On fluctuation properties of MACS

Abstract

The Maxwellian Average Cross Section (MACS) is usually calculated with help of the statistical codes that do not take into account fluctuations of individual resonance parameters. The actual MACS can substantially deviate from its expectation value. This work focuses on description of various sources and aspects of these fluctuations. Simulated resonance sequences considering all the fluctuations involved in the statistical model are used for this purpose. Contribution of various sources of the fluctuations and neutrons with different orbital momenta are thoroughly investigated and described. Impact of available cross section data at low neutron energies is also checked. Based on this analysis simple empirical formulae for estimating relative fluctuations of MACS using solely $s$-wave resonance spacing $D_0$ and the temperature of the stellar environment are derived. It is shown that real nuclei follow the proposed formula well. The expected MACS fluctuations increase with $D_0$ and can be significant. While for isotopes with $D_0$ in eV range the possible deviation from calculated values are small, for nuclei with $D_0$ in the keV range the full-width half-maximum of the expected distribution is larger than about 25\% and 10\% for astrophysically relevant temperatures of $kT=8$ and 30 keV. At least for these nuclei the predictions from statistical codes must be taken with caution.