VbvAstE-001

10.3 The screening with relativistic electrons
In the case the ≪bare≫ nucleus, there is nothing to prevent the electron to approach
it at an extremely small distance λ min, which is limited by its own than its de Broglie’s
wavelength. Its movement in this case becomes relativistic at β → 1 ξ ≫ 1. In this
case, at not too small ξ, we obtain
(
Y ≈ 2 1 − 4 )
, (10.24)
3ξ
and at ξ ≫ 1
Y → 2 . (10.25)
In connection with it, at the distance r → λ min from a nucleus, the equilibrium
equation (10.21) reforms to
λ min ≃ Zαλ C . (10.26)
and the density of electron gas in a layer of thickness λ min can be determined from
the condition of normalization. As there are Z electrons into each cell, so
Z ≃ n λ e · λ min
3
(10.27)
From this condition it follows that
ξ λ ≃
1
2αZ 2/3 (10.28)
Where n λ e and ξ λ are the density of electron gas and the relative momentum of electrons
at the distance λ min from the nucleus. In accordance with Eq.(10.4), the energy of all
the Z electrons in the plasma cell is
E ≃ Zm ec 2 ξ λ (10.29)
At substituting of Eq.(10.28), finally we obtain the energy of the electron gas in a
plasma cell:
E ≃ mec2
2α Z1/3 (10.30)
This layer provides the pressure on the nucleus:
P ≃ E
( ξ
˜λ C
) 3
≈ 10 23 dyne/cm 2 (10.31)
This pressure is in order of value with pressure of neutronization
(
(10.1).
)
Thus the electron cloud forms a barrier at a distance of α
m ec
from the nucleus.
This barrier is characterized by the energy:
E ≃ cp max ≃ mec2
α
≈ 70Mev. (10.32)
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