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grb absorption spectroscopy - Inaf

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Balance equation:<br />

dN t<br />

u<br />

dt<br />

( )<br />

TIME DEPENDENT MODELING<br />

= N ( ) ( ) ( ) ( )<br />

l t Blu F! t $ Nu t "<br />

% Aul + BulF t #<br />

! &<br />

% ! % " % 2<br />

& t ' & $ ' & d '<br />

( ) ( ) ( )<br />

* tc + * $ c + * dL<br />

+<br />

were: F ( t) = C [ 1+<br />

z]<br />

hν<br />

Absorption<br />

#<br />

up<br />

low<br />

hν<br />

Spontaneous emission<br />

% 1<br />

up up<br />

hν<br />

low low<br />

Stimulated emission

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