DOCSLIB.ORG

Bose-Einstein Condensation

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Bose-Einstein Condensation features Physics World March 1997 29 Bose-Einstein condensation is an exotic quantum phenomenon that was observed in dilute atomic gases for the first time in 1995, and is now the subject of intense theoretical and experimental study Bose-Einstein condensation CHRISTOPHER TOWNSEND, WOLFGANG KETTERLE AND SANDRO STRINGARI IN 1924 the Indian physicist Satyendra Nath Bose sent Order reigns in the ground state Einstein a paper in which he derived the Planck law for black-body radiation by treating the photons as a gas of The dynamical behaviour of a gas at room temperature is identical particles. Einstein generalized Bose's theory to not affected by the fact that one atom cannot be distin- an ideal gas of identical atoms or molecules for which the guished from another. In accordance with the Heisenberg number of particles is conserved and, in the same year, uncertainty principle, the position of an atom is smeared predicted that at sufficiently low temperatures the par- out over a distance given by the thermal de Broglie wave- 2 12 ticles would become locked together in the lowest quan- length, XdB = (2TtH /kBmTy , where kB is the Boltzmann tum state of the system. We now know that this phenomenon, called Bose-Einstein condensation radio-frequency (BEC), only happens for "bosons" - particles antenna with a total spin that is an integer multiple of % curvature coil bias field coil the Planck constant divided by 2n. This Bose condensate, and the process of con- densation itself, was predicted to have many unusual properties and for years experimenters have tried to produce Bose-Einstein condensa- tion in the laboratory. Finally in 1995 groups at JILA, a laboratory run by the National Institute of Standards and Technology and the University of Colorado in Boulder, Colorado, and the Massachusetts Institute of Technology (MIT) obtained compelling evidence for Bose-Einstein condensation in dilute atomic gases. Both the Boulder and MIT groups, and a group at Rice University in Houston, Texas, have since improved the techniques for creating and observing this exotic quantum phenomenon, and rapid progress has been made in under- standing its dynamic and thermodynamic prop- 1 The set-up for evaporative cooling from the cloverieaf magnetic trap at MIT. The erties. At MIT we have recently verified the central (curvature) coils provide axial confinement while the outer colls (the "cloverleaves" or gradient coils) give tight radial confinement. The resulting intriguing feature that Bose-condensed atoms anisotroplc potential gives rise to cigar-shaped clouds. Radio-frequency radiation are "laser-like" - in other words, that the matter from an antenna selectively flips the spin of the most energetic atoms, and waves of the atoms are coherent. In these experi- the remaining atoms retheimalize to a lower temperature. Cooling Is forced by ments we have succeeded in observing coher- lowering the radio-frequency. ence directly, and have demonstrated a rudimentary "atom laser" that generates a beam of constant, m is the atomic mass and T is the temperature of coherent atoms, in analogy to emission of coherent the gas. At room temperature the de Broglie wavelength is photons by an optical laser. At the same time, theorists typically about ten thousand times smaller than the have clarified many fundamental issues and have de- average spacing between the atoms. This means that the veloped powerful methods to simulate real systems. matter waves of the individual atoms are uncorrelated or 30 Phy«tes World March 1997 "disordered", and the gas can cooling, polarization-gradient thus be described by classical cooling and magneto-optical Boltzmann statistics. trapping were developed to cool As the gas is cooled, however, and trap atoms. These techniques the smearing increases, and profoundly changed the nature of eventually there is more than atomic physics and provided a one atom in each cube of dimen- new route to ultracold tempera- sion ^.dB. The wavefunctions of tures that does not involve cryo- adjacent atoms then "overlap", genics. Atoms at sub-millikelvin causing the atoms to lose their temperatures are now routinely identity, and the behaviour of used in a variety of experiments. the gas is now governed by Alkali atoms are well suited to quantum statistics. laser-based methods because Bose-Einstein statistics dra- their optical transitions can be matically increase the chances of excited by available lasers and finding more than one atom in because they have a favourable the same state, and we can think internal energy-level structure for of the matter waves in a Bose cooling to low temperatures. gas as "oscillating in concert". However, the lowest temperat- The result is Bose—Einstein con- ure that these laser cooling tech- densation, a macroscopic occu- niques can reach is limited by the pation of the ground state of energy of a single photon. As a the gas. (In contrast, fermions - result, the "phase-space density" particles with a total spin of - the number of atoms within a l (n + /2)'h, where n is an integer - volume A.dB - is typically about a cannot occupy the same quan- million times lower than is tum state.) Einstein described needed for BEC. the process as condensation The successful route to BEC without interactions, making it turned out to be a marriage of an important paradigm of quan- the cooling techniques developed tum statistical mechanics. for hydrogen and those for the The density distribution of the alkalis: an alkali vapour is first condensate is represented by a laser cooled and then evapor- single macroscopic wavefunction atively cooled. In evaporative with a well denned amplitude and cooling, high-energy atoms are phase, just as for a classical field. allowed to escape from the sam- Indeed, the transition from dis- ple so that the average energy of ordered to coherent matter waves the remaining atoms is reduced. can be compared to the change Elastic collisions redistribute the from incoherent to laser light. energy among the atoms such Intensity (arbitrary units) that the velocity distribution Chilling the atoms reassumes a Maxwell-Boltzmann 2 Direct and non-destructive observation of the formation of form, but at a lower temperature. a Bose condensate by dispersive light scattering (phase- Bose-Einstein condensation has contrast Imaging) at MIT. The Intensity of scattered light is This is the same evaporation been cited as an important phe- shown as a function of position in the trap, which Is process that happens when tea nomenon in many areas of proportional to the column density of atoms along the line- cools, but the extra trick for physics, but until recently the of-sight. The Image on the left shows the cloud cooled to trapped atoms is that the thresh- only evidence for condensation just above the BEC transition temperature, and the old energy can be gradually came from studies of superfluid distribution of atoms is almost classical. As the temperature lowered. This allows the atomic is lowered through the phase transition a sharp peak of sample to be cooled by many liquid helium and excitons in atoms begins to appear at the trap centre (middle), and semiconductors. In the case of further cooling increases the condensate fraction to almost orders of magnitude, with the liquid helium, however, the 100% (right). only drawback being that the strong interactions that exist in a number of trapped atoms is liquid qualitatively alter the nature of the transition. For reduced {Physics Vforld 1995 July p21; August p21). this reason a long-standing goal in atomic physics has The challenge in combining these two cooling schemes been to achieve BEC in a dilute atomic gas. The challenge for alkalis was a question of atomic density. Optical was to cool the gases to temperatures around or below one methods work best at low densities, where the laser light is microkelvin, while preventing the atoms from condensing not completely absorbed by the sample. Evaporation, on into a solid or a liquid. the other hand, requires high atomic densities to ensure Efforts to Bose condense atoms began with hydrogen rapid rethermalization and cooling. This changed the more than 15 years ago. In these experiments hydrogen emphasis for optical methods: while they had previously atoms are first cooled in a dilution refrigerator, then been used to produce low temperatures and high phase- trapped by a magnetic field and further cooled by space density simultaneously, they now needed to produce evaporation (see below). This approach has come very high elastic collision rates. Furthermore, this had to be close to observing BEC, but is limited by the recombi- achieved in an ultrahigh vacuum chamber to prolong the nation of individual atoms to form molecules and by lifetime of the trapped gas. Thus no new concept was the detection efficiency. needed to achieve BEC, but rather it was an experimental In the 1980s laser-based techniques such as Doppler challenge to improve and optimize existing techniques. Phyaica Worid March 1997 31 These developments were pursued mainly at MIT and down states. The frequency of the field is adjusted so that Boulder from die early 1990s. it only affects the atoms at the edge of the cloud - in an harmonic oscillator potential, these atoms have the Improved techniques in magnetic trapping highest energy. When the moments of these atoms are flipped, the magnetic forces become anti-trapping and the For evaporative cooling to work, die atoms must be ther- atoms are expelled from the trap. As the cloud cools it mally isolated from their surroundings. This must be done shrinks towards the centre of the trap, so die frequency of with electromagnetic fields, since at ultracold temperat- the radio-frequency field must be continually reduced to ures atoms stick to all surfaces.
Load more

Recommended publications
  • Equations of State and Thermodynamics of Solids Using Empirical Corrections in the Quasiharmonic Approximation
    PHYSICAL REVIEW B 84, 184103 (2011) Equations of state and thermodynamics of solids using empirical corrections in the quasiharmonic approximation A. Otero-de-la-Roza* and V´ıctor Luana˜ † Departamento de Qu´ımica F´ısica y Anal´ıtica, Facultad de Qu´ımica, Universidad de Oviedo, ES-33006 Oviedo, Spain (Received 24 May 2011; revised manuscript received 8 October 2011; published 11 November 2011) Current state-of-the-art thermodynamic calculations using approximate density functionals in the quasi- harmonic approximation (QHA) suffer from systematic errors in the prediction of the equation of state and thermodynamic properties of a solid. In this paper, we propose three simple and theoretically sound empirical corrections to the static energy that use one, or at most two, easily accessible experimental parameters: the room-temperature volume and bulk modulus. Coupled with an appropriate numerical fitting technique, we show that experimental results for three model systems (MgO, fcc Al, and diamond) can be reproduced to a very high accuracy in wide ranges of pressure and temperature. In the best available combination of functional and empirical correction, the predictive power of the DFT + QHA approach is restored. The calculation of the volume-dependent phonon density of states required by QHA can be too expensive, and we have explored simplified thermal models in several phases of Fe. The empirical correction works as expected, but the approximate nature of the simplified thermal model limits significantly the range of validity of the results. DOI: 10.1103/PhysRevB.84.184103 PACS number(s): 64.10.+h, 65.40.−b, 63.20.−e, 71.15.Nc I.
    [Show full text]
  • 2007-2008 Physics at Brown Newsletter
    Physics at Brown NEWS FOR ALUM N I an D FRIE N DS 2007 ISSUE GREETINGS FROM THE CHAIR - SP RING 2008 elcome to another issue of the Brown Physics newsletter. the rank of Associate Professor with tenure. We also report on WI wrote three years ago, during my first term as the some notable faculty achievements for the past year. department chair--with a committed faculty, dedicated staff, enthusiastic students, supportive administration, and engaged e continue the tradition of highlighting the research of alumni and friends--that the future of physics at Brown looked Wour 2007 Galkin Foundation Fellow on page 2. Also bright. Many things have taken place since then. Here we the effort in enriching our physics instruction continues. Three highlight some of the activities of the past year. new courses are offered this year and proposals for three new physics concentrations are under way. Other noteworthy 007 marked the 50th anniversary of the BCS Theory activities include WiSE, Poster Session, UTRA Awards, 2of Superconductivity. We honored Prof. Leon Resource Center, etc. In addition, community outreach Cooper with a two-day symposium on April remains a priority for the Department with a weekly 12-13. A brief description of this event is open house at Ladd and a greatly expanded five- provided on page 3. year NSF supported GK-12 program. e also report on the establishment hanks to a generous gift from his family, an Wof the Institute for Molecular and TAnthony Houghton Prize will be awarded Nanoscale Innovation, which represents an annually for the best theoretical thesis.
    [Show full text]
  • States of Matter Lesson
    National Aeronautics and Space Administration STATES OF MATTER NASA SUMMER OF INNOVATION LESSON DESCRIPTION UNIT This lesson explores the states of matter Physical Science—States of Matter and their properties. GRADE LEVELS OBJECTIVES 4 – 6 Students will CONNECTION TO CURRICULUM • Simulate the movement of atoms and molecules in solids, liquids, Science and gases TEACHER PREPARATION TIME • Demonstrate the properties of 2 hours liquids including density and buoyancy LESSON TIME NEEDED • Investigate how the density of a 4 hours Complexity: Moderate solid behaves in varying densities of liquids • Construct a rocket powered by pressurized gas created from a chemical reaction between a solid and a liquid NATIONAL STANDARDS National Science Education Standards (NSTA) Science and Technology • Abilities of technological design • Understanding science and technology Physical Science • Position and movement of objects • Properties and changes in properties of matter • Transfer of energy MANAGEMENT For the first activity you may need to enhance prior knowledge about matter and energy from a supplemental handout called “Diagramming Atoms and Molecules in Motion.” At the middle school level, this information about the invisible world of the atom is often presented as a story which we ask them to accept without much ready evidence. Since so many middle school students have not had science experience at the concrete operational level, they are poorly equipped to work at an abstract level. However, in this activity students can begin to see evidence that supports the abstract information you are sharing with them. They can take notes on the first two descriptions as you present on the overhead. Emphasize the spacing of the particles, rather than the number.
    [Show full text]
  • The Development of the Science of Superconductivity and Superfluidity
    Universal Journal of Physics and Application 1(4): 392-407, 2013 DOI: 10.13189/ujpa.2013.010405 http://www.hrpub.org Superconductivity and Superfluidity-Part I: The development of the science of superconductivity and superfluidity in the 20th century Boris V.Vasiliev ∗Corresponding Author: [email protected] Copyright ⃝c 2013 Horizon Research Publishing All rights reserved. Abstract Currently there is a common belief that the explanation of superconductivity phenomenon lies in understanding the mechanism of the formation of electron pairs. Paired electrons, however, cannot form a super- conducting condensate spontaneously. These paired electrons perform disorderly zero-point oscillations and there are no force of attraction in their ensemble. In order to create a unified ensemble of particles, the pairs must order their zero-point fluctuations so that an attraction between the particles appears. As a result of this ordering of zero-point oscillations in the electron gas, superconductivity arises. This model of condensation of zero-point oscillations creates the possibility of being able to obtain estimates for the critical parameters of elementary super- conductors, which are in satisfactory agreement with the measured data. On the another hand, the phenomenon of superfluidity in He-4 and He-3 can be similarly explained, due to the ordering of zero-point fluctuations. It is therefore established that both related phenomena are based on the same physical mechanism. Keywords superconductivity superfluidity zero-point oscillations 1 Introduction 1.1 Superconductivity and public Superconductivity is a beautiful and unique natural phenomenon that was discovered in the early 20th century. Its unique nature comes from the fact that superconductivity is the result of quantum laws that act on a macroscopic ensemble of particles as a whole.
    [Show full text]
  • Chapter 3 Bose-Einstein Condensation of an Ideal
    Chapter 3 Bose-Einstein Condensation of An Ideal Gas An ideal gas consisting of non-interacting Bose particles is a ¯ctitious system since every realistic Bose gas shows some level of particle-particle interaction. Nevertheless, such a mathematical model provides the simplest example for the realization of Bose-Einstein condensation. This simple model, ¯rst studied by A. Einstein [1], correctly describes important basic properties of actual non-ideal (interacting) Bose gas. In particular, such basic concepts as BEC critical temperature Tc (or critical particle density nc), condensate fraction N0=N and the dimensionality issue will be obtained. 3.1 The ideal Bose gas in the canonical and grand canonical ensemble Suppose an ideal gas of non-interacting particles with ¯xed particle number N is trapped in a box with a volume V and at equilibrium temperature T . We assume a particle system somehow establishes an equilibrium temperature in spite of the absence of interaction. Such a system can be characterized by the thermodynamic partition function of canonical ensemble X Z = e¡¯ER ; (3.1) R where R stands for a macroscopic state of the gas and is uniquely speci¯ed by the occupa- tion number ni of each single particle state i: fn0; n1; ¢ ¢ ¢ ¢ ¢ ¢g. ¯ = 1=kBT is a temperature parameter. Then, the total energy of a macroscopic state R is given by only the kinetic energy: X ER = "ini; (3.2) i where "i is the eigen-energy of the single particle state i and the occupation number ni satis¯es the normalization condition X N = ni: (3.3) i 1 The probability
    [Show full text]
  • Laser Cooling of Atoms
    Information sheet 2 Laser cooling of atoms In 1985, Alain Aspect joined Claude Cohen-Tannoudji, professor at the Collège de France (Chair of atomic and molecular physics), at the Laboratoire Kastler-Brossel (ENS Paris/CNRS/Université Paris VI), and embarked on research into the laser cooling of atoms with Jean Dalibard, and later with Christophe Salomon, physicists at CNRS. The aim is to control the movement of atoms, by using the force of radiation pressure exerted by lasers. It turns out to be possible to reduce the speed of atoms down to extremely low values, in the region of a few centimeters per second. The gas thus obtained has an extraordinarily low temperature: around one microkelvin, which is only a millionth of a degree above absolute zero. Among the many results obtained at ENS and which were rewarded in particular by the 1997 Nobel prize awarded to Claude Cohen-Tannoudji2, Alain Aspect especially contributed to the development of the first cooling method which made it possible to slow down the speed at which atoms move to below the “photon recoil”. This is the speed gained by an atom which emits a photon, rather like a gun recoiling when it is fired. The photon recoil was considered at that time to be an unsurmountable barrier. Note that the process used to obtain this result (dubbed “velocity-selective black resonance”) Cooling of atoms to “below photon recoil”. This leads to each atom being placed into a quantum shows the tracks left on a fluorescent screen by superposition where it is simultaneously present in several hundred atoms which were cooled and several areas of space that are a few centimeters released above the screen.
    [Show full text]
  • Sounds of a Supersolid A
    NEWS & VIEWS RESEARCH hypothesis came from extensive population humans, implying possible mosquito exposure long-distance spread of insecticide-resistant time-series analysis from that earlier study5, to malaria parasites and the potential to spread mosquitoes, worsening an already dire situ- which showed beyond reasonable doubt that infection over great distances. ation, given the current spread of insecticide a mosquito vector species called Anopheles However, the authors failed to detect resistance in mosquito populations. This would coluzzii persists locally in the dry season in parasite infections in their aerially sampled be a matter of great concern because insecticides as-yet-undiscovered places. However, the malaria vectors, a result that they assert is to be are the best means of malaria control currently data were not consistent with this outcome for expected given the small sample size and the low available8. However, long-distance migration other malaria vectors in the study area — the parasite-infection rates typical of populations of could facilitate the desirable spread of mosqui- species Anopheles gambiae and Anopheles ara- malaria vectors. A problem with this argument toes for gene-based methods of malaria-vector biensis — leaving wind-powered long-distance is that the typical infection rates they mention control. One thing is certain, Huestis and col- migration as the only remaining possibility to are based on one specific mosquito body part leagues have permanently transformed our explain the data5. (salivary glands), rather than the unknown but understanding of African malaria vectors and Both modelling6 and genetic studies7 undoubtedly much higher infection rates that what it will take to conquer malaria.
    [Show full text]
  • Arxiv:2102.13616V2 [Cond-Mat.Quant-Gas] 30 Jul 2021 That Preserve Stability of the Underlying Problem1
    Self-stabilized Bose polarons Richard Schmidt1, 2 and Tilman Enss3 1Max-Planck-Institute of Quantum Optics, Hans-Kopfermann-Straße 1, 85748 Garching, Germany 2Munich Center for Quantum Science and Technology, Schellingstraße 4, 80799 Munich, Germany 3Institut f¨urTheoretische Physik, Universit¨atHeidelberg, 69120 Heidelberg, Germany (Dated: August 2, 2021) The mobile impurity in a Bose-Einstein condensate (BEC) is a paradigmatic many-body problem. For weak interaction between the impurity and the BEC, the impurity deforms the BEC only slightly and it is well described within the Fr¨ohlich model and the Bogoliubov approximation. For strong local attraction this standard approach, however, fails to balance the local attraction with the weak repulsion between the BEC particles and predicts an instability where an infinite number of bosons is attracted toward the impurity. Here we present a solution of the Bose polaron problem beyond the Bogoliubov approximation which includes the local repulsion between bosons and thereby stabilizes the Bose polaron even near and beyond the scattering resonance. We show that the Bose polaron energy remains bounded from below across the resonance and the size of the polaron dressing cloud stays finite. Our results demonstrate how the dressing cloud replaces the attractive impurity potential with an effective many-body potential that excludes binding. We find that at resonance, including the effects of boson repulsion, the polaron energy depends universally on the effective range. Moreover, while the impurity contact is strongly peaked at positive scattering length, it remains always finite. Our solution highlights how Bose polarons are self-stabilized by repulsion, providing a mechanism to understand quench dynamics and nonequilibrium time evolution at strong coupling.
    [Show full text]
  • Bose-Einstein Condensation
    Low Dimensional Systems and Nanostructures Jon Ander Arregi Bose-Einstein Condensation A Bose-Einstein condensate is a state of a dilute gas, sometimes also called fifth state of matter, of weakly interacting bosons (i.e., particles with integer spin) confined by an external potential and cooled down to temperatures very near to the absolute zero. At low enough temperatures the system undergoes a transition to a state with a large fraction of the bosons occupying the lowest energy level, corresponding to a zero momentum state, at which quantum effects become apparent on a macroscopic scale. In 1924, the indian physicist Satyendra Nath Bose was working on the quantum statistics of light quanta (nowadays called photons) but he had troubles getting people to accept his ideas. He sent his results to Albert Einstein, who realised of the importance of his work and he translated and sent Bose's paper for publication [1]. Einstein extended the description for massive particles and he found out that something very unusual was supposed to happen at very low temperatures [2]. It was not until 1995, after decades of huge efforts seeking for the experimental evidence, that the first realization of the Bose-Einstein condensate of a gas of around two thousand 87Rb atoms cooled down to 170 nanokelvin (nK) was made by Eric Cornell, Carl Wieman and co-workers at the University of Colorado at Boulder [3]. Four months later, the group led by Wolfgang Ketterle at MIT created a condensate of 23Na with a hundred times more atoms [4], allowing him to observe important effects such as quantum mechanical interference between different condensates [5].
    [Show full text]
  • Multidisciplinary Design Project Engineering Dictionary Version 0.0.2
    Multidisciplinary Design Project Engineering Dictionary Version 0.0.2 February 15, 2006 . DRAFT Cambridge-MIT Institute Multidisciplinary Design Project This Dictionary/Glossary of Engineering terms has been compiled to compliment the work developed as part of the Multi-disciplinary Design Project (MDP), which is a programme to develop teaching material and kits to aid the running of mechtronics projects in Universities and Schools. The project is being carried out with support from the Cambridge-MIT Institute undergraduate teaching programe. For more information about the project please visit the MDP website at http://www-mdp.eng.cam.ac.uk or contact Dr. Peter Long Prof. Alex Slocum Cambridge University Engineering Department Massachusetts Institute of Technology Trumpington Street, 77 Massachusetts Ave. Cambridge. Cambridge MA 02139-4307 CB2 1PZ. USA e-mail: [email protected] e-mail: [email protected] tel: +44 (0) 1223 332779 tel: +1 617 253 0012 For information about the CMI initiative please see Cambridge-MIT Institute website :- http://www.cambridge-mit.org CMI CMI, University of Cambridge Massachusetts Institute of Technology 10 Miller’s Yard, 77 Massachusetts Ave. Mill Lane, Cambridge MA 02139-4307 Cambridge. CB2 1RQ. USA tel: +44 (0) 1223 327207 tel. +1 617 253 7732 fax: +44 (0) 1223 765891 fax. +1 617 258 8539 . DRAFT 2 CMI-MDP Programme 1 Introduction This dictionary/glossary has not been developed as a definative work but as a useful reference book for engi- neering students to search when looking for the meaning of a word/phrase. It has been compiled from a number of existing glossaries together with a number of local additions.
    [Show full text]
  • Scientific and Related Works of Chen Ning Yang
    Scientific and Related Works of Chen Ning Yang [42a] C. N. Yang. Group Theory and the Vibration of Polyatomic Molecules. B.Sc. thesis, National Southwest Associated University (1942). [44a] C. N. Yang. On the Uniqueness of Young's Differentials. Bull. Amer. Math. Soc. 50, 373 (1944). [44b] C. N. Yang. Variation of Interaction Energy with Change of Lattice Constants and Change of Degree of Order. Chinese J. of Phys. 5, 138 (1944). [44c] C. N. Yang. Investigations in the Statistical Theory of Superlattices. M.Sc. thesis, National Tsing Hua University (1944). [45a] C. N. Yang. A Generalization of the Quasi-Chemical Method in the Statistical Theory of Superlattices. J. Chem. Phys. 13, 66 (1945). [45b] C. N. Yang. The Critical Temperature and Discontinuity of Specific Heat of a Superlattice. Chinese J. Phys. 6, 59 (1945). [46a] James Alexander, Geoffrey Chew, Walter Salove, Chen Yang. Translation of the 1933 Pauli article in Handbuch der Physik, volume 14, Part II; Chapter 2, Section B. [47a] C. N. Yang. On Quantized Space-Time. Phys. Rev. 72, 874 (1947). [47b] C. N. Yang and Y. Y. Li. General Theory of the Quasi-Chemical Method in the Statistical Theory of Superlattices. Chinese J. Phys. 7, 59 (1947). [48a] C. N. Yang. On the Angular Distribution in Nuclear Reactions and Coincidence Measurements. Phys. Rev. 74, 764 (1948). 2 [48b] S. K. Allison, H. V. Argo, W. R. Arnold, L. del Rosario, H. A. Wilcox and C. N. Yang. Measurement of Short Range Nuclear Recoils from Disintegrations of the Light Elements. Phys. Rev. 74, 1233 (1948). [48c] C.
    [Show full text]
  • Glossary of Terms
    GLOSSARY OF TERMS For the purpose of this Handbook, the following definitions and abbreviations shall apply. Although all of the definitions and abbreviations listed below may have not been used in this Handbook, the additional terminology is provided to assist the user of Handbook in understanding technical terminology associated with Drainage Improvement Projects and the associated regulations. Program-specific terms have been defined separately for each program and are contained in pertinent sub-sections of Section 2 of this handbook. ACRONYMS ASTM American Society for Testing Materials CBBEL Christopher B. Burke Engineering, Ltd. COE United States Army Corps of Engineers EPA Environmental Protection Agency IDEM Indiana Department of Environmental Management IDNR Indiana Department of Natural Resources NRCS USDA-Natural Resources Conservation Service SWCD Soil and Water Conservation District USDA United States Department of Agriculture USFWS United States Fish and Wildlife Service DEFINITIONS AASHTO Classification. The official classification of soil materials and soil aggregate mixtures for highway construction used by the American Association of State Highway and Transportation Officials. Abutment. The sloping sides of a valley that supports the ends of a dam. Acre-Foot. The volume of water that will cover 1 acre to a depth of 1 ft. Aggregate. (1) The sand and gravel portion of concrete (65 to 75% by volume), the rest being cement and water. Fine aggregate contains particles ranging from 1/4 in. down to that retained on a 200-mesh screen. Coarse aggregate ranges from 1/4 in. up to l½ in. (2) That which is installed for the purpose of changing drainage characteristics.
    [Show full text]