### Abstract

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 α^{2} S_{ h.f.} were investigated. Besides the expected presence of corrections of order α^{3} ln αS_{ h.f.}, a larger correction of order α^{3}ln^{2} S_{ h.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.

Original language | English (US) |
---|---|

Pages (from-to) | 77-80 |

Number of pages | 4 |

Journal | Il Nuovo Cimento Series 10 |

Volume | 34 |

Issue number | 1 |

DOIs | |

State | Published - Oct 1964 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Il Nuovo Cimento Series 10*,

*34*(1), 77-80. https://doi.org/10.1007/BF02725870

**Radiative corrections to hyperfine structure in hydrogen.** / Zwanziger, D. E.

Research output: Contribution to journal › Article

*Il Nuovo Cimento Series 10*, vol. 34, no. 1, pp. 77-80. https://doi.org/10.1007/BF02725870

}

TY - JOUR

T1 - Radiative corrections to hyperfine structure in hydrogen

AU - Zwanziger, D. E.

PY - 1964/10

Y1 - 1964/10

N2 - 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 α2 S h.f. were investigated. Besides the expected presence of corrections of order α3 ln αS h.f., a larger correction of order α3ln2 S h.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.

AB - 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 α2 S h.f. were investigated. Besides the expected presence of corrections of order α3 ln αS h.f., a larger correction of order α3ln2 S h.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.

UR - http://www.scopus.com/inward/record.url?scp=51249195746&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249195746&partnerID=8YFLogxK

U2 - 10.1007/BF02725870

DO - 10.1007/BF02725870

M3 - Article

VL - 34

SP - 77

EP - 80

JO - La Rivista del Nuovo Cimento

JF - La Rivista del Nuovo Cimento

SN - 0393-697X

IS - 1

ER -