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Abstract
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In this paper, it is shown that a mass densi ty limit exists beyond which the relativ istically
degenerate matter would cry stallize. The mass density limit, found here, is quite analogous to the
mass limit pr edicted by Chandra sekhar for a type of compact stars called white dw arfs
( MCh ’ 1 :43 Solar Mass). In this study, the old problem of white dwarf core collapse, which has
been previously investigated by Chandrasekhar using hydrostatic stability criteria, is revisited in
the framework of the quantum hydrodynamics model by inspection of the charge screening at
atomic scales in the relativistic degeneracy plasma regime taking into account the relativistic
Fermi-Dirac statistics and electron interaction features such as the quantum statistical pressure,
Coulomb attraction, electron exchange-correlation, and quantum recoil effects. It is revealed that
the existence of ion correlation and crystallization of matter in the relativistically degenerate
plasma puts a critical mass density limit on white dwarf core region. It is shown that a white dwarf
star with a core mass density beyond this critical limit can undergo the spontaneous core collapse
(SCC). The SCC phenomenon, which is dominantly caused by the electron quantum recoil effect
(interference and localization of the electron wave function), leads to a new exotic state of matter.
In such exotic state, the relativistic electron degeneracy can lead the white dwarf crystallized core
to undergo the nuclear fusion and an ultimate supernova by means of the volume reduction (due to
the enhanced compressibility) and huge energy release (due to the increase in cohesive energy),
under the stars huge inward gravitational pressure. Moreover, it is found that the SCC phenomenon
is significantly affected by the core composition (it is more probable for heavier plasmas). The
critical mass density found here is consistent with the values calculated for core density of typical
white dwarf stars.
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