Theory of the Fireball

Since the interesting values of R are of the order of a few hundred
meters, the emitting layer will be def ined by the fact that the mean
free path is about 5 to 10 meters.
Equations (3.18) to (3.21) hold for emission in the exactly radial
direction. At an angle 8 with the radius we get instead
The apparent temperature of the emitting layer is then, according to
where T(R,O) is the emission temperature for forward emission. The
intensity of emission is a known (Planck) function of the wave length
and the temperature. Since the apparent temperature decreases (though
slowly) with 0, according to (3.23) there will be limb darkening. On
the many photographs of atomic explosions, it should be possible to
observe this Limb darkening and thus check the value of n.
The relation (3.17) needs to hold only in the neighborhood of the
value ( 3 -21) of 4 and is therefore quite general as long as 4, decreases
with increasing temperature. The exponent n should be determined at
constant pressure. For certain wave lengths, especially in the ultra-
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