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The energy levels of pi-muonium

Энергетические уровни пи-мюония

  • Published:
Il Nuovo Cimento A (1965-1970)

Summary

An experiment was recently proposed and planned to measure the energy levels of the π-μ atom (pi-muonium). In this note expressions are obtained for all QED contributions to the 2S 1/2, 2P 1/2 and 2P 3/2 level shifts of pi-muonium accurate to 10−4 eV. Detailed discussions are given for the recoil corrections to the spinor-scalar system by means of an effective-potential method. The contributions of the total hadronic vacuum polarization and the weak interaction are also discussed. If the 2S-2P energy level difference in pi-muonium can be measured accurately to 10−4 eV, one can obtain an independent determination of the pion charge radius. We also discuss briefly the π-e and the π-π atoms which are also produced in K decay.

Riassunto

Si è recentemente proposto e progettato un esperimento per misurare i livelli energetici dell’atomo π-μ (pi-muonio). In questo articolo si ottengono delle espressioni per tutti i contributi QED agli spostamenti dei livelli 2S 1/2, 2P 1/2, 2P 3/2 del pi-muonio, valutati con la precisione di 10−4 eV. Si discutono dettagliatamente le correzioni di rinculo del sistema spinore-scalare per mezzo di un metodo a potenziale effettivo. Si discutono anche i contributi della polarizzazione adronica totale del vuoto e delle interazioni deboli. Se si riesce a misurare con la precisione di 10−4 eV la differenza fra i livelli energetici 2S-2P nel pi-muonio, si può ottenere una determinazione indipendente del raggio della carica del pione. Si discutono brevemente anche gli atomi π-e e π-π, anch’essi prodotti nel decadimento del K.

Реэюме

Недавно был предложен зксперимент для иэмерения знергетических уровней π-μ атома (пи-мюония). В зтой работе получены выражения для всех вкладов квантовой злектродинамики в сдвиги уровней 2S 1/2, 2P 1/2 и 2P 3/2 пи-мюония с точностью 10−4 зВ. Проводится подробное обсуждение зффектов отдачи в спинор-скалярной системе, испольэуя метод зффективного потенциала. Также обсуждаются полная поляриэация адронного вакуума и слабое вэаимодействие. Если раэность знергетических уровней 2S-2P в пи-мюонии может быть иэмерена с точностью 10−4 зВ, то можно получить неэависимое определение радиуса пионного эаряда. Мы также вкратце рассматриваем π-e и π-π атомы, которые также обраэуются при К распаде.

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Author notes

  1. C. F. Cho

    Present address: Max-Planck-Institut für Physik und Astrophysik, Munich

Authors and Affiliations

  1. Institute of Theoretical Physics Department of Physics, Stanford University, Stanford, Cal.

    C. F. Cho

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Additional information

Work supported in part by the National Science Foundation, Grant No. GP-39158.

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Cho, C.F. The energy levels of pi-muonium. Nuov Cim A 23, 557–580 (1974). https://doi.org/10.1007/BF02821234

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  • DOI: https://doi.org/10.1007/BF02821234

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