Motion of spin-half particles in the axially symmetric field of naked singularities of the static <Emphasis Type="Italic">q</Emphasis>-metric |
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Authors: | V P Neznamov V E Shemarulin |
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Affiliation: | 1.Russian Federal Nuclear Center—All-Russia Research Institute of Experimental Physics,Sarov, Nizhny Novgorod region,Russia;2.National Research Nuclear University MEPhI,Moscow,Russia |
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Abstract: | Quantum-mechanical motion of a spin-half particle is examined in the axially symmetric fields of static naked singularities formed by a mass distribution with a quadrupole moment (q-metric). The analysis is performed by means of the method of effective potentials of the Dirac equation generalized to the case where radial and angular variables are not separated. If ?1 < q < qlim, |qlim| ? 1, where q is the quadrupolemoment in proper units, the naked singularities do not exclude the existence of stationary bound states of Dirac particles for a prolate mass distribution in the q-metric along the axial axis. For an oblate mass distribution, the naked singularities of the q-metric are separated from a Dirac particle by infinitely large repulsive barriers followed by a potential well which deepens while moving apart from the equator (from θ = θ min or θ = π ? θ min) toward the poles. The poles make an exception, and at 0 < q < q*, there are some points θ i for particle states with j ≥ 3/2. |
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