Mean proton andα-particle reduced widths of the Porter-Thomas distribution and astrophysical applications

Abstract

The Porter-Thomas distribution is a key prediction of the Gaussian orthogonal ensemble in random matrix theory. It is routinely used to provide a measure for the number of levels that are missing in a given resonance analysis. The Porter-Thomas distribution is also of crucial importance for estimates of thermonuclear reaction rates where the contributions of certain unobserved resonances to the total reaction rate need to be taken into account. In order to estimate such contributions by randomly sampling over the Porter-Thomas distribution, the mean value of the reduced width must be known. We present mean reduced width values for protons and $\ensuremath{\alpha}$ particles of compound nuclei in the $A=28--67$ mass range. The values are extracted from charged-particle elastic scattering and reaction data that were measured at the Triangle Universities Nuclear Laboratory over several decades. Our new values differ significantly from those previously reported that were based on a preliminary analysis of a smaller data set. As an example for the application of our results, we present new thermonuclear rates for the ${}^{40}$Ca($\ensuremath{\alpha}$,$\ensuremath{\gamma}$)${}^{44}$Ti reaction, which is important for ${}^{44}$Ti production in core-collapse supernovae, and compare with previously reported results.