Lawrence Livermore National Laboratory Environmental Report 2014

Abstract

's (LLNL's) compliance with environmental standards and requirements, describe LLNL's environmental protection and remediation programs, and present the results of environmental monitoring at the two LLNL sites-the Livermore site and Site 300. The report is prepared for the U.S. Department of Energy (DOE) by LLNL's Environmental Protection Department. Submittal of the report satisfies requirements under DOE Order 231.1A, Environmental Safety and Health Reporting, and DOE Order 5400.5, Radiation Protection of the Public and Environment. The report is distributed electronically and is available at https://saer.llnl.gov/, the website for the LLNL annual environmental report. Previous LLNL annual environmental reports beginning in 1994 are also on the website. Some references in the electronic report text are underlined, which indicates that they are clickable links. Clicking on one of these links will open the related document, data workbook, or website that it refers to.

The Khuri-Jones Threshold Factor as an Automorphic Function

“…x = cosh u cos v and y = sinh u sin v, the upper half of the z-plane is conformally mapped onto the interior of a strip in the w-plane bounded by the line u = 0 on the right, and the lines v = 0 on the bottom and v = π on the top. The partial wave amplitude, (2), then reduces to (−1) /(2 + 1) at the pole, so that the contribution from one Regge pole at = α to the partial wave projection, as k 2 → 0, is…”

“…We will show that, for real angular momenta, the partial wave amplitude is such an automorphic function corresponding to the dihedral group. According to Khuri [1] and Jones [2], the partial wave amplitude derives its form from the asymptotic large angular momentum limit of the Legendre function of the second kind which has three singular points. These singular points are homologues of vertices of triangles in a conformal mapping, and the group we will be dealing with is the triangular group.…”