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/E F= (αw/π)(-2/3 ln2 + lnw · · [8/3 ln2 — 37/72 — 4/15]), wherew=(αZ)2 andE fis 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/E F= 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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Research supported in part by U.S. Atomic Energy Commission while the author was at the Courant Institute of New York University.
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Layzer, A. New logarithmic radiative corrections to the hyperfine splitting in hydrogenic atoms. Nuovo Cim 33, 1538–1543 (1964). https://doi.org/10.1007/BF02749672
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DOI: https://doi.org/10.1007/BF02749672