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 α-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(α,γ) 44 Ti reaction, which is important for 44 Ti production in core-collapse supernovae, and compare with previously reported results.

Nuclear astrophysics in the laboratory and in the universe

“…c A first step in this regard was the recent extraction of mean reduced widths from high-resolution data measured at TUNL for target nuclei in the A = 28−40 (α-particles) and A = 34−67 (protons) mass ranges. 54 For example, a mean value of θ 2 α = 0.018, averaged over target nuclei, spin-parities, and excitation energies, was obtained for α-particles, almost a factor of two larger than the preliminary value suggested in Longland et al 48 An example for the relevance of these results is given in Fig. 10.…”

“…However, the experimental values cover only a small part of the A-J π -E x parameter space and it is clearly desirable to have access to θ 2 values for all cases of interest. Considering that the data analyzed in Pogrebnyak et al 54 were accumulated over a period of more than 40 years at the now decommissioned 3-MeV Van de Graaff accelerator laboratory at TUNL, it is clear that the desired θ 2 values need to be obtained from nuclear theory, perhaps using the shell model. More work is needed in this regard for the future.…”

“…So far, the only systematic analysis of mean values for dimensionless reduced widths is presented in Pogrebnyak et al 54 As already mentioned, these values were extracted from the available experimental data, both for protons and α-particles, for a range of compound nuclei, A, spin-parities, J π , and excitation energies, E x . However, the experimental values cover only a small part of the A-J π -E x parameter space and it is clearly desirable to have access to θ 2 values for all cases of interest.…”

Thermonuclear reaction rate ofNe18(α,p)Na21Mohr1, Longland2, Iliadis3 2014Phys. Rev. CSelf Cite2618932View full textAdd to dashboardCite

“…In this work, we randomly sample θ 2 α for all states in Category D from a Porter-Thomas distribution with a mean reduced width of θ 2 α = 0.03 ± 0.01. We obtain this value by extrapolating the recent results of Pogrebnyak et al [26] for nuclei with slightly larger mass numbers A. In the latter work, θ 2 α = 0.018 was found with a trend to increasing values for smaller mass numbers.…”

“…Our recommended resonance strengths, ωγ αp , are listed in Table I. For states in category D we provide ωγ in parenthesis which are calculated from Γ α = 0.03×Γwhere the factor of 0.03 is taken from the systematics of reduced widths [26]. Note that these resonance strengths are used in the presentation of the recommended astrophysical S-factor in the next paragraph; however, these numbers do not enter directly in the calculation of N A σv because here a Porter-Thomas distribution will be sampled using the Monte-Carlo method.…”