valori di ΔE. I risultati sono stati paragonati con quelli ottenuti eseguendo la somma sulle autofunzioni esatte degli stati legati dell’oscillatore di Morse. Si è riscontrato che la forma di linea è qualitativamente corretta, anche se l’approssimazione introduce dei picchi negativi spurii.

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Fano, G., Ortolani, F. & Poggi, G. Use of the local harmonic approximation in the theory of radiationless transitions. Il Nuovo Cimento D 2, 1–14 (1983). https://doi.org/10.1007/BF02451225

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  • DOI: https://doi.org/10.1007/BF02451225

PACS. 33.50

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