Maxwellian-Averaged Cross Sections (MACS) and Astrophysical Reaction Rates Help

Maxwellian-Averaged Cross Sections (MACS) were calculated by Simpson method for neutron-induced reactions using the following expression:

σMaxw(kT)=2a2/(√π(kT)2)∫ σ(En)Enexp(-aEn/kT)dEn   

where:

  • En is the neutron energy in the laboratory system,
  • a = mt/(mn+mt), where mn is the mass of the neutron and mt is the mass of the target nucleus.
  • σ(En) is the cross section obtained from the JENDL-4.0, CENDL-3.1, ROSFOND 2010, ENDF/B-VII.0, JEFF 3.1, JENDL 3.3 and ENDF/B-VI.8 libraries.

Astrophysical reaction rates, R(kT), were calculated using:

R(kT) = 10-24NAσMaxw(kT)vT   [cm3/mole*s],

where:

  • NA is the Avogadro constant,
  • vT = √(2kT/μ), with μ the reduced mass of the neutron-target system.

Uncertainties in the cross sections and reaction rates are available in the latest release Nuclear Data Sheets 113, 3120 (2012).

Last Modified: February 22, 2013