Abstract
The properties of spin-1/2 fields in strong external potentials are investigated, motivated by the question ‘What happens to the electron orbitals as the charge of the nucleus is increased without bounds?’ Interest in this problem and in the related Klein paradox extends back nearly to the beginnings of relativistic quantum mechanics. However, the correct interpretation of the theory for overcritical potentials, where the parts of the complete set of sing le-particle solutions associated with particles and antiparticles are no longer distinct, was given only recently. The understanding of the spectrum of the Dirac equation is essential in order to obtain an appropriate physical description in the frame of quantum field theory. The strong binding by more than twice the rest mass of the particles in overcritical external potentials leads to spontaneous particle emission, accompanied by creation of a charged lowest energy state, i.e., a charged vacuum. In the limit of ever-increasing background (nuclear) charge, the charge of the vacuum can be described with the help of a relativistic Thomas-Fermi approximation. As a result, an average constant potential is found within the range of the back-ground charge.
Lectures given at NATO Advanced Study Institute on Nonlinear Equations in Physics and Mathematics, Istanbul, August 1977.
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© 1978 D. Reidel Publishing Company, Dordrecht, Holland
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Rafelski, J. (1978). Bound States of Fermions in External and Self-Consistent Fields. In: Barut, A.O. (eds) Nonlinear Equations in Physics and Mathematics. NATO Advanced Study Institutes Series, vol 40. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9891-9_18
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