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Abstract
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n this paper, we study the charge shielding within the relativistic Thomas-Fermi model for a wide
range of electron number-densities and the atomic-number of screened ions. A generalized energydensity relation is obtained using the force-balance equation and taking into account the
Chandrasekhar’s relativistic electron degeneracy pressure. By numerically solving a second-order
nonlinear differential equation, the Thomas-Fermi screening length is investigated, and the results
are compared for three distinct regimes of the solid-density, warm-dense-matter, and white-dwarfs
(WDs). It is revealed that our nonlinear screening theory is compatible with the exponentially
decaying Thomas-Fermi-type shielding predicted by the linear response theory. Moreover, the variation of relative Thomas-Fermi screening length shows that extremely dense quantum electron
fluids are relatively poor charge shielders. Calculation of the total number of screening electrons
around a nucleus shows that there is a position of maximum number of screening localized electrons
around the screened nucleus, which moves closer to the point-like nucleus by increase in the plasma
number density but is unaffected due to increase in the atomic-number value. It is discovered that
the total number of screening electrons, (Ns / rTF3 =rd3 where rTF and rd are the Thomas-Fermi and
interparticle distance, respectively) has a distinct limit for extremely dense plasmas such as WDcores and neutron star crusts, which is unique for all given values of the atomic-number. This is
equal to saying that in an ultrarelativistic degeneracy limit of electron-ion plasma, the screening
length couples with the system dimensionality and the plasma becomes spherically self-similar.
Current analysis can provide useful information on the effects of relativistic correction to the charge
screening for a wide range of plasma density, such as the inertial-confined plasmas and compact
stellar objects.
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