Research Paper: Perturbations on The Energy Levels of Electron in The Penning Trap, Due to The Dirac Equation

Document Type : Research Paper

Authors

1 PhD Student, Department of Physics, Faculty of Physics, Alzahra University, Tehran, Iran

2 Associate Professor, Department of Physics, Faculty of Physics, Alzahra University, Tehran, Iran

3 Professor, Department of Physics, Faculty of Physics, Alzahra University, Tehran, Iran

Abstract

The penning trap, invented in 1959 by H. Dehmelt, is a combination of an inner electric dipole field and a constant magnetic field. A charged particle trapped in the Penning trap is called a geonium atom. The energy levels of the geonium atom are known in the non-relativistic limit, using the solutions of the Schrodinger equation, and for the case when the gravitational field of the Earth is negligible. In this article we write the Dirac equation for the geonium atom, coupled to the weak gravitational field of the Earth, and study its energy levels using perturbation techniques. If the Newtonian gravitational potential is , the dimensionless perturbing parameter is  , where c is the velocity of light. It is found that the effect of these perturbations affects the energy levels by a factor of almost . This tiny shift in the energy levels may be used to investigate the effect of the gravitational field on earth.

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References

[1] Morishima, Takahiro, Toshifumi Futamase, and Hirohiko M. Shimizu. "The general relativistic effects on the magnetic moment in Earth’s gravity." Progress of Theoretical and Experimental Physics 2018(6), 063B07, 2018.
[2] Ulbricht, S., R. A. Müller, and A. Surzhykov. "Gravitational effects on geonium and free electron g s-factor measurements in a Penning trap." Physical Review D 100(6), 064029, 2019.
[3] Ito, Asuka. "Inertial and gravitational effects on a geonium atom." Classical and Quantum Gravity 38(19), 195015, 2021.
[4] Brown, Lowell S., and Gerald Gabrielse. "Geonium theory: Physics of a single electron or ion in a Penning trap." Reviews of Modern Physics 58(1), 233, 1986.
[5] Dehmelt, Hans. "Experiments with an isolated subatomic particle at rest." In AIP Conference Proceedings, 233(1), 28-45. American Institute of Physics, 1991.
[6] Dehmelt, Hans. "Less is more: experiments with an individual atomic particle at rest in free space." American Journal of Physics 58(1), 17-27, 1990.
[7] Itzykson, C., and J. B. Zuber. "Quantum field theory (4th printing 1988) c McGraw–Hill.", 1980.

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History

  • Receive Date: 23 October 2022
  • Revise Date: 28 January 2023
  • Accept Date: 19 February 2023

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