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- W3102829123 abstract "Creation of charged fermion pair from a vacuum in so-called supercritical Coulomb potential is examined for the case when fermions can move only in the same (one) plane. In which case, quantum dynamics of charged massive or massless fermions can be described by the two-dimensional Dirac Hamiltonians with an usual [Formula: see text] Coulomb potential. These Hamiltonians are singular and require the additional definition in order for them to be treated as self-adjoint quantum-mechanical operators. We construct the self-adjoint two-dimensional Dirac Hamiltonians with a Coulomb potential and determine the quantum-mechanical states for such Hamiltonians in the corresponding Hilbert spaces of square-integrable functions. We determine the scattering amplitude in which the self-adjoint extension parameter is incorporated and then obtain equations implicitly defining possible discrete energy spectra of the self-adjoint Dirac Hamiltonians with a Coulomb potential. It is shown that this quantum system becomes unstable in the presence of a supercritical Coulomb potential which manifests in the appearance of quasi-stationary states in the lower (negative) energy continuum. The energy spectrum of those states is quasi-discrete, consists of broadened levels with widths related to the inverse lifetimes of the quasi-stationary states as well as the probability of creation of charged fermion pair by a supercritical Coulomb field. Explicit analytical expressions for the creation probabilities of charged (massive or massless) fermion pair are obtained in a supercritical Coulomb field." @default.
- W3102829123 created "2020-11-23" @default.
- W3102829123 creator A5082742172 @default.
- W3102829123 date "2017-12-14" @default.
- W3102829123 modified "2023-09-23" @default.
- W3102829123 title "Quasi-stationary states and fermion pair creation from a vacuum in supercritical Coulomb field" @default.
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- W3102829123 doi "https://doi.org/10.1142/s0217732317502005" @default.
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