## Nuclear Reaction Rates

The nuclear reaction rates are mainly determined by the cross-sections a of the particles, i.e., the effective surface of the particles for the considered interaction. The cross-section of a given reaction is the product of several terms (Sect. 9.3): the probability of geometrical encounter, the probability of barrier penetration, the probability that the compound nucleus decays into the considered channel, with an appropriate overall average on the velocity distribution of particles.

Let us first examine the global relations between the cross-sections and the nuclear reactions rates. We suppose that particles "X" are bombarded by particles "a" with a uniform flux as in lab experiments. The cross-section is defined by number of reactions of "X" due to "a" per second a =---, (9.4)

flux of incident particles "a"

with a in cm2. If the nuclei "X" have a uniform concentration nX, the number of reactions by units of volume and time is the product of anX by the flux of incident particles. This flux is the number of particles "a" by cm2 and by second passing near particle "X", i.e., na v if the concentration of particles "a" is uniform and if v the relative velocity is the same for all particles. The reaction rate by volume unit is raX = a(v) v nanX, expressed in number of reactions per cm3 and second. In general, one writes raX = nanX I va(v)\$(v)dv = nanX < av >aX, (9.5)

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