Abstract:
We find exact solutions of the Dirac equation and the fermion energy spectrum in the Coulomb (vector and scalar) potential and Aharonov–Bohm potential in 2+1 dimensions taking the particle spin into account. We describe the fermion spin using the two-component Dirac equation with the additional (spin) parameter introduced by Hagen. We consider the effect of creation of fermion pairs from the vacuum by a strong Coulomb field in the Aharonov–Bohm potential in 2+1 dimensions. We obtain transcendental equations implicitly determining the electron energy spectrum near the boundary of the lower energy continuum and the critical charge. We numerically solve the equation for the critical charge. We show that for relatively weak magnetic flows, the critical charge decreases (compared with the case with no magnetic field) if the energy of interaction of the electron spin magnetic moment with the magnetic field is negative and increases if this energy is positive.
Citation:
V. R. Khalilov, “Spontaneous fermion creation in the Coulomb field and Aharonov–Bohm potential in 2+1 dimensions”, TMF, 158:2 (2009), 250–262; Theoret. and Math. Phys., 158:2 (2009), 210–220
\Bibitem{Kha09}
\by V.~R.~Khalilov
\paper Spontaneous fermion creation in the~Coulomb field and Aharonov--Bohm potential in $2+1$~dimensions
\jour TMF
\yr 2009
\vol 158
\issue 2
\pages 250--262
\mathnet{http://mi.mathnet.ru/tmf6312}
\crossref{https://doi.org/10.4213/tmf6312}
\zmath{https://zbmath.org/?q=an:1175.81186}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2009TMP...158..210K}
\transl
\jour Theoret. and Math. Phys.
\yr 2009
\vol 158
\issue 2
\pages 210--220
\crossref{https://doi.org/10.1007/s11232-009-0017-3}
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Linking options:
https://www.mathnet.ru/eng/tmf6312
https://doi.org/10.4213/tmf6312
https://www.mathnet.ru/eng/tmf/v158/i2/p250
This publication is cited in the following 10 articles:
Luis B. Castro, Antonio S. de Castro, “Effects of the Lorentz symmetry violation on relativistic neutral scalar bosons: Scattering and bound states”, EPL, 149:5 (2025), 50003
Andrés G. Jirón, Angel E. Obispo, J. D. Espinoza Loayza, Juan Carlos Quispe, L. B. Castro, “Effect of a critical magnetic field on the control of scalar neutral boson pair production in the context of Lorentz-symmetry violation”, EPL, 145:4 (2024), 40002
Oliveira R.R.S., Araujo Filho A.A., Maluf V R., Almeida C.A.S., “The Relativistic Aharonov-Bohm-Coulomb System With Position-Dependent Mass”, J. Phys. A-Math. Theor., 53:4 (2020), 045304
Oliveira R.R.S., Maluf R.V., Almeida C.A.S., “Bound-State Solutions of the Dirac Oscillator in An Aharonov-Bohm-Coulomb System”, Ann. Phys., 400 (2019), 1–8
I. V. Mamsurov, V. R. Khalilov, “Induced vacuum charge of massless fermions in Coulomb and
Aharonov–Bohm potentials in 2+1 dimensions”, Theoret. and Math. Phys., 188:2 (2016), 1181–1196
V. R. Khalilov, “Zero-mass fermions in Coulomb and Aharonov–Bohm potentials in 2+1 dimensions”, Theoret. and Math. Phys., 175:2 (2013), 637–654
Khalilov V.R., “Creation of Planar Charged Fermions in Coulomb and Aharonov-Bohm Potentials”, Eur. Phys. J. C, 73:8 (2013), 2548
V. R. KHALILOV, K. E. LEE, I. V. MAMSUROV, “SPIN-POLARIZED FERMIONS IN AN AHARONOV–BOHM FIELD”, Mod. Phys. Lett. A, 27:05 (2012), 1250027
Khalilov V.R., Lee K.E., “Bound Fermion States in a Vector 1/R and Aharonov-Bohm Potential in (2+1) Dimensions”, Modern Phys Lett A, 26:12 (2011), 865–883
V. R. Khalilov, K. E. Lee, “Discrete spectra of the Dirac Hamiltonian in Coulomb and Aharonov–Bohm potentials in 2+1 dimensions”, Theoret. and Math. Phys., 169:3 (2011), 1683–1703
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