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5. The constant rs can be calculated from the atomic weight of the target, A(g), its specific gravity d(g/cm3), and the number of valence electrons per target atom, N2, as rs = 1.389 (A/N2)1/3 a.u. Correspondingly, ρ0 = 8.92 x 10-2 (N2d/A) a.u. = 0.602 x 10 (N2d/A)cm-3. The electron gas has. in atomic units, the Fermi momentum
$${k_{F}} = {(3{\pi ^{2}}{\rho _{O}})^{{1/3}}} = {(9\pi /4)^{{1/3}}}{r_{s}}^{{ - 1}} = 1.917{r_{s}}^{{ - 1}} \simeq 2{r_{s}}^{{ - 1}} $$
; the Fermi velocity becomes
$${V_{F}} = {k_{F}} = 2{r_{s}}^{{ - 1}} $$
, the Fermi energy
$${E_{F}} = {v_{F}}^{{2/2}} = 2r{{}_{s}^{{ - 2}}} $$
and the plasma frequency
$${\omega _{p}} = {(4\pi {\rho _{O}})^{{1/2}}} = {3^{{1/2}}}{r_{s}} - 3/2 $$
.