Il Nuovo Cimento (1955-1965)

, Volume 34, Issue 1, pp 77–80 | Cite as

Radiative corrections to hyperfine structure in hydrogen

  • D. E. Zwanziger


Because of a reported discrepancy of (34±21) parts per million between measured and calculated values of the hyperfine separation of the ground state of atomic hydrogen, the next higher-order radiative corrections beyond the previously calculated order of α2Sh.f. were investigated. Besides the expected presence of corrections of order α3 ln αSh.f., a larger correction of order α3ln2Sh.f. was found. The calculation of the level shift of both of these logarithmic orders has been completed yielding results which agree with those of Layzer. In the case of hydrogen the numerical contribution is − 9.28 ppm. When this is combined with previous results, the discrepancy between measured and calculated values is increased to (43±21) ppm. The uncertainty is due largely to the uncertainty in the value of α, which is obtained from finestructure measurements, and which appears in the theoretical formula for the hyperfine separation. Possible explanations of the discrepancy are either an inaccuracy in the accepted value of the fine-structure constant or an inadequate evaluation of the contribution from intermediate states in which mesons are excited.


A causa di una discrepanza, già nota, di (34±21) p.p.m. fra i valori misurati e quelli calcolati della separazione iperfine dello stato fondamentale dell’idrogeno atomico, si sono analizzate le correzioni radiative dell’ordine superiore successivo a quelle già calcolate di ordine α2Sh.f.. Oltre la prevista presenza di correzioni dell’ordine di α3 lnSh.f., sí è trovata una correzione di rilievo di ordine α3 ln2Sh.f.. Si è completato il calcolo dello spostamento di livello di questi due ordini logaritmici ottenendo risultati che concordano con quelli di Layzer. Nel caso dell’idrogeno il contributo numerico è − 9.28 p.p.m. Se si combina questo con i risultati precendenti, la discrepanza fra i valori misurati e quelli calcolati sale a (43±21) p.p.m. L’incertezza è dovuta principalmente all’incertezza nel valore di α, che è ottenuto da misure di struttura fine e che compare nella formula teorica della separazione iperfine. Spiegazioni possibili di questa discrepanza sono o un’inaccuratezza nel valore accettato della costante della struttura fine o una inadeguata valutazione del contributo degli stati intermedi in cui i mesoni sono eccitati.


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Copyright information

© Società Italiana di Fisica 1964

Authors and Affiliations

  • D. E. Zwanziger
    • 1
  1. 1.Service de Physique ThéoriqueCentre d’Etudes Nucléaires de SaclayGif-sur-Yvette

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