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We analyze the leading and higher-order quantum electrodynamic corrections to the energy levels for a single electron bound in a Penning trap, including the Bethe logarithm correction due to virtual excitations of the reference quantum cyclotron state. The effective coupling parameter αc in the Penning trap is identified as the square root of the ratio of the cyclotron frequency, converted to an energy via multiplication by the Planck constant, to the electron rest mass energy. We find a large, state-independent, logarithmic one-loop self-energy correction of order α α4c mc2 lnðα−2 c Þ, where m is the electron rest mass and c is the speed of light. Furthermore, we find a state-independent “trapped” Bethe logarithm. We also obtain a state-dependent higher-order logarithmic self-energy correction of order α α6c mc2 lnðα−2 c Þ. In the high-energy part of the bound-state self- energy, we need to consider terms with up to six magnetic interaction vertices inside the virtual photon loop.
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Radiative energy and mass shifts of quantum cyclotron states
AbstractWe discuss relativistic and radiative corrections to the energies of quantum cyclotron states. In particular, it is shown analytically that the leading logarithmic radiative (self-energy) correction to the bound-state energy levels of quantum cyclotron states is state independent and must be interpreted as a magnetic field-dependent correction to the electron’s mass in a Penning trap. Graphical abstract
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- Award ID(s):
- 2110294
- PAR ID:
- 10590483
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- The European Physical Journal D
- Volume:
- 79
- Issue:
- 4
- ISSN:
- 1434-6060
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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