From the charge
neutrality condition, the electron concentration in the freeze-out range is expressed
as
.
(1)
When we define as
,
(2)
Eq. (1) can be rewritten as a quadratic
equation:
,
(3)
where
,
(4)
,
(5)
and
.
(6)
The solution of Eq.
(3) is
(7)
or
.
(8)
When
(9)
that is
,
(10)
the solution is
(11)
that is
.
(12)
Therefore, is derived as
.
(13)
Since
,
(14)
we obtain the following relationship:
.
(15)