New light on electromagnetic corrections to the scattering parameters obtained from experiments on pionium

We calculate the electromagnetic corrections needed to obtain isospin invariant hadronic pion-pion s-wave scattering lengths a^0, a^2 from the elements a_cc, a_0c of the s-wave scattering matrix for the (\pi^+ \pi^-, \pi^0 \pi^0) system at the \pi^+ \pi^- threshold. These elements can be extracted from experiments on pionium. Our calculation uses energy independent hadronic pion-pion potentials that satisfactorily reproduce the low-energy phase shifts given by two-loop chiral pertur- bation theory. We also take into account an important relativistic effect whose inclusion influences the corrections considerably.Comment: 14 pages including 3 figures. Uses elsart.cls. Some numbers have been updated and a few typos have been correcte

The extraction of hadronic parameters from experiments on pionium

Experimental values of the lifetime of the 1s level of pionium and of the difference between the energies of the 2s and 2p levels yield values of the a(0c) and a(cc) elements of the s-wave scattering matrix for the 2-channel (pi+ pi-, pi0 pi0) system at the pi+ pi- threshold. We develop a method for obtaining the isospin invariant quanties a20 - a00 and 2a00 + a20 from a(0c) and a(cc). We emphasize that the isospin invariant scattering lengths a00 and a20 universally used in the literature cannot be considered to be purely hadronic quantities.Comment: 17 pages, Revtex, 1 postscript figure, new version of figure which removes ghostscript problem

The effects of the new energy regime on economic capacity, production, and prices

Energy policy ; Production (Economic theory) ; Prices

Energy resources and potential GNP

Natural resources ; Gross national product

Electromagnetic corrections for the analysis of low energy pi-p scattering data

We calculate the electromagnetic corrections to the isospin invariant mixing angle and to the two eigenphases for the s and p-waves for low energy pi-p elastic and charge exchange scattering. These corrections have to be applied to the nuclear quantities obtained from phase shift analyses of the experimental data in order to obtain the hadronic phases. We compare our results with earlier calculations and estimate the uncertainties in the corrections.Comment: 19 pages, 5 figures. Uses elsart.cls Accepted for publication in Nuclear Physics

The effect of vacuum polarisation on muon-proton scattering at small energies and angles

We give a compact expression for the unpolarised differential cross section for muon-proton scattering in the one photon exchange approximation. The effect of adding the vacuum polarisation amplitude to the no-spin-flip amplitude for one photon exchange is calculated at small energies and scattering angles and is found to be negligible for present experiments.Comment: 6 pages, one figur

Hadronic Effects in the Pionium Ion

The hadronic properties of the pionium ion (Coulomb bound system of three charged pions) are estimated using the results for the positronium ion $P{s}^{-}$. It turns out that the hadronic shift of the ground state energy and the lifetime of the pionium ion are approximately the same as for pionium.Comment: RevTex, 5 page

Birds of Lake McConaughy and the North Platte River Valley, Oshkosh to Keystone

Cedar Point Biological Station was established in 1975 at a site approximately one mile below Kingsley Dam in Keith County, Nebraska. Since that time, summer ornithology classes have been periodically offered beginning in 1977 when it was taught by Dr. Stephen Fretwell. A variety of ornithologists have kept records of the summer birds of the area. Beginning in 1970, when he first visited the area, the senior author has accumulated a large amount of data covering all seasons of the year, which form the primary basis for the seasonal information in this paper. In addition, much information was contributed by C. Fred Zeillemaker from late 1977 to early 1982, when he was Manager at nearby Crescent Lake National Wildlife Refuge. Other contributors include: Charles Brown, Craig Faanes, Don Mahoney, Dorothy and Mark Rasche, and Melly Zeillemaker. Because of the unusual diversity of terrestrial and aquatic habitats within the rather circumscribed area of Lake McConaughy and adjoining localities, it is of special interest to ornithologists. Furthermore, the area is essentially in the middle of the east-west faunal transition zone in the Great Plains, so that a number of closely related species-pairs (buntings, grosbeaks, tanagers, orioles, et al.) are represented. Finally the annual concentration of biologists at Cedar Point makes it desirable that a comprehensive bird list for the area be prepared. The following is largely limited to the North Platte River Valley from Oshkosh east to the vicinity of Keystone as indicated in Figure 1. Major birding areas include the Oshkosh sewage lagoons, the Lewellen area, Ash Hollow State Historical Park, Clear Creek State Game Management Area, Lake McConaughy, Lake Ogallala, Keystone Lake, and Cedar Point Biological Station. Except where otherwise indicated, the observations are those of the authors