Abstract
Due to strong enhancement of loop effects in a superstrong magnetic field (B ≫ m2=e3) the Coulomb potential becomes screened. This phenomenon dramatically changes the dependence of the electron energy levels on magnetic field. In particular, the freezing of energy levels occurs so the ground energy level of light ions can never reach the lower continuum (become critical), no matter how strong the field is. Therefore, the magnetic field affects the critical nucleus charge Zcr in two ways: i. it makes the electron movement essentially one-dimensional diminishing the value of Zcr; ii. it makes the potential weaker increasing the value of critical charge. The phenomenon of critical charge itself is also discussed.
Highlights
The Dirac equation cannot be solved for the electron in the potential of the pointlike Coulomb center with charge Z > 137
More accurate results taking into account higher Landau Levels were found numerically in [6]
In an external magnetic field vacuum polarization in one loop is strongly enhanced and proportional to magnetic field strength B. It was discovered by Shabad and Usov [7, 8] that this enhancement leads to the significant modification of the Coulomb potential for B m2/e3 where m and e are electron mass and charge1
Summary
The Dirac equation cannot be solved for the electron in the potential of the pointlike Coulomb center with charge Z > 137 It can be done if the finite size of a nucleus is taken into account (see, for example, [1,2,3]; more references can be found in [4]). More accurate results taking into account higher Landau Levels were found numerically in [6] In those papers the potential was taken to be the Coulomb one. In an external magnetic field vacuum polarization in one loop is strongly enhanced and proportional to magnetic field strength B It was discovered by Shabad and Usov [7, 8] (see [9]) that this enhancement leads to the significant modification (screening) of the Coulomb potential for B m2/e3 where m and e are electron mass and charge. This talk is based on papers [4, 10,11,12,13,14,15,16]
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