Typical Broadened Cross Sections
The effects of temperature on typical cross sections is best
illustrated by giving several examples. First, here is the
(n,α) cross section for B-10 shown for temperatures of
0K, 3000K, and 3000000K. This shows that a 1/v
cross section is invariant under Doppler broadening.
Next, here is the elastic cross section for carbon shown for temperatures of 0K, 300K, 3000K, and 30000K. This shows that a constant cross section will develop a 1/v tail under Doppler broadening.
Finally, here is how resonance cross section behave under Doppler broadening. The (n,gamma) cross section for Pu-240 is shown for temperatures of 0K, 30000K, and 300000K. Resonances with energies larger than kT/A broaden symmetrically (and their areas tend to remain constant). Low energy resonances develop an additional 1/v tail, and their areas do not remain constant under Doppler broadening.
These effects are best understood by noting that Doppler broadening preserves the reaction rate v*σ(v), and a finite reaction rate is expected for T larger than zero even as v goes to zero.
|23 January 2013||T-2 Nuclear Information Servicefirstname.lastname@example.org|