A New Method for Estimating Neutron Reaction Cross Sections Based on Wick’s Limit

Abstract

Wick's limit is an inequality that relates the zero-degree differential elastic scattering cross section to the total cross section. The deviation of Wick's limit from an exact equality is small over a wide range of incident energies and target masses. Under these circumstances we show that Wick's limit can be used to correlate the uncertainties in the two terms of the reaction (nonelastic) cross section expressed as the difference between the total and angle-integrated elastic cross sections. When suitable elastic angular distributions are available, we show that the reaction cross section may be obtained with small errors (typically 1.5-3%). Examples are shown for 208 Pb, 54 56 Fe, 232 Th, and 238 U. WICK'S LIMITwhere f´0 o µ is the zero-degree scattering amplitude, σ tot is the total cross section, and k is the center-of-mass wave number. The zero-degree differential elastic cross section σ 0 is given byThus the zero-degree differential elastic cross section σ 0 must be equal to or exceed Wick's limit which isWe define the fractional deviation of the zero-degree differential cross section from Wick's limit asWick's limit is a useful concept when η is small. Figure 1 shows the fractional deviation η vs. energy for several nuclei, using the global optical potential of Koning and Delaroche [2]. For all nuclei shown, there is a significant energy range (approximately 5-60 MeV) in which the deviation from Wick's limit does not exceed a few percent.Insight into this behavior is provided by the Ramsauer model, a simple single-phase-shift model that reproduces FIGURE 1. Fractional deviation η using the optical potential of [2].total cross sections at the 1% level from 5-60 MeV [3]. We define a quantity resembling an S-matrix element in terms of the forward scattering amplitude by S 1 · 2i f´0 o µ k´R ·λ µ 2 (5)

Modeling of High-Precision Neutron Nonelastic Cross Sections

“…5,6 In this paper we analyze these data using two distinct methods. Since the nonelastic cross section is close to the "black" nucleus value, we use the nuclear Ramsauer model 7,8 (a semiclassical calculation) to estimate a small correction factor.…”