Neutron Resonances: Widths Distribution versus the Porter-Thomas Law

Abstract

The neutron resonance scattering off heavy nuclei is a paradigmatic example of the chaotic processes that are well described within the framework of the standard Random Matrix Theory (RMT). In zero approximation of non-overlapping resonances, the resonance width distribution is given by the standard Porter-Thomas law (PTD), where x = Γ / Γ is the resonance width measured in the units of its mean value. We analyze the influence of the resonance overlapping and show that the experimentally observed deviations from of the PTD arise due to the influence of a moderate number of neighboring resonances located inside a restricted energy interval within which the mean level spacing D remains constant.

Test of the Porter-Thomas distribution with the total cross section autocorrelation function

“…Moreover, subsequent analyses [7,8] of the reduced neutron widths in the nuclear data ensemble seem to overturn the long held belief that it furnishes persuasive evidence for the applicability of the Gaussian orthogonal ensemble (GOE) of Hamiltonian matrices [9] in the description of CN fluctuation properties. There have been several attempts to reconcile these new findings with the standard statistical models of CN processes [10][11][12][13][14][15][16][17][18][19][20][21][22], but there is a consensus [23][24][25] that more data is needed to guide theoretical considerations.…”