Majorana solutions to the two-electron problem

A review of the known different methods and results devised to study the two-electron atom problem, appeared in the early years of quantum mechanics, is given, with particular reference to the calculations of the ground state energy of helium. This is supplemented by several, unpublished results obtained around the same years by Ettore Majorana, which results did not convey in his published papers on the argument, and thus remained unknown until now. Particularly interesting, even for current research in atomic and nuclear physics, is a general variant of the variational method, developed by Majorana in order to take directly into account, already in the trial wavefunction, the action of the full Hamiltonian operator of a given quantum system. Moreover, notable calculations specialized to the study of the two-electron problem show the introduction of the remarkable concept of an effective nuclear charge different for the two electrons (thus generalizing previous known results), and an application of the perturbative method, where the atomic number Z was treated effectively as a continuous variable, contributions to the ground state energy of an atom with given Z coming also from any other Z. Instead, contributions relevant mainly for pedagogical reasons count simple broad range estimates of the helium ionization potential, obtained by suitable choices for the wavefunction, as well as a simple alternative to Hylleraas' method, which led Majorana to first order calculations comparable in accuracy with well-known order 11 results derived, in turn, by Hylleraas.Comment: amsart, 20 pages, no figure

Pathways from agriculture-to-nutrition: Design and conduct of the National PoSHAN surveys of Nepal

Pathways through which agricultural production may influence markets, household food security, dietary patterns and nutritional status remain incompletely understood. While cross-sectional surveys are common, national, population-based, standardized data collection systems that annually monitor markets, local services, food security, dietary intake and nutritional status may be needed to understand time trends and relationships. We describe the design and methods of an annual nationally representative series of surveys of households with preschool aged children in 7 Village Development Committees (VDCs) sampled across each agroecological zone (mountains, hills and plains) in Nepal. Our sampling methodology yielded 21 VDCs, 63 wards (3 per VDC) and 40 markets in 2013, 2014 and 2016. Each year between ~ 4286-5097 consenting households were assessed for agricultural practices, socioeconomic conditions and food security; diet by 7-day food frequency and nutritional status by anthropometry (weight, height and arm circumference) of women (n=4509-5458) and children (n=5401- 5468) using standardized procedures. Due to a major earthquake in April 2015, a truncated sample (wards n=27) was reached in 2015. Three VDCs, each representing a centroid of surveyed VDCs in each zone, served as year-round sentinel sites in which we conducted six surveys of seasonal conditions from 2013-2015. Representative, sameseason, same-site surveys offer a feasible national framework for assessing annual status and trends in agricultural, food security and nutritional conditions to identify opportunities for policy and program interventions and observe population responses along a continuum leading from agriculture to nutrition

Background studies in support of a feasibility assessment on the use of copper-base materials for nuclear waste packages in a repository in tuff

This report combines six work units performed in FY`85--86 by the Copper Development Association and the International Copper Research Association under contract with the University of California. The work includes literature surveys and state-of-the-art summaries on several considerations influencing the feasibility of the use of copper-base materials for fabricating high-level nuclear waste packages for the proposed repository in tuff rock at Yucca Mountain, Nevada. The general conclusion from this work was that copper-base materials are viable candidates for inclusion in the materials selection process for this application. 55 refs., 48 figs., 22 tabs