Relativistic three-particle scattering equations

We derive a set of relativistic three-particle scattering equations in the three-particle c.m. frame employing a relativistic three-particle propagator suggested long ago by Ahmadzadeh and Tjon in the c.m. frame of a two-particle subsystem. We make the coordinate transformation of this propagator from the c.m. frame of the two-particle subsystem to the three-particle c.m. frame. We also point out that some numerical applications of the Ahmadzadeh and Tjon propagator to the three-nucleon problem use unnecessary nonrelativistic approximations which do not simplify the computational task, but violate constraints of relativistic unitarity and/or covariance.Comment: 5pages, text and one ps figure (in revtex) include

The Separable Kernel of Nucleon-Nucleon Interaction in the Bethe-Salpeter Approach

The dispersion relations for nucleon-nucleon (NN) T-matrix in the framework of Bethe-Salpeter equation for two spin one-half particle system and with separable kernel of interaction are considered in the paper. The developed expressions are applied for construction of the separable kernel of interaction for S partial-waves in singlet and triplet channels. We calculate the low energy scattering parameters and the phase shifts and also the deuteron binding energy with the separable interaction. The approach can be easily extended to higher partial-waves for NN-scattering and other reactions (anti N N-, pi N-scattering).Comment: RevTex 4 style, 9 pages, 1 figur

Relativistic Corrections to the Triton Binding Energy

The influence of relativity on the triton binding energy is investigated. The relativistic three-dimensional version of the Bethe-Salpeter equation proposed by Blankenbecler and Sugar (BbS) is used. Relativistic (non-separable) one-boson-exchange potentials (constructed in the BbS framework) are employed for the two-nucleon interaction. In a 34-channel Faddeev calculation, it is found that relativistic effects increase the triton binding energy by about 0.2 MeV. Including charge-dependence (besides relativity), the final triton binding energy predictions are 8.33 and 8.16 MeV for the Bonn A and B potential, respectively.Comment: 25 pages of text (latex), 1 figure (not included, available upon request

Yang-Lee zeros for a nonequilibrium phase transition

Equilibrium systems which exhibit a phase transition can be studied by investigating the complex zeros of the partition function. This method, pioneered by Yang and Lee, has been widely used in equilibrium statistical physics. We show that an analogous treatment is possible for a nonequilibrium phase transition into an absorbing state. By investigating the complex zeros of the survival probability of directed percolation processes we demonstrate that the zeros provide information about universal properties. Moreover we identify certain non-trivial points where the survival probability for bond percolation can be computed exactly.Comment: LaTeX, IOP-style, 13 pages, 10 eps figure

The New Albany Shale gas play in southern Indiana

This poster was presented at the 2006 Eastern Section American Association of Petroleum Geologists, 35th Annual Meeting, in Buffalo, N.Y., October 8-11, 2006.The New Albany Shale (Devonian and Mississippian) in Indiana is mostly brownish-black organic-rich shale with lesser greenish-gray shale. The formation is 100 to 140 feet thick in southeastern Indiana and dips and thickens to the southwest into the Illinois Basin, where it attains a thickness of more than 360 feet in Posey County. Gas production from New Albany Shale began in 1885 and drilling activity continued into the 1930s, when interest waned in favor of more lucrative opportunities elsewhere. Renewed activity, driven by higher gas prices, has been brisk since the mid-1990s, witnessed by the completion of more than 400 productive wells. The majority of these wells were drilled in Harrison County, where production typically occurs at depths from 500 to 1,100 feet and production rates generally range from 20 to 450 MCFGPD. In the past 2 years, Daviess County and surrounding areas have become the focus of New Albany exploration after the El Paso Production No. 2-10 Peterson horizontal discovery well was rumored to have tested 1.3 MMCFGPD at an approximate measured depth of 2,200 feet. New Albany production is mostly from the organic-rich Clegg Creek Member. Gas compositions (C1-C4 and CO2) and carbon and hydrogen isotopic signatures indicate that both purely thermogenic and mixed thermogenic and biogenic gases are produced from the New Albany. Produced water ranges from brine to water diluted through recharge by modern precipitation; the brine zones contain primarily thermogenic gas and the diluted water zones contain gas of mixed thermogenic and biogenic origin

Web-based glacial and bedrock geologic map products and databases for Marion County, Indiana

This poster was presented at the 2010 meeting of the North-Central and South-Central Sections of the Geological Society of America, 44th Annual Meeting, in Branson, MO, April 11-13, 2010.The Internet has become a medium of choice for delivering geologic information to both technical users and the general public. The Indiana Geological Survey (IGS) is creating a Web-based glacial and bedrock geologic map site for Marion County in central Indiana to provide detailed geologic information needed to address environmental and resource management issues related to a growing population and land-use conflicts. Marion County is the location of Indianapolis, the state capital and largest city. The IGS anticipates that the information available via the Web site will be widely used by the general public, industry, and government entities concerned about the geology, groundwater, and other natural resources in this county. The Marion County Web site links an Internet map server (IMS) and database to provide a portal to the IGS’s enterprise geodatabases that allows users to efficiently create, manage, update, and distribute maps and data. The IMS site retrieves maps and cross sections of Marion County completed during earlier IGS mapping projects. Map layers pertaining to bedrock geology, surficial geology, hydrology, infrastructure, and imagery are included. Database information includes (1) lithologic information compiled from water-well records stored in the Indiana Department of Natural Resources, Division of Water archives, (2) natural gamma-ray geophysical log data, (3) stratigraphic test hole data, and (4) petroleum-well-record data. The development of the Web site is funded by the IGS and the Great Lakes Geologic Mapping Coalition.Great Lakes Geologic Mapping Coalitio

Images in Christmas Balls

We describe light-reflection properties of spherically curved mirrors, like balls in the Christmas tree. In particular, we study the position of the image which is formed somewhere beyond the surface of a spherical mirror, when an eye observes the image of a pointlike light source. The considered problem, originally posed by Abu Ali Hasan Ibn al-Haitham -- alias Alhazen -- more than a millennium ago, turned out to have the now well known analytic solution of a biquadratic equation, being still of great relevance, e.g. for the aberration-free construction of telescopes. We do not attempt to perform an exhaustive survey of the rich historical and engineering literature on the subject, but develop a simple pedagogical approach to the issue, which we believe to be of continuing interest in view of its maltreating in many high-school textbooks.Comment: 13 pages, 7 figures plain LaTeX; Also see http://cft.fis.uc.pt/eef/mirrors.htm, revised version has simplified formulas, more transparent for a wider audience, one reference adde

Relativistic Effect on Low-Energy Nucleon-Deuteron Scattering

The relativistic effect on differential cross sections, nucleon-to-nucleon and nucleon-to-deuteron polarization transfer coefficients, and the spin correlation function, of nucleon-deuteron elastic scattering is investigated employing several three-dimensional relativistic three-body equations and several nucleon-nucleon potentials. The polarization transfer coefficients are found to be sensitive to the details of the nucleon-nucleon potentials and the relativistic dynamics employed, and prefer trinucleon models with the correct triton binding energy. (To appear in Phys. Rev. C)Comment: pages: 21, LaTex text + 7 ps-figures at the en

Web-Based Geologic Maps, Databases, and HTML Pages for Marion County, Indiana

This poster was presented at the 2011 meeting of the Indiana Academy of Science, 126th Annual Academy Meeting, March 4-5, 2011, Indianapolis, Indiana.The Indiana Geological Survey (IGS) has created an internet map server for Marion County in central Indiana. The site provides detailed geologic information needed to address environmental issues, resource management issues, and land-use conflicts related to a growing population. Marion County is the location of Indianapolis, the state capital and largest city. The IGS anticipates that the Web site will be widely used by the general public, industry, and government entities concerned about the geology, groundwater, and other natural resources. The Marion County Web site links an Internet map server (IMS) and database to provide a portal to the IGS‘s enterprise geodatabases, which allow users to efficiently create, manage, update, and distribute maps and data. The IMS site retrieves maps of bedrock and surficial geology completed during earlier IGS mapping projects. Hydrogeology, infrastructure, and imagery map layers are also included. Database information includes lithologic information (iLITH) compiled from water-well records stored in the Indiana Department of Natural Resources, Division of Water archives and natural gamma-ray geophysical log data, stratigraphic test hole data, and petroleum well-record data from the IGS. Currently, the following products are being prepared: (1) illustrated Web pages discussing the surficial geology, bedrock geology, and bedrock topography; (2) illustrated Web pages discussing digital elevation model terrain, gamma-ray log, iLITH, and clay thickness data sets; (3) online glossary; and (4) metadata for the map layers. The development of the Web site is funded by the IGS and the Great Lakes Geologic Mapping Coalition.Great Lakes Geologic Mapping Coalitio

Quantum Monte Carlo Studies of Relativistic Effects in Light Nuclei

Relativistic Hamiltonians are defined as the sum of relativistic one-body kinetic energy, two- and three-body potentials and their boost corrections. In this work we use the variational Monte Carlo method to study two kinds of relativistic effects in the binding energy of 3H and 4He. The first is due to the nonlocalities in the relativistic kinetic energy and relativistic one-pion exchange potential (OPEP), and the second is from boost interaction. The OPEP contribution is reduced by about 15% by the relativistic nonlocality, which may also have significant effects on pion exchange currents. However, almost all of this reduction is canceled by changes in the kinetic energy and other interaction terms, and the total effect of the nonlocalities on the binding energy is very small. The boost interactions, on the other hand, give repulsive contributions of 0.4 (1.9) MeV in 3H (4He) and account for 37% of the phenomenological part of the three-nucleon interaction needed in the nonrelativistic Hamiltonians.Comment: 33 pages, RevTeX, 11 PostScript figures, submitted to Physical Review