Summary
A low-frequency approximation to the previously derived Born series for charged-particle elastic scattering in the presence of a laser radiation field is presented. The approximation procedure is based upon the condition that the transition frequency from the initial to the intermediate free states be much greater than the field frequency. The resulting elastic-scattering Born series with the field has the same analytic structure as the corresponding field-free Born series, but with free-particle energies and momenta duly renormalized to incorporate the effect of the field. As part of the results presented here has been obtained also by Kroll and Watson in a different treatment, the present approach is additionally meant to provide a detailed alternative derivation of these results.
Riassunto
Si presenta un'approssimazione di bassa frequenza della serie di Born per lo scattering da potenziale di particelle cariche in presenza di un campo di radiazione laser derivata in precedenza. La procedura dell'approssimazione è basata sulla condizione che la frequenza di transizione dallo stato libero iniziale ad uno stato libero intermedio arbitrario sia molto più grande della frequenza del campo. La serie di Born per lo scattering elastico in presenza di campo che si ottiene ha la stessa struttura analitica della corrispondente serie di Born senza campo, ma con energie e momenti delle particelle libere opportunamente ridefiniti per incorporare l'effetto del campo. Poiché parte dei risultati presentati qui sono stati ottenuti anche da Kroll e Watson con un trattamento differente, il presente approccio fornisce anche una dettagliata derivazione alternativa dei succitati risultati.
Резюме
Предлагается низкочастотное приближение для ранее полученного борновского ряда для упругого рассеяния заряженных частиц в присутствии поля излучения лазера. Предложенное приближение основано на условии, что частота перехода из начального состояния в промежуточное свободное состояние много больше, чем частота поля излучения. Борновский ряд упругого рассеяния при наличии поля имеет ту же аналитическую структуру, как и соответствующий борновский ряд в случае отсутствия поля, но энергии и импульсы свободных частиц, перенормированные правильным образом, включают эффект поля. Предложенный подход обеспечивает подробный альтернативный вывод результатов, полученных Кроллем и Ватсоном при другом рассмотрении.
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Ferrante, G. S-matrix formulation of the charged-particle scattering in the presence of a laser radiation field. Nuov Cim B 52, 229–243 (1979). https://doi.org/10.1007/BF02739037
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DOI: https://doi.org/10.1007/BF02739037