Stars as Laboratories for Fundamental Physics - MPP Theory Group

Particle Dispersion and Decays in Media 223
to spatial anticorrelations of like-charged particles. Fourier transforming
Eq. (6.64) yields the important result
S(q) =
q2
q 2 + k 2 S
(6.65)
for the structure factor.
The assumption of one mobile species of particles on a uniform
background corresponds to the model of a “one-component plasma.”
It is approximately realized in the interior of hot white dwarfs or the
cores of red-giant stars where the degenerate electrons form a “stiff”
background of negative charge in which the nondegenerate ions move.
In a nondegenerate situation, however, there are at least two mobile
species, ions of charge Ze and electrons. For this two-component
plasma Salpeter (1960) derived the structure functions
S ee (q) =
S ii (q) =
q 2 + ZkD
2 ,
q 2 + (1 + Z)kD
2
q 2 + kD
2 ,
q 2 + (1 + Z)kD
2
S ei (q) =
k 2 D
. (6.66)
q 2 + (1 + Z)kD
2
The Fourier transform of the screening cloud around an electron is
S(q) = S ee (q) − ZS ei (q) =
q2
, (6.67)
q 2 + kS
2
with kS 2 = kD 2 + ki
2 = (1 + Z) kD. 2 (Note that for only one species of ions
ki
2 = ZkD.) 2 Hence one reproduces a screened charge distribution which
causes a Yukawa potential. However, the small-q behavior of S ee or S ii
is very different: S ee (0) = Z/(1 + Z) in a two-component plasma while
S ee (0) = 0 for only one component.
6.4.3 Strongly Coupled Plasma
For low temperatures, the screening will not be of Yukawa type and
the structure factor will deviate from the simple Debye formula. A
plasma can be considered cold if the average Coulomb interaction energy
between ions is much larger than typical thermal energies. To
quantify this measure, one introduces the “ion-sphere radius” a i by
virtue of n −1
i = 4πa 3 i /3 where n i is the number density of the mobile