Il Nuovo Cimento (1955-1965)

, Volume 33, Issue 6, pp 1538–1543 | Cite as

New logarithmic radiative corrections to the hyperfine splitting in hydrogenic atoms

  • A. Layzer
Article
First Online:
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Summary

We report here on the calculation of new radiative corrections to the hyperfine splitting in hydrogenic atoms. The result for the correction ΔE to the 1S state is ΔE/EF= (αw/π)(-2/3 ln2 + lnw · · [8/3 ln2 — 37/72 — 4/15]), wherew=(αZ)2 andEfis the lowest-order splitting. The last term is due to vacuum polarization. A brief description is given of the method of calculation, which employs the free-propagator expansion of the bound-electron Green’s function. In the important case of hydrogen, the new corrections tend to slightly worsen the already unsatisfactory agreement of theory with experiment. The relevance of this result to the proton structure problem is briefly discussed. Integral expressions are given for the « mean electromagnetic radius » of the proton in terms of the proton charge and magnetic moment form factors in momentum space.

Riassunto

Si riferisce sul calcolo di nuove correzioni radiative alla separazione iperfina negli atomi di idrogeno. Il risultato, per quanto riguarda la correzione ΔE allo stato 1S, è ΔE/EF= αw/π(− 2/3 lnw + lnw [8/3 ln 2 - 37/72 - 4/15]), dovew ≡ (αZ)2 ed EF è la separazione di ordine inferiore. Si dà una breve descrizione del metodo di calcolo, che impiega lo sviluppo di propagatore libero della funzione di Green dell’elettrone legato. Nel caso importante dell’idrogeno, le nuove correzioni tendono a peggiorare leggermente l’accordo, già insoddisfacente, fra teoria ed esperimento. Si discute brevemente l’importanza di questo risultato nel problema della struttura del protone. Si dànno le espressioni del « raggio elettromagnetico medio » del protone in funzione dei fattori di forma della carica protonica e del momento magnetico nello spazio degli impulsi.

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References

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Copyright information

© Società Italiana di Fisica 1964

Authors and Affiliations

  • A. Layzer
    • 1
  1. 1.Stevens Institute of TechnologyHoboken

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