Page 15 - 83 basic knowledge of astronomy

Z n E=E n

Z m E=E m
Spontaneous Emission Absorption Induced Emission

Figure 14: The three possible transitions between two energy states.

certain coefficient α m as:
n
m
df sp = α dν dΩ dt. (9)
n

E= E n

E= E m

dΩ
-s

Figure 15: Spontaneous emission of radiation.

(2) Absorption Z m → Z n
Some of the radiation passing through the gaseous medium may be ab-
sorbed in a transition from Z m to Z n , at a frequency around ν mn = (E n −
E m ) / h (Figure 16). The absorption probability df ab for the radiation inci-
dent from a direction within a small solid angle dΩ around s, and in a small
frequency bandwidth dν, during a short time interval dt, must be propor-
tional to dν dΩ dt and to the spectral energy density per unit solid angle,
u ν (s), of the radiation itself. Therefore, introducing a proportionality coeffi-
n
cient β , we have:
m
n
df ab = β u ν (s) dν dΩ dt. (10)
m
(3) Induced (or stimulated) emission Z n → Z m
Radiation with a frequency ν incident from a certain direction s may
induce (or ‘stimulate’) transitions of gas particles from higher to lower energy

15