This textbook brings together nuclear and particle physics, presenting a balanced overview of both fields as well as the interplay between the two. The theoretical as well as the experimental foundations are covered, providing students with a deep understanding of the subject In-chapter exercises ranging from basic experimental to sophisticated theoretical questions provide an important tool for students to solidify their knowledge Suitable for upper undergraduate courses in nuclear and particle physics as well as more advanced courses, the book includes road maps guiding instructors on tailoring the content to their course. Online resources including color figures, tables, and a solutions manual complete the teaching package. This textbook will be essential for students preparing for further study or a career in the field who requireasolidgraspofbothnuclear andparticlephysics.
Keyfeatures
Containsup-to-datecoverageofbothnuclear andparticlephysics,particularlythe areas where the two overlap, equipping students for the real-world occasions whereaspectsofbothfieldsarerequiredfor study
Covers the theoretical as well as the experimental foundations,providingstudents withadeepunderstandingofthefield
Exercises ranging frombasic experimental to sophisticated theoretical questions provideanimportanttool for readerstoconsolidatetheir knowledge
THOMAS WILLIAM DONNELLY is a Senior Research Scientist at MIT. He received his PhDinTheoretical Nuclear Physicsin1967fromtheUniversityofBritishColumbia.
JOSEPHANGELOFORMAGGIO is anAssociate Professor ofPhysics atMIT. He received his PhDinPhysics atColumbia Universityin2001. He has beena member ona number of experiments including the Sudbury Neutrino Observatory and the KATRIN neutrino experiment.
BARRYR HOLSTEIN is anEmeritus Professor Physics attheUniversityofMassachusetts. He received his PhDinPhysics fromCarnegie MellonUniversityin1969. He is Editor of Annual Reviews of Nuclear and Particle Physics, ConsultingEditor ofthe American Journal of Physics,andAssociateEditor ofthe Journal of Physics G.
RICHARD GERARD MILNER is a Professor ofPhysics atMIT. He received his PhDfrom the California Institute of Technologyin1985. He has proposed and led experiments at SLAC,DESY,MIT-Bates,andJeffersonLaboratory.
BERND SURROW is a Professor of Physics at Temple University. He gained his PhD in Physics at the University of Hamburg in 1998. He has been a member of a number of experiments includingthe STARexperimentatBNL, the CMS and OPALexperiments at
Foundationsof NuclearandParticle Physics
T. W. DONNELLY
Massachusetts Institute of Technology, Cambridge, MA
J. A. FORMAGGIO
Massachusetts Institute of Technology, Cambridge, MA
B. R. HOLSTEIN
University of Massachusetts, Amherst, MA
R. G. MILNER
Massachusetts Institute of Technology, Cambridge, MA
B. SURROW
Temple University, Philadelphia, PA
University PrintingHouse, Cambridge CB2 8BS, United Kingdom
Cambridge University Press is part of the University of Cambridge.
It furthers the University’s mission by disseminatingknowledge in the pursuit of education, learning, and research at the highest internationallevels of excellence www.cambridge.org
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Printed in the United States of America by Sheridan Books
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Library of Congress Cataloguing in Publication Data
Names:Donnelly, T W (T William), 1943– author |Formaggio, Joseph A, 1974– author | Holstein, Barry R., 1943– author. |Milner, Richard Gerard, 1956– author. |Surrow, Bernd, 1998– author.
Title:Foundations of nuclear and particle physics / T. William Donnelly (Massachusetts Institute of Technology), Joseph A Formaggio (Massachusetts Institute of Technology), Barry R Holstein (University of Massachusetts, Amherst), Richard G. Milner (Massachusetts Institute of Technology), Bernd Surrow (Temple University, Philadelphia).
Description:Cambridge, United Kingdom ; New York, NY:Cambridge University Press, [2016] |Includes index.
Identifiers:LCCN 2016026959|ISBN 9780521765114 (hardback) | ISBN 0521765110 (hardback)
Classification:LCC QC776 .D66 2016 |DDC 539.7–dc23 LC record available at https://lccn.loc.gov/2016026959
ISBN 978-0-521-76511-4 Hardback
Additionalresources for this publication at www.cambridge.org/9780521765114.
Cambridge University Press has no responsibility for the persistence or accuracy of URLs for externalor third-party Internet Web sites referred to in this publication, and does not guarantee that any content on such Web sites is, or willremain, accurate or appropriate.
Bill ⇔ toBarbara
Joe ⇔ to Mike, Hamish, Janet, and John, for their unwavering wisdom; to Jaymi, Coby,andJoshua,fortheirunquestioninglove
Barry ⇔ toJeremyandJesse
Richard ⇔ to LiamMilner for inspiration and to Eileen, Will, Sam, and David for love andsupport
The firstquestionone mightaskaboutthis bookis: Whydo we need another textonthe subjectofnuclear andparticlephysicswhenexcellenttextsalreadyexistinbothofthese areas? Indeed, it is true that eachsub-discipline has texts that range fromelementaryto veryadvancedandcover specifictopics invaryingdegrees ofdepththatcanbeusedfor the appropriate types of courses. For instance, there are fine books on quantum field theory[Bjo64, Pes95, Wei05, Sch14], onthe constituent quarkmodel [Clo79], onhighenergy physics [Gri08, Hal84], on hadron scattering [Col84], and on nuclear structure [Des74, Wal95, Won98, Pov08, Row10]. However, there are relatively few textbooks that cover several sub-disciplines in a coherent and balanced way, and those that do exist are either more elementary, e.g., Povhet al. [Pov08] thanthe present book, or are cast at a more theoretical level and are too advanced for the goals we as authors have set for ourselves. Having a book that stresses the interconnections between the two areas of subatomic physics is crucial, since increasingly one finds that the two fields overlap and that it is essential for a graduate student conducting frontier research and preparingfor a career inthe field to have anunderstandingof both. Anexample of this overlap occurs, for instance, in modern neutrino physics wherein experiments utilizing several-GeV neutrinos as probes almost always involve targets/detectors constructed from nuclei and specifics of nuclear structure are unavoidably required to properly interpretsuchdata.
One specific decision we have made in designing this book is to assume that the reader is familiar with the basics of quantum field theory. More elementary texts typically do not make this assumption and thus much of the discussion, for instance, of leptonscatteringfromhadrons and nuclei, or of the foundations of chiral symmetryand effective field theoryis limited and not at the frontier of the field. We realize that many students today do have at least an introductory course in quantum field theory, or are taking one simultaneously with a course that this book covers, and thus we have followed a somewhat more advanced approach than has been customary. We have included inAppendixB anoverview ofthe essential aspects ofquantummechanics and quantum field theory that are needed for the book. Furthermore, the subject of manybody theory underlies much of nuclear physics and the presentation of this subject can also be rather elementary, as is usuallythe case intexts thatcover the two fields, or too advanced for our purposes, focusingonGreen’s functions, diagrammatic techniques and nonperturbative approximations ata theoretical level We have chosena middle course: we have covered the basics of many-bodytheory, but also have introduced some of the important diagrammatic representations of the nonperturbative approximations employed very widely in quantum physics ranging from atomic and condensed matter
The book’s central focus is to describe the current understanding of the sub-atomic world within the framework of the Standard Model. The layout of the book is summarized as follows: In the first quarter of the book, the Standard Model is developed Thestructureofthenucleonandfew-bodynuclei arediscussedinthesecond quarter. Inthe third quarter, the structure and properties of atomic nuclei are described. Lepton scattering is the principal tool used in the central narrative of the book to understand hadrons. Inthe final quarter ofthe bookwe present extensions ofthe earlier focus onEMleptonscatteringto include the weakinteractions ofleptons withnucleons and nuclei. This begins witha chapter onbeta-decayand progresses to intermediate-tohigh energy neutrino-induced reactions. These two chapters are followed by two more that build on what occurs earlier in the book, namely, on applications to nuclear and particle astrophysics and to studies of the hot, dense phase of matter formed in heavyioncollisions The bookcloses witha briefperspective onphysics beyond the Standard Model.
We should also emphasize that the use of word “foundations” inthe title of the book is intentional, indicating that this text is not an encyclopedia where one might find material on all of the major topics in the field, albeit at a superficial level. Rather, we have consciouslymade choices inwhat and what not to present. We have, for instance, not developed the topic of intermediate-energy hadron scattering, emphasizing lepton scatteringinstead and have notattempted to cover the lattice approachto the solutionof QCD. While the important areas of nuclear structure and the high-energy frontier are covered, we note thatexcellent, up-to-date, comprehensive textbooks onthese important areas are available. Our intent has beento provide the reader withbasic material upon whichto build bysubsequentlyemployingthe more advanced sources thatexistwhenit becomes necessary for a more in-depth understanding of specific subjects. In this regard, we have included references to review articles, so thatthe interested reader can pursue material to a more advanced level. Just what to emphasize and what merely to refer to in passing is, of course, subjective; however, having five co-authors has allowedustodebatethechoiceswehavemade
We view the approximately120 exercises provided throughout the bookand located at the end of each chapter as an important tool for the reader to consolidate their understanding of the material in the book. There exists significant variety in these exercises, rangingfrombasic experimental issues to sophisticated theoretical questions. Manyowe their origins to other sources, butwe have tried to tailor themto the material discussedhere.
The authors have all taught courses of the type described above at various levels. Specifically, at MIT the book covers the scopes set out for the introductory first-year graduate course in nuclear and particle physics (8.701), together with the second-year graduate courses in nuclear (8.711) and particle (8.811) physics. All graduate students inexperimental nuclear/particle physics atMIT are required to take the latter two, with theformer beingaprerequisite.Additionally,atMITthereisanadvancedundergraduate course innuclear/particle physics (8.276), as well as more advanced courses inmanybody theory (8.361), nuclear theory (8.712) and electroweak interactions (8.841) – all
We acknowledge that the derivation of the QCD Lagrangian in Chapter 5 owes its origins to Professor FrankWilczek. We acknowledge thatChapter 19 was shaped bythe work of Professor Berndt Müller and his colleagues. We thank the Super-Kamiokande Collaborationfor permissiontousetheir imageonthecover
The book’s evolution profited from its use in draft form as a resource for the MIT course 8.711 taught by one of us (RGM) and Dr. Stephen Steadman in the spring semesters of2014,2015,and2016.We acknowledge the constructive feedbackfromthe MIT graduate students in those classes. Further, we acknowledge careful and critical readingofdrafts byDr.JanBernauer,Charles Epstein,Dr.Douglas Hasell,Dr.Rebecca Russell, Dr. Axel Schmidt, Dr. Stephen Steadman, Reynier Cruz Torres and Constantin Weisser at MIT, Professor James Napolitano, Dr. Matt Posik, Devika Gunarathne, Amani KraishanandDaniel OlvittatTemple University,Rosi ReedatLehighUniversity andRosi Esha atUCLA.We are grateful toDr.BrianHendersonfor a careful readingof all ofthe exercises. We thankConnor Dorothy-Pachuta for his considerable expertise in creatingmanyofthe figures inthe book. There are, ofcourse, manyothers to thankwho, over the years, have beenour collaborators – we cannotlistthemall, buttheywill find their efforts reflected inmanyofour choices for whatto present. We do, however, wish to acknowledge three who directly played roles in developing some of the figures in Chapters 16 and 18, namely, Professors Maria Barbaro and Juan Caballero, and GuillermoMegias.
Inadditionto beinganintegrated text, there are other aspects ofthis presentationthat we feel are important. Specifically, we have attempted to make strongconnections with contemporaryexperimentsandhavetried,whenever possible,tohelpthereader become aware ofthe relevantfrontier experimental facilities available and planned worldwide. Doingsois,ofcourse,timedependent;butwehavetriedtobeasuptodateaspossible. We have also made liberal use of the Particle Data Group website [PDG14] as a resource withwhichwe encourage all students tobecome familiar.Finally,inAppendix Awehavecollectedinformationthatwebelievewill beuseful toreaders.
1
Introduction
The past one hundred years has witnessed enormous advances in human understanding of the physical universe in which we have evolved. For the past fifty years or so, the Standard Model of the subatomic world has been systematically developed to provide the quantummechanical description of electricity and magnetism, the weak interaction, and the strong force. Symmetry principles, expressed mathematically via group theory, serve as the backbone of the Standard Model. At this time, the Standard Model has passed all tests in the laboratory. Notwithstanding this success, most of the matter available to experimental physicists is inthe formofatomic nuclei. The mostsuccessful descriptionofnuclei is interms ofthe observable protons, neutrons, and other hadronic constituents,andnotthe fundamental quarks andgluons ofthe StandardModel.Thus,the professional particle or nuclear physicist should be comfortable in applying the hadronic description of nuclei to understanding the structure and properties of nuclei. Experimentally, lepton scattering has proved to be the cleanest and most effective tool for unraveling the complicated structure of hadrons. Its application over different energies and kinematics to the nucleon, few-body nuclei, and medium- and heavy-mass nuclei has provided the solid bodyof precise experimental data onwhichthe Standard Model isbuilt.
In addition, the current understanding of the microcosm described in this book provides answers to manybasic questions: How does the Sunshine? Whatis the origin of the elements? How old is the Earth? Further, it underscores manyaspects of modern human civilization, e.g., MRI imaging uses the spin of the proton, nuclear isotopes are essential medical tools, nuclear reactions have powered the Voyager spacecraft since 1977intointerstellar space.
The purpose of the book is to allow the graduate student to understand the foundations and structure of the Standard Model, to apply the Standard Model to understanding the physical world with particular emphasis on nuclei, and to establish the frontiers ofcurrentresearch. There are manyoutstandingquestions thatthe Standard Model cannot answer. In particular, astrophysical observation strongly supports the existenceofdarkmatter,whosedirectdetectionhasthusfar remainedelusive.
Essential to making progress in understanding the subatomic world are the sophisticated accelerators that deliver beams of particles to experiments. Existing lepton scattering facilities include Jefferson Laboratory in the US, muon beams at CERN, and University of Mainz and University of Bonn in Germany. Intense photon beams areusedattheHIγ SfacilityatDuke Universityinthe U.S.,andinJapanatLEPS atSPring-8, and atElphs atTohokuUniversity. Hadrons beams are used atthe TRIUMF
laboratory in Vancouver, Canada, using the COSY accelerator in Juelich, Germany, at the Paul Scherrer Institute (PSI) in Switzerland, and at the Joint Institute for Nuclear Research (JINR), Dubna, Russia. Neutron beams are used for subatomic physics research at the Institut Laue-Langevin (ILL), Grenoble, France, at both the Los Alamos NeutronScience Center (LANSCE) and the SpallationNeutronSource (SNS) inthe US, and at the future European Spallation Source (ESS) in Sweden. The hot, dense matter presentinthe earlyuniverse is studied usingheavy-ionbeams atthe Relativistic Heavy Ion Collider (RHIC) in the US and at the Large Hadron Collider (LHC) at CERN. Of course, searches for new physics beyond the Standard Model are underwayat the highenergy frontier of 13 TeV at CERN. Understanding the structure of nuclei, with particular emphasis onthe limits ofstability, is a major worldwide endeavor. The most powerful facility at present is the Rare Isotope Beam Facility (RIBF) at RIKEN in Japan. In the US, the frontier experiments at present are carried out at the National Superconducting Cyclotron Laboratory at Michigan State University (MSU) and at the ATLAS facility at Argonne National Laboratory. A future Facility for Rare Isotope Beams (FRIB) is under construction at MSU and is expected to have world-leading capabilities by 2022, as is a facility in South Korea, the Rare Isotope Science Project (RAON). Hadron beams for research are available at Los Alamos and the Spallation Neutron Source in the US, GSI in Germany, J-PARC in Japan, and NICA at Dubna, Russia. Amajor new facility FAIR is planned at GSI. Neutrino beams are generated at Fermilab, CERN, and J-PARC and directed at detectors located both at the Earth’s surface and deep underground. A major new Deep Underground Neutrino Experiment (DUNE) is planned in the US using the Fermilab beam and the Sanford Underground ResearchLaboratoryinSouthDakota.BelleII,anexperimentatthehighluminosity e+e collider SuperKEKB in Japan, will come online within the next several years and provide new stringent tests of flavor physics. Annihilationof electrons and positrons is used to probe the Standard Model at both the Double Annular ϕ Factory for Nice Experiments (DAFNE) collider in Frascati, Italy as well as the Beijing Electron PositronCollider (BEPC) inChina. Finally, a highluminosityelectron–ioncollider has beenwidelyidentified byas the next machine to studythe fundamental quarkand gluon structure of nuclei and machine designs are under development in the US, Europe, and China.
To begin, let us remind the reader of the particles that comprise the Standard Model (see Fig. 1.1). As will be discussed in due course, the Standard Model starts with massless particles and then, through spontaneous symmetry breaking, these interacting particles acquire masses inalmostall cases. The measured spectrumofmasses is still a mystery; indeed, inthe case of the neutrinos, intense effort is goinginto determiningthe actual pattern of masses in Nature. Note that at this microscopic level, but also at the hadronic/nuclear level, when one says that particles interact with one another what is meantis thatsome particle is exchanged betweentwo other particles, therebymediating the interaction For instance, an electron can exchange a photon with a quark whereby the photon mediates the e q interaction. Or two nucleons (protons and neutrons) can exchangeapionandonehasthelong-rangepartofthe NN interaction.
Fig. 1.1 The particles of the Standard Model.
The organizational principle for this book centers on building from the underlying fundamental particles (leptons, quarks, and gauge bosons) to hadrons (mesons and baryons) built from q q and qqq, respectively, and on to many-body nuclei or hypernuclei built from these hadronic constituents. At very low energies and momenta the last are the relevant effective degrees of freedom, since, using the Heisenberg Uncertainty Principle, such kinematics translate into large distance scales where the microscopic ingredients are packaged into the macroscopic hadronic degrees of freedom. Then, as the energy/momentum is increased, more and more of the substructure becomes relevant, until atveryhighenergy/momentumscales the QCDdegrees offreedommustbeusedtorepresentwhatisobserved.
Naturally, there can be a blending between the different degrees of freedom and, where they overlap, it may be possible to use one language or the other. And in some cases it turns out to be important to address both the “fundamental” physics issues and the larger-scale nuclear structure issues at the same time. This bookattempts to present the foundations of the general field of nuclear/particle physics – sometimes called subatomic physics – in a single volume, trying to maintain a balance between the very microscopicQCDpictureandthehadronic/nuclear picture.
The outline ofthe bookis the following. After this introductorychapter, inChapter 2 the basic ideas ofsymmetries are introduced. Ingeneral discussions ofquantumphysics it is oftenadvantageous to exploit the exact (or at least approximate) symmetries inthe problem, for then selection rules emerge where, for instance, matrix elements between specific initial and final states of certain operators can only take on a limited set of
values. An example of what will be important in later discussions is the use of good angular momentum quantum numbers and the transformation properties of multipole operators (see Chapter 7) where conservationofangular momentumleads to a small set of allowed values for matrixelements of suchoperators takenbetweenstates that have known spins Another example of an important (approximate) symmetry is provided by invariance under spatial inversion, namely, parity: to the extent that parity is a good symmetry again only specific transitions can occur. Other symmetries discussed in Chapter 2 include charge conjugation and time reversal, as well as discrete unitary flavor symmetries, the latter being important for classifying the hadrons built from constituentquarks,namely,thesubjectofChapter 3.
After these introductorydiscussions the bookproceeds to build up fromparticles to hadrons to many-bodynuclei, startinginChapter 4 withthe Standard Model of particle physics. In this one begins with massless leptons, quarks, and gauge bosons together with the Higgs and then through spontaneous symmetry breaking generates the basic familiar buildingblocks withtheir measuredmasses.The recentsuccessful discoveryof theHiggsbosonattheLargeHadronCollider (LHC) issummarized.
The Standard Model has proven to be extremely successful and, at the time of writing, there is as yetno clear evidence thateffects beyond the Standard Model (BSM) are needed;inthe final chapter ofthe book, Chapter 21 we returnto summarize some of these BSM issues. For the present, following the path of increasing complexity, in Chapters 5 and 6 the ideas and models employed in descriptions of low-Q2 , strong couplingQCDare discussed insome detail, includingwhatis nottypicallycovered ina bookatthislevel,namely,chiral symmetry.
Chapters 7 through 10 form a distinct section where the aim is to visualize the structureofthe proton,neutron,andnuclei interms ofthefundamental quarks andgluons of QCD. At low and mediumenergies, this is carried out usingleptonscatteringwhere intense beams of high quality are available. Thus, snapshots of the nucleon charge and magnetism and quark momentum and spin distributions are directly obtainable in the form of structure functions and form factor distributions. Chapter 7 provides an introduction to lepton scattering, including both parity-conserving and parity-violating scattering. Since leptonscatteringis beingused as a commontheme inmuchof the rest ofthebook,Chapter 7 is the firststop alongthe waywhere the multipole decomposition of the electromagnetic current is developed insome detail. This is followed inChapter 8 bya discussionofelastic scatteringfromthe nucleon. Atthis time, a directconnection betweenelastic scatteringand QCDremains elusive and the mostsuccessful theoretical descriptionis interms of hadrons. Chapter 9 describes the current understandingof the structure of hadrons in terms of high-energy lepton scattering and this is directly interpretable in terms of perturbative QCD. Further, the gluon momentum and spin distributions are indirectly determined via the QCD evolution equations The parton distributions are snapshots of nucleon structure over different spatial resolutions and with different shutter speeds Lepton scattering constitutes a theme of the book at both high- andlow-energyscales andwiththe full electroweakinteraction.Duetothe lackof suitable lepton beams, QCD is at present probed at the highest energies using hadron beams. This is the focus of Chapter 10 and the measurements extend and complement
those with lepton beams in the previous chapters. For example, direct experimental informationonthe contributionof gluons to the spinof the protonhas become possible onlythroughpolarizedproton–protoncollisions.
The above constitutes the first part of the book after which the building-up process moves fromhadrons to nuclei The next step is to deal with the simplest systemthat is not a single baryon, namely, the system of two nucleons, discussing NN scattering and the properties ofthe onlybound state withbaryons number two, the deuteroninChapter 11. For the latter the EM form factors and electrodisintegration are treated in some detail. After this, inChapter 12 the so-called few-bodynuclei, those with A = 3 and 4, constitutethefocus.
For nuclei heavier than the A = 2, 3, and 4 cases, treating the many-body problem forms the basic issue, and accordinglyinChapter 13 anoverview ofthe general nuclear “landscape” is presented, showing the typical characteristics of nuclei, including the regions where nuclei are stable (the “valley of stability”) out to where they are just unstable (the “drip lines”), and their regions of especially tight binding (the “magic numbers”). Also inthis chapter the conceptofinfinite nuclear matter and neutronmatter is introduced and treated insome detail. This is followed inChapter 14 bya discussion ofa selectionoftypical nuclear models. As mentioned earlier, this bookis notintended to be a theoretical text on nuclear many-body theory. That said, this chapter has sufficient detail that the basic issues in this area can be appreciated. Importantly, the tools used in this part of the field must be capable of dealing with nonperturbative interacting systems and accordingly this provides a theme in this chapter where discussions of the so-called Hartree–Fock (HF) and Random Phase Approximations (RPA) are provided together withanintroductionto diagrammatic representations ofthe approximations. Also typical collective models are discussed as examples of how one may start with some classical oscillation or vibration of the nuclear fluid, make harmonic approximations to those movements, and then quantize the latter to arrive at semi-classical descriptions of nuclear excitations (“surfons,” “rotons,” etc.), as is done inmanyareasofphysicswheresimilar techniquesareemployed.
The above discussions are then followed by two chapters focused on electron scattering from nuclei, Chapter 15 where elastic scattering is treated in some detail, together with some applications of the models introduced in Chapter 14 for low-lying excited states. Chapter 16 continues this by treating higher-lying excitations where differentmodelingis required. Specifically, the Relativistic Fermi Gas (RFG) model is derivedandusedasaprototypefor moresophisticatedapproaches.Itisalsothestarting point for similar discussions ofneutrino scatteringfromnuclei to follow inChapter 18. Before those are presented, in Chapter 17 the weak interaction provides the focus and we see how precision beta-decay experiments can be used as a probe for beyond StandardModel physics. Chapter 18 deals withthe subjectofneutrinos and the factthat one flavor can oscillate into another, since neutrinos are known to have mass. At the time ofwriting, the detailed nature ofthe mass spectrum, whether or notCPviolationis presentinthe leptonic sector and whether neutrinos are Dirac or Majorana particles are still under investigation and intensive efforts are being undertaken worldwide to shed lightontheseinterestingquestions.
In Chapter 19 the high-energy regime (essentially quark–quark scattering) is revisited within the context of relativistic heavy-ion scattering. Here the nature of the modelingis somewhat different fromthat discussed inmost of the rest of the bookwith statistical mechanics being called into play together with fluid dynamics. An informed practitioner inthe general field of nuclear/particle physics should be familiar withthis subjectaswell.
ThebookconcludeswithChapter 20onnuclear andparticle astrophysics usingmany of the concepts treated in the rest of the book, and with Chapter 21 where the types of signatures of effects beyond the Standard Model are summarized, together with two appendiceswheresomeuseful material isgathered.
While we strongly advocate using the book to explore both nuclear and particle physics ina coherent, balanced way, nevertheless itmightbe thatitwill also be used in a course that emphasizes one subfield or the other. Accordingly, we suggest the following“roadmaps” tohelpthe reader negotiatethe textfor those purposes.Whenthe emphasis is placed on particle physics we suggest paying the closest attention to Chapters2 to 10 and 21, withsome parts ofChapters17,18, and perhaps 19, and when theemphasisisonnuclear physicsChapters2,7,11to18,20andperhaps19.
We strongly recommend the following online resources as important tools for enhancingthematerial presentedinthisbook.
1. TheReview ofParticlePhysics,ParticleDataGroup
http://pdg.lbl.gov includes a compilation and evaluation of measurements of the properties of the elementary particles. There is an extensive number of review articles onparticle physics, experimental methods, and material properties as well asasummaryofsearchesfor new particlesbeyondtheSM.
2. National Nuclear DataCenter
http://www.nndc.bnl.gov is a source of detailed information on the structure, properties,reactions,and decays ofknownnuclei.Itcontains aninteractive chartof the nuclides as well as a listingof the properties for ground and isomeric states of all knownnuclides.
We conclude this introductory chapter with some exercises designed to introduce some of the concepts which we hope our particle/nuclear students will be able to address.
Exercises
1.1 USEnergyProduction
In 2011, the United States of America required 3,856 billion kW-hours of electricity. About 20% of this power was generated by ∼100 nuclear fission reactors About67% was producedbythe burningoffossil fuels,whichaccounted for aboutone-third ofall greenhouse gas emissions inthe US. The remaining13% was generated using other renewable energy resources. Consider the scenario where all the fossil fuel power stations are replaced bynew 1-GWnuclear fission
1.2 GeothermalHeating
Itisestimatedthat20TWofheatingintheEarthisduetoradioactivedecay: 8TW from 238Udecay, 8 TWfrom 232Thdecay, and 4 TWfrom 40K decay. Estimate the total amount of 238U, 232Th, and 40K present in the Earth in order to produce such heating.
1.3 Radioactive ThermoelectricGenerators
A useful form of power for space missions which travel far from the Sun is a radioactive thermoelectric generator (RTG) Suchdevices were first suggested by the science fictionwriter Arthur C. Clarke in1945. AnRTG uses a thermocouple to convert the heat released bythe decayof a radioactive material into electricity bythe Seebeckeffect. The two Voyager spacecrafthave beenpowered since 1977 byRTGsusing238Pu.Assuminga mass of5kgof 238Pu,estimate the heatproduced and the electrical power delivered. (Do not forget to include the ∼ 5% thermocoupleefficiency.)
a) Consider the fissionof 235Uinto 117Snand 118Sn, respectively. Using the mass information from a table of isotopes, calculate (i) the energy released per fissionand(ii) theenergyreleasedper atomicmassoffuel.
b) Consider thedeuteron–tritonfusionreaction
Using the mass information from the periodic table of the isotopes, calculate (i) the energyreleased per fusionand (ii) the energyreleased per atomic mass unitoffuel.
1.5 AbsorptionLengths
A flux of particles is incident upon a thick layer of absorbing material Find the absorption length, the distance after which the particle intensity is reduced by a factor of1/e ∼ 37% (theabsorptionlength) for eachofthefollowingcases:
a) When the particles are thermal neutrons (i e, neutrons having thermal energies),theabsorber iscadmium,andthecrosssectionis24,500barns.
b) When the particles are 2MeV photons, the absorber is lead, and the cross sectionis157barnsper atom
c) Whenthe particles are anti-neutrinos froma reactor, the absorber is the Earth, andthecrosssectionis10 19 barnsper atomicelectron.
Symmetries
2.1 Introduction
Whenstudyingquantumsystems, exploitingknowledge about the inherent symmetries is usually an important step to take before addressing issues of dynamics [Sch55, Sak94, Rom64, Gri08]. This motivates a discussion of group theory, and so we shall begin by summarizing some of the basic elements needed, particularly when discussing symmetries in particle and nuclear physics. More details can be found in specialized texts onthe subject[Ham62,Clo79]. Noether’s theoremstates thatifthe Hamiltonianis invariant under a continuous group of transformations, then there exist corresponding conserved quantities and accordingly one wants to discuss various natural symmetries and the conservation laws that accompany them (see [Rom64] Chapter IV for a clear discussionof Noether’s theorem, and also see Exercise 2.1). Specifically, in Table 2.1 are several important examples that are believed to be absolute symmetries and hence exact conservationlaws. Some of these specific examples are discussed inmore detail inwhatfollows.
Symmetry
Conservation law
translation in time energy
translation in space linear momentum rotation in space angular momentum
localgauge invariance charge
transformations in color space color
Furthermore, there are symmetries that are not completely respected in Nature, although characterizing the states used in terms of eigenstates of these approximate symmetries often proves fruitful; some examples are given in Table 2.2. We shall be usingall of these concepts throughout the book. Next let us turnto a brief discussionof someofthebasicsneededwhentreatingsymmetriesusinggrouptheory.
Approximate symmetry Conservation law
spatialinversion
particle–antiparticle interchange
Table 2.1 Exact conservation laws
Table 2.2 Approximate conservation laws
temporalinversion time-reversalinvariance, T transformations in isospace isospin, I (or T) transformations in flavor space flavor
Representations
Byan n-dimensional representationofagroup G onemeansamapping (2.1) (2.2) whichassigns toeveryelement g a linear operator A(g) insome n-dimensional complex vector space, the so-called carrier space of the representation GL(n), such that the imageoftheidentity e istheunitoperator I andthatgroupoperationsarepreserved (2.3)
Throughout the book we shall frequently encounter infinite-dimensional continuous groups (Lie groups) whose elements are labeled uniquelybya set of parameters which can change continuously (see [Rom64] for an introductory discussion). An example is provided by the rotation group, that is, the group of continuous rotations. For the Lie groups that are encountered frequently in this book it is sufficient to study the mapping fromtheLiealgebrainto GL(n), (2.4)
where the {Tα} preserve the Lie-algebra commutation relations. If a subspace of the carrier spaceofsomerepresentationisleftunchangedbyall operators Tα,itis calledan invariantsubspace and the representationis reducible;otherwise itis irreducible. Ifthe correspondence (2.5) definesarepresentationofthegroup G,thenthecorrespondence (2.6) also defines a representationof the group, the so-called conjugate representation. For a Lie group we find that the representation matrices for the conjugate representation are givenby
(27)
When discussing the implications of symmetries in particle and nuclear physics one frequentlyencounters the special unitarygroups in N dimensions, SU(N), which can be representedusing N × N matrices U satisfying (2.8)
The importance of the continuous Lie group SU(N) lies in the fact that these matrices describe transformations between N basis states {|eα , α = 1, ..., N} preserving orthonormality (2.9)
We shall see several examples of physical states labeled using various symmetries, specifically by spin and by isospin (SU(2)), by flavor and by color (SU(3)), or by higher groups, e.g., SU(6) for spin-flavor. Withinthe context of SU(N), a representation is reducible if it is possible to choose a basis in which the matrices Tα take the block form (2.10)
where A, B, C, ... are lower-dimensional irreducible sub-matrices when the original matrix Tα is fully reduced. Given an irreducible representation {Tα}, the only linear operators O which commute with every Tα are multiples of the identity and also the converse: (2.11)
Anyunitarymatrixcanbewrittenas (2.12) where H is a traceless Hermitianmatrix. For a Lie group the elements of the group are characterized by a finite number of real parameters {aα} and for SU(N) one finds that thereare n = N2 1suchparameters.Accordingly,onecanwrite (2.13)
where the {Lα} forma basis for the N × N Hermitianmatrices knownas the generators of the group SU(N). To study the representations, it is sufficient to study the generators andtheir commutationrelations, (2.14) wherethelatter arecharacterizedbytheantisymmetricstructureconstants
2.2 AngularMomentumand SU(2)
Let us begin by discussing the representations of SU(2) in a systematic way. The basis space is three-dimensional and is spanned by S = (S1, S2, S3), that satisfy the commutationrelations[Edm74]
(2.15)
where ϵijk is the antisymmetric tensor, +1 if ijk is an evenpermutationof 123, 1 if an odd permutation and zero otherwise. In the carrier space a Hermitian scalar product exists: (2.16)
Next we need to label the states in the carrier space using the Cartan subalgebra, namely, the maximal setofmutuallycommutingoperators thatspanthe space. For SU(2) the subalgebra onlycontains a single operator, usuallychosento be Sz, where the z-axis is chosen by convention to point in some convenient direction; later in Section 2.4 we shall seethatfor SU(N) with N ≥3the situationis more complicated.The importance of devising such a mutually commuting set is well-known from quantum mechanics: it is thenpossible to diagonalize all ofthe matrices inthe setsimultaneouslyand to label the states withthe correspondingeigenvalues. Fromthis set of generators there are special operators that can be constructed which commute with all generators of the group, namely, the so-called Casimir operators. Again for SU(2) there is only one such operator (althoughmorefor SU(N) with N ≥3) namelythequadraticCasimir operator (2.17)
Asdiscussedabove,suchoperatorscommutewithall generatorsofthegroup, (218) and hence mustbe proportional to the unitmatrix, i.e., their eigenvalues maybe used to
label the representations. Letus now proceed to constructexplicitrepresentations using the commutation relations. One labels the basis states or representations with λ, the eigenvalues of the Casimir operator, and with quantum numbers m, the eigenvalues belongingtotheoperatorsintheCartansubalgebra,
Since S2 and Sz are Hermitian, λ and m are both real, and moreover, λ is positive and maybechosenbyconventiontobe
where j thenlabelstherepresentation.Correspondingly,wenow have
and,beingeigenstates ofHermitianmatrices,the states |j, m are orthogonal and canbe normalized Definingraisingandloweringoperators
itisstraightforwardtoshow that (2.25) (2.26)
Next using Eq. (2.25) one proves that, after operating on the states |j, m with the raising or lowering operators to form new states, S± |j, m, the latter are also eigenstatesof S2 and Sz, (2.27) (2.28)
thatis,witheigenvalues j(j +1) and m ±1.Writingthisresultintheform
andusingthefactthat
onethenhasthat (2.33)
Since ismadeupfromquadraticHermitianoperators,onehasthat (2.34)
and, since the allowed m-values change only in steps of 1 with the highest value mmax occurringwhen
one finds that mmax = j, justifying the choice made in the definition in Eq. (2.21). Collectingthese developments together, insummarywe have basis states characterizing the representation {|j, m} with non-negative Casimir quantum number j and quantum number m havingvalues runninginsteps ofunityfrom j to+j;thus the dimensionofthe representation is 2j + 1. The choice of phase usually made [Con35] is such that the raisingand loweringoperators actingonstates |j, m yield real c-numbers times states with m ±1: (2.36)
Next let us focus onspin SU(2), taking j → S with m → Sz and discuss the lowestdimensional representations in somewhat more detail. The simplest is the onedimensional,singletrepresentation(S =0) withbasisstate|0,0andhaving Sz |0,0 = S+ |0,0= S |0,0=0.Thefirstnontrivial representationistheso-calledfundamental one, which for SU(2) is two-dimensional (S = 1/2) with basis states |S = 1/2, Sz = ±1/2
Letting S± and Sz act on the basis states, it is straightforward to obtain explicit expressionsfor therepresentationmatrices: (2.38) or equivalently (2.39)
Conventionallyone writes Si ≡ σi/2,therebydefiningthe Pauli matrices σi, with i = 1, 2, 3,correspondingto x, y, z,respectively;weusethetwotypesofnotationinterchangably. Amorecomplicatedcaseistheonefor S =1(dimensionthree) withbasis states labeled |S, Sz: (2.40)
Asabove,letting S± and Sz actonthesestates,oneobtains (2.41) or equivalently (2.42)
This is the so-called adjoint or regular representation. This is anexample of an N2 1 dimensional representationof SU(N) givenbythe mappinginEqs. (2.1) and (2.2) with structureconstants(seeEq.(2.14)) (2.43)
Later when building hadrons in Chapter 3 we shall find it convenient to use weight diagrams. Since the generator in the Cartan subalgebra can be used to label states of a representation, the corresponding eigenvalues can be plotted in a diagramof this type, which here for SU(2) amounts to drawing a line with dots to indicate where the eigenvalues occur, as shown in Fig. 2.1. Below we shall see that in SU(N) with N ≥ 3
onehaspatternsin(N 1)-dimensional space.
Fig. 2.1 Weight diagrams for SU(2) for spins S =1/2, 1, and 3/2.
Coupling of AngularMomentum
Bytakingthe directproductoftwo representations, we find a new representationwhich in general is reducible. For instance, as an example in SU(2) let us consider the direct product of two S = 1/2 (two-dimensional) representations (see Eq. (2.37)), written in thefollowingway|S(1) =1/2, S3(1) =±1/2; S(2) =1/2, S3(2) = ±1/2, now for brevity simplyindicated|±±,yieldingfour states
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Story of Philip Brusque.
CHAPTER VII.
A new effort to form a government.—Speeches.—Anarchy and violence.—Despotism.
T morning after the events detailed in the last chapter, was one of deep interest to the people of Fredonia. Brusque, in connection with others, had taken pains to call a meeting of all the men, to consult once more upon events of common importance, and to make another effort to form some kind of government, that might establish order, protect life, and ensure freedom. There were none whose feelings were more deeply enlisted than those of the women; and, as is usual with this sex in matters of a public nature, they were on the right side. They felt their own weakness and dependence, and appreciated the necessity of government and law to protect them from brutality and violence. Nor did they feel alone for themselves; they perceived that where there is no government, there can be no safe and comfortable home; that children cannot live quietly and securely with their parents; that everything we cherish in life is insecure, and liable to be taken away by the wicked and the violent.
The several dwellings of the settlement being near together, on the occasion of which we are speaking, the women were gathering in groups, with anxious faces; those who had young children, were seen hugging them to their bosoms, as if, before night, these innocent and helpless things might have no other protection than a mother’s arm could give. There was much passing to and fro among them, and they spoke with their heads close together, and in whispers, as if fearful of being overheard.
At nine o’clock in the morning, persons began to assemble upon the southern slope of the beautiful hill on which the cave called the “Castaway’s Home” was situated. It was a lovely spot, covered with
a thick clump of palm-trees, and commanding, through the openings of the branches, a wide prospect of the surrounding ocean. All the men of the island were soon there, and as they gathered under the trees, they were divided into two groups, by their sympathies, feelings, and purposes, though not by design. In one group was the father of Emilie, M. Bonfils, a man of more than seventy years, whose locks were as white as the snow, and whose face beamed at once with benevolence and spirit. There was, however, in his countenance, at this time, a mingled look of grief and anxiety by no means usual to him. By his side sat all the oldest men of the company, together with Brusque, and most of the educated and intelligent men of the island.
The other group was composed of Rogere, most of the sailors, and several other men. They were generally young persons, whose education had been neglected, and whose course of life had left them to the indulgence of their passions. There were two or three of them who were kind-hearted, though ignorant and simple men.
The two parties consisted of about equal numbers, some twenty of each. They sat for some time, looking each other in the face, but saying little. The Rogereites looked gloomy and scowling; the Brusqueites had an air of anxiety, but still of resolution. It was apparent to all, that, if something could not be done for the cause of good order on the present occasion, riot and bloodshed were likely to be the inevitable and immediate consequence.
After a long period of silence, M. Bonfils, being the oldest man in the assembly, arose, and proposed that they should come to order by choosing a moderator to preside over the assembly. There was instantly a shout of “M. Bonfils! M. Bonfils!” and as Rogere’s people took no part, one of the men put it to vote whether M. Bonfils should preside, and it was decided in the affirmative. The old man, therefore, taking off his broad-brimmed palm-leaf hat, his long white hair floating down upon his shoulders, stood before the company. His lip quivered, and for a moment he seemed hardly able to utter a word; but at length, in a tone tremulous and faint, and exceedingly touching from its thrill of feeling, he spoke as follows:
“My friends and compatriots; we are all members of the great human family, companions in the misfortunes that have borne us hither, and the mercy which has saved us from a horrible fate. We should then have a common feeling; we certainly have the same interests.
“I ask you to come to the consideration of the great question to be proposed here to-day, with a sense of our responsibility, and a due regard to these considerations. The question to be here proposed is, I believe, whether this little community shall be delivered from that state of lawless anarchy and violence which now afflicts it, and be blessed with a government that shall at once secure liberty and peace. The real questions are these: Shall our lives be secure? Shall our homes be safe? Shall our wives and children live in quiet? Shall right, and not might, be the governing principle of society?
“It is to decide questions thus vital to our happiness and that of those who are dependent upon us, that we have now met; and I beg you as fellow-men, as brothers, as friends and neighbors, as you value life, and liberty, and justice, and a good conscience, to come to their consideration ready and determined to act for the best good of the greatest number. Let no man act for himself alone; let no man indulge prejudices or private feelings. Let us look to the good of all— the best interests of society, and proceed accordingly.”
Having uttered these words, the aged moderator sat down upon a little elevation that was near. There was then a deep silence around. At last Rogere arose, and every eye was fixed upon him, while he spoke as follows:
“Mr. Moderator; I respect the feelings that have dictated the speech just uttered by yourself. I acknowledge the obligation to cast aside selfishness, and look only to the public good. But in reasoning according to my sense of duty, I come to a very different conclusion from what some others do. We are all bound to consult the greatest good of the whole; but how shall we do it? That is the question. We have already met once before, and the persons here present, after mature deliberation, have decided that they will have no other government than such as is founded in nature; they have decided
that an artificial system of government and laws only tends to mischief, to enslave the many and favor the few. Then why this meeting? Are we a parcel of boys or silly women, as fickle as the winds, undoing one day what we have done another?
“Sir, I am opposed to a constitution; I am opposed to enacted statutes and laws. I am opposed to kings, presidents, judges, legislators, and magistrates. What are these but public bloodsuckers, living upon the toil and sacrifices of the rest of the community? Away with them, and let every man do what seemeth good in his own eyes. Things will all get adjusted to this system in good time. There is an instinct in the animal tribes which is thought to be borrowed from divine wisdom. The heron and the bittern are astronomers and navigators by nature; they know by instinct what man learns with difficulty. They are legislators too, but that divine instinct bids them leave things to their natural course. The strongest, by necessity and the laws of nature, become the leaders, and the rest have only to follow and obey. This is the great system of the universe; and man, by adopting an artificial scheme of government, is only sinning against nature, history and experience. I move you, therefore, that this assembly do now adjourn.”
Scarcely had Rogere finished, when his party shouted in the most animated manner, and there was a look of satisfaction and triumph in their faces that seemed to say that their leader had settled the whole question. When the applause had subsided, the moderator stated that there was a motion to adjourn, and asked if any one had anything to say against it. Upon this, Brusque rose, and spoke as follows:
“Mr. Moderator; you have already stated the high and solemn purposes of this meeting. We are to decide, in the first place, whether we will adopt some form of government, and if so, what system shall be established? At the very outset, and before the subject has been discussed, a motion is offered that we adjourn. It is moved that we separate, and leave this little colony to that anarchy which is now desolating the island. We are asked to adjourn, and follow the bittern and the heron as our examples in legislation. Man
is to be the pupil of the bird; the brute is to be the lawgiver of human beings!
“What, sir, is the state of things? Riot, crime, and violence are now the order of the day. One murder has already been committed, and the man whose hand is stained with his brother’s blood is here, as free as the rest; and that murderer’s hand is lifted up in an assembly, as if entitled to all the privileges of citizenship. Sir, look at the fruits of the island, lately so abundant; they are fast disappearing, for no one has any interest to preserve or increase them. Not only are we in a state of confusion and fear, not only are the women and children in the community in distress from apprehension, but, sir, our means of living are wasting away,—starvation is at our very doors.
“And what is the remedy for all these evils? A good government, that shall parcel out these lands to the people, and secure to each man his own; a good government, that shall protect a man in his home, his earnings, his property; a good government, that will enforce right and restrain might; a good government, that will punish murder, theft, violence, and crime. This, and this alone, will bring peace to the island; this, and this alone, will give security and happiness to all. Let us have a government, to secure the rights of the people and punish injustice, and this island may become a paradise. Its rich hillsides and lovely valleys will be cultivated, and will produce the greatest abundance of comforts and luxuries. Let us have protection to life, home, and property, and commerce will spring up, and we can get from other lands all that they produce which can minister to our enjoyment.
“Who will till the soil, if any man stronger than himself can drive the laborer away and take the produce? Who will toil, if the violent, and selfish, and powerful man may take away the result of that toil? Sir, we are told to follow nature, to look to the instinct of animals for a guide. And is man, gifted with reason, to throw that reason aside and follow instinct? The proposition is absurd. If we follow animals, we must adopt their modes of life. If you adopt the government of wolves, you must live in rocks and dens, feast upon blood, and have no other covering than nature provides. If you allow the strong to take what they can grasp, we go back at once to the savage state.
“Let us then be more wise, more reasonable, more just Let us remember that we men act not only for ourselves, but for others. I beseech you to look upon the anxious groups of wives, mothers, and daughters in that little valley, whose hearts are now palpitating with anxiety; they are waiting the result of our deliberations, as involving interests more dear than life to them. Let them know that you have this day resolved to establish a good government, and they will ask ten thousand blessings on your heads. Let them know that this state of anarchy is to continue, and they will mourn the day that saved them from the billows to which the relentless pirate had doomed them.”
This speech of Brusque’s had an evident effect, and when the question of adjournment was put, there was a majority against it. Brusque, greatly encouraged, then rose, and moved, that it was the sense of the assembly that the best good of the people required the immediate adoption of some form of government. No sooner was this motion put, than Rogere, fearing that it might be carried, sprang to his feet, and, drawing a dagger, brandished it in the air, at the same time addressing his party as follows:
“My friends, are you not sick of this folly, this hypocrisy, this child’s play? Away with it all! let us be men—let us be free. Down with that hoary fool, and this false-hearted knave!” Saying this, and pointing to M. Bonfils and Brusque, he led the way, and rushed upon them. His men followed as with one impulse. The aged moderator was struck to the ground by a single blow, and Brusque, taken by surprise, was thrown down, and two stout men, seizing upon him, tied his hands and feet fast. The rest of Brusque’s party, after a short skirmish, fled down the hill to the village, where they were received with cries of consternation and despair.
M. Bonfils and Brusque were taken to the “Castaway’s Cave,” which Rogere now made his head-quarters, and where his party soon assembled. After a brief interval, it was proposed by one of the men that Rogere should be chief of the island, with full power in his hands to govern as he pleased. His motion was carried by acclamation, and M. Bonfils and Brusque were required to give their consent. Refusing to do this, they were bound and taken into one of
the lower apartments of the cave, and, totally unable to move, they were left to themselves.
(To be continued.)
The Siberian Sable-Hunter.
CHAPTER IV.
A meeting with Tunguses.—A great feast.—The travellers proceed.
T long story of Linsk being finished, Alexis remarked that, although it was not the best he had heard in his life, he was still obliged, for he had never heard a Samoide tale before.
“Well,” said the old hunter, a little snappishly, “if you don’t like my stories, you need not listen to ’em. I didn’t make ’em myself, and only tell what other people have told me. And as to these Samoides, what can you expect, when the men are not taller than a keg of brandy, and the women are about the height of a five-gallon jug? Can we expect to make a silk purse of a sow’s ear? I could tell you a story of Tartar robbers and enchanted castles, if you would like that better.”
“I beg your pardon,” said Alexis; “I did not mean to offend you. The Samoide story will do, but I should like to hear a Tartar tale very much.”
“Well,” said Linsk, “I will tell you one;” but just as he was about to begin, they came in sight of some huts belonging to the Tunguses, a very singular race of people, who inhabit the middle portions of Siberia. They resemble the Ostiacks, like them living in houses built of poles set in a circle. They have no towns or villages, but they wander from place to place, living entirely by hunting and fishing, in which they display wonderful skill and perseverance. In summer, they dwell on the banks of the rivers, and in winter retire to the wooded regions, where they pursue the sable, ermine, marten, and black fox. They have no fire-arms, but are adroit in the use of the
bow and arrow In the spring, they carry or send their furs to Yakoutsk, a considerable town on the Olekminsk river, and the great fur-market of Siberia.
In a short time, our adventurers came to the group of huts which they had before descried, and Linsk, who knew the habits of the people, did not hesitate at once to go up to one of them and prepare to enter it through a hole about three feet high, that was left as a door. He was met at the entrance by a man of about fifty years of age, and dressed in a short coat made of a wolf-skin, and a pair of flannel trowsers, that looked as much like a petticoat as anything else. He gazed at the four hunters for a moment with some distrust, but then seemed satisfied, and made a sign of welcome.
The conversation soon brought other persons out of the several huts around. These consisted of men, women, and children—all low in stature, and with skins of the color of a smoked ham. The men were dressed nearly in the same fashion as the person first described. The women were attired in short cotton gowns and flannel petticoats that reached but little below the knee. The children were half naked, or clad in cotton wrappers. Several of them had on castoff seal-skin jackets reaching down to the middle, and making them look like half boys and half beasts.
They were a queer-looking set of people, but seemed frank and good-natured, and invited the strangers to spend the night, which was now approaching, with them. Linsk, who knew the language pretty well, accepted the offer, and the party was led to one of the largest huts. Alexis noticed two large rein-deer in a little pen attached to the dwelling, and observed several large dogs, who now awoke from their repose and came smelling suspiciously around the newcomers.
On entering the hut, the scene presented was a curious one. The whole interior consisted of one room. This was circular, of a conical form, and about twenty feet across. Benches were set around, upon which the wife and one or two other women were sitting. The fire was built in the centre, and, there being no chimney, the whole hut
was filled with smoke; but the inmates did not seem to mind it. The children were crawling upon the floor like pigs.
After staying a while in the hut, it was announced that supper was ready, and the travellers soon found that it was to be a feast. The men of the party had been on a fishing expedition, and, having been absent a week, had scarcely tasted a bit of food during that period, and their families at home had been fasting in the mean time. One of the huts had been assigned to the cooking of the meal, and it was to be eaten in the same place.
When the sable-hunters came to the hut, they found about sixty people there, of all sexes and sizes. Already had the revel begun; for the hunger of the party was beyond control. The feast itself was a sight to see. Four large iron caldrons had been set over the fire, filled with fishes of all sorts, though chiefly cod. They were thrown in together without dressing—heads, tails, entrails, fins, and scales! A huge quantity of deer’s-grease and a little salt had been put in. A brisk fire had then been kindled beneath, and the whole fried or boiled into a mighty chowder. The steam that gushed from the door of the hut, was almost strong enough for a supper It was so rank as to satisfy Alexis and his two younger companions, who soon went out of doors, and mingled with the people there.
A feast of wolves could not have been more voracious. Knives, forks, and plates were not thought of; each one ran into the hut with a wooden bowl, and, dipping it into the caldron, brought forth the seething mass, and while it yet seemed boiling hot, they devoured it with a rapacity absolutely amazing. The scalding heat seemed not to be the least hindrance; there was no ceremonious blowing and cooling—down it went, one dishful after another, as if it were a strife to see who could devour the most in the shortest space of time!
In two or three instances the children upset their bowls, and picking up the food from the ground, heedless of the dirt attached to it, ate it down; no matter if it was trodden upon, it was all the same. One of the children was seen by Alexis, flat upon his stomach, lapping up the broth, from the earth, that had been spilt. Among this
crowd, the dogs came in for their share; but they were often obliged to dispute their claims to the remnants with the greedy children.
Among all this coarseness, the strangers were treated with the utmost hospitality, as, indeed, they had been ever since their departure from Tobolsk. After the meal had been finished, a few of the men treated themselves, apart, to brandy, in which entertainment our adventurers were permitted to join. A scene of drunkenness followed, after which the men staggered to their several houses. Linsk and his companions were comfortably lodged, having drank but sparingly.
In the morning the travellers left their Tungusian friends, and set out on their journey, offering to pay for their entertainment, which was, however, refused. Indeed, this had been generally the case, and they had hardly found any necessity of having money. Proceeding upon their journey, Linsk, according to his wont, began to talk, and these Tungusians were naturally the subject of his discourse.
“They are very numerous,” said he, “occupying nearly half of Siberia, and being confined to the central portions of it. They are as restless as Tartars, always moving from place to place, and alternately feasting and starving. They go without food as long as a wolf, and, like a wolf, they will gorge themselves when they get a chance. They eat food when and where they can get it. This is the way they are brought up. I have seen them eat candles, soap, and raw pork. I was once at a place where a reindeer died of disease; they threw him whole upon a fire, singed him a little, and then eat him, leaving nothing but the bones! A real hungry Tungusian will eat twenty pounds of meat in a day!”
Alexis would have expressed some doubt of all this, had not the scene he had witnessed prepared him to believe it, and had he not found that Linsk, though loyal to servility, and not a little inclined to superstition, was still a man of veracity in all that related to his own observation and experience. He went on with his description, therefore, without interruption.
“Yet, greedy as these people are, they have their good points, as I believe all God’s creatures have. They are honest, frank, and hospitable. If they love feasting, their willingness to share the meal with a stranger is a greater virtue. And they are not so stupid as one might expect, from their swallowing such oceans of lard. I know of no people so cunning in catching fish and game. In the winter season, many establish themselves in the forests along the branches of the Wittim and Olekminsk regions, lying to the south of where we now are. A young hunter from Tobolsk, whom I knew, and who dwelt there one winter, told me that they were the keenest fellows he had ever met with. They would trace a fox by his foot-prints upon the frozen snow, and could tell whether it was grey or black by the shape of his track! They killed their game with blunt arrows, so as not to injure the skin; and so careful were they of the sable, that when they found one on a tree, they would not shoot him, but make fires beneath, and smoke him, until the creature would fall at their feet.
“The fact is, that the Tunguses are such good hunters that the wild beasts have found them out, and have pretty much left their country. The fine sables are now seldom found where they used to be abundant, and those who would hunt them must go farther north, where we are going. These people have no books, and their religion is a strange belief in stupid gods, whom they worship under the guise of little wooden images. They believe in witchcraft and sorcery; and there are a good many cheats among them, who pretend to practise these forbidden arts.”
(To be continued.)
Wisdom of the Creator.
T fact that the Creator is a Being who thinks, who exercises wisdom, and exerts power, is illustrated by the provision he has made for the wants of animals, arising from their peculiar condition. The human teeth afford a striking instance of this. The infant is to live by milk taken from its mother, and it can take its nourishment in without teeth much more conveniently to itself and its nurse, than with them. Accordingly, it has no teeth; nor do they come till about the time that it takes other food that may require teeth. We see the same careful foresight in providing that the horns of calves and lambs do not grow till they have done sucking, as they would be in the way in performing that operation. But in regard to the human teeth, a still further prospective contrivance is made at the very beginning. The jaw of a grown person is much larger than that of an infant, and the first teeth are therefore entirely too small to fill the jaw of an adult. It is accordingly provided that, at the age of eight or ten years, the first set of teeth shall be shed, and larger ones come in their place. And the preparation for them is made at the outset—a row of teeth being actually set in below the first, ready to grow when these are gone!
The providing of milk for young animals is another admirable proof of the designing wisdom of the Creator. Milk is a fluid of a very nutritious quality, and no art of man can make it. As soon as the young are produced, the milk is ready for it, and not before. And how wonderful, how ingenious, is the whole contrivance by which young animals are provided with food, in a manner the most curious, and of a kind the most suitable!
Washington a Teacher to the Young.
T is no name in the annals of any country more revered than that of George Washington. It is a matter of interest to inquire how he became so good and great, and how he obtained such a desirable reputation; how he was able to do so much good to his country and to mankind; how he was qualified to leave behind him so excellent an example; how he acquired that great wisdom which guided him in life, and prepared him for death—which made him, like Moses in ancient days, the leader of a nation through a wilderness of trial, and suffering, and danger, and now that he has been dead more than forty years, renders him still the teacher, not only of the United States, but all the civilized world.
It is a good plan for every one who wishes to be useful, good, and happy, to study the story of Washington, and see how it was that he became so useful, so good, and so happy. It is only by study that we can gain knowledge; and the best way to find out the path of duty and of success, is carefully to read the history of those who have been successful. I propose, therefore, to give you a brief outline of Washington’s life, taking care to present those points in his career which seem to have been the most influential in forming his character and shaping his fortunes.
George Washington was born in Virginia, on the 22d of February, 1732. His father was a wealthy planter; but he died in 1743, when George was eleven years old. He was, therefore, left to the care of his mother, who was a good and wise woman.
Now you must remember that when Washington was a boy, young people had not the advantages that they have now In Virginia, there were no academies, high-schools, or colleges. He had, therefore, only the privileges of a common-school education,
where writing, reading, arithmetic, and a little of geometry, were taught.
Now some boys with these simple helps had never been great; the reason why they were sufficient for Washington I will tell you. In the first place, he had a good mother, who, like almost all good mothers, frequently counselled and advised her son to make the best use of his time at school; to pay attention to his lessons; to learn them well; and thus, not only to store his mind with knowledge, but to get into the habit of studying thoroughly, and of improving his mind. In the second place, Washington had the good sense, the virtue, and the wisdom to mind his mother in these things. These are the two great reasons why a common-school education was sufficient for so great a man, and they are the two chief reasons why he became so great.
Now this shows that the advantages a boy possesses are of less consequence than the way in which he improves them. A boy may be sent to a high-school, and go through college, and have good natural capacity, and yet turn out to be a useless, weak, and ignorant man. Merely going through a high-school, or an academy, or a college, cannot make a good, useful, or great man. In order to be good, useful, great, or even happy, it is necessary in youth to do as Washington did.
Another thing to be noticed here is, that Washington had none of that folly which some boys think smartness, or a mark of genius, or manliness—a disposition to disobey a mother or a schoolmaster. Washington was obedient to both of them. If, therefore, a boy wishes to be successful in life, let him cultivate obedience to parents and teachers.
One of the great advantages that followed from Washington’s making the best of his school privileges was, his adopting good habits. He got into the habit of doing everything thoroughly. He was not willing to learn a lesson by halves, and when he came to recite, to guess and shuffle his way out. No, indeed! He did not leave a lesson till he had mastered it—till he knew all about it—till he had stamped it so firmly in his mind as to make the impression indelible.
The reason why habits are so important, is, that they hang about a person, and actually guide him through life. When a man has got the habit of doing a thing, it is easy to repeat it, and it is hard to act otherwise. Habits may be illustrated by a rail-road. The cars run easily upon the track, and it is difficult for them to get away from it. What work a car would make in attempting to run over the rough ground! Now, the mind is very like the car; it slides along glibly enough upon the rails of habit, but it works hard and makes little progress over a place where it has not been before. Thus, if a boy gets into the habit of lying, he lies, as a locomotive glides upon its track, with great rapidity, smoothness, and ease. And if he has once got into this habit of lying, and then attempts to tell the truth, he feels as if he had got off the track, and is like a car running over the common ground.
The importance of this matter of habit is seen upon a little reflection. We must remember what has been said before, that the things we do once or twice, we are likely to repeat. We are, therefore, always forming habits, good or bad; and children frequently get them settled as a rail-road track, before they are aware of it. Now, these habits may ruin those who adopt them, and turn into evil the best advantages that they can enjoy.
If a boy gets the habit of studying in a half-way, slovenly, slip-shod manner, he is almost certain to be greatly injured thereby. If he goes to college, he there continues the same habit; when he comes out, he still carries it with him; when he enters upon business, it still hangs about him. He does nothing well, or thoroughly; he is careless and slovenly in all he does; there is imperfection and weakness in his career, and finally he turns out an unsuccessful man If he is a merchant, he usually fails in business; if a lawyer, a physician, or minister, he is generally at the tail-end of his profession, poor, useless, and despised. Such is the mighty influence of our habits; and remember that they are formed in early life. Remember that every day feeds and fosters our habits.
It is interesting to trace the way that Washington’s youthful habits operated upon him. Some of his early schoolbooks are extant, and these show that he was very thorough in writing. He even took the
pains to write out, in a fine hand, the forms in which notes of hand, bills of exchange, receipts, bonds, deeds, wills, should be drawn. Thus he cultivated the habit of writing neatly, of being patient in copying papers, and of being accurate in making copies; and at the same time he made himself acquainted with the forms of drawing up business documents. In all this, we see the habit of doing things patiently, accurately, and thoroughly. We see that Washington had so trained himself, that he could sit down and do that which was mere toil, and which some boys would think stupid drudgery.
Another thing that is remarkable at this early period of Washington’s life, is, that in writing he was careful to study neatness and mechanical precision. Several quires of his school-manuscripts remain, in which he worked out questions in arithmetic and mathematics. These manuscripts are very neatly executed; there are several long sums which are nicely done and beautifully arranged. There are, also, extensive columns of figures, and all set down with careful precision.
Another thing visible in these manuscripts, is, that Washington studied accuracy; his sums were all right. What a beautiful illustration of the great man’s life! His youthful manuscripts show that he learned to render his school-boy pages fair; to work out all his sums right. Thus he started in life—and thus he became qualified to make the pages of his history glorious; the footing up of his great account such as the sentiment of justice throughout the world would approve!
Another thing that had great influence in the formation of Washington’s character and in securing success in life, was, that very early he adopted a code or system of rules of behavior. This was found among his papers after his death, in his own hand-writing, and written at the age of thirteen. I will give you a few extracts from this code of manners, or rules of conduct:
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“Every action in company ought to be with some sign of respect to those present.
“Be no flatterer, neither play with any one that delights not to be played with.
“Read no letters, books, or papers in company
“Come not near the books or papers of another so as to read them.
“Look not over another when he is writing a letter.
“Let your countenance be cheerful, but in serious matters be grave.
“Show not yourself glad at another’s misfortune.
“Let your discourse with others on matters of business be short.
“It is good manners to let others speak first.
“Strive not with your superiors in argument, but be modest.
“When a man does all he can, do not blame him though he succeeds not well.
“Take admonitions thankfully.
“Be not hasty to believe flying reports to the injury of another.
“In your dress, be modest, and consult your condition.
“Play not the peacock, looking vainly at yourself.
“It is better to be alone than in bad company
“Let your conversation be without malice or envy.
“Urge not your friend to discover a secret.
“Break not a jest where none take pleasure in mirth.
“Speak not injurious words either in jest or earnest.
“Gaze not on the blemishes of others.
“When another speaks, be attentive.
“Be not apt to relate news.
“Be not curious to know the affairs of others.
“Speak not evil of the absent.
“When you speak of God, let it ever be with reverence.
“Labor to keep alive in your heart that spark of heavenly fire called conscience.”
Such are some of those rules that Washington wrote out in a fair hand at thirteen. Most of these rules turn on one great principle, which is, that you treat others with respect; that you are tender of the feelings, and rights, and characters of others; that you do to others as you would have others do to you.
But another thing, also, is to be considered, which is, that Washington not only had a set of good rules of behavior, all written out in a fair hand and committed to memory, but he was in the habit of observing them; and he not only observed them when a child, but after he became a man. He got into the habit of obeying every one of these rules, and every one of them became a rail-road track to him, and he therefore followed them; and thus it was that his manners were always so dignified, kind, and noble; thus it was that his character and conduct became so great and good.
Now, I would not have my readers suppose that Washington was always a man; on the contrary, when he was a boy, he loved fun as well as anybody. He liked to run, to leap, to wrestle, and play at games. He had a soldierly turn, even in boyhood, and was fond of heading a troop of boys, and marching them about with a tin kettle for a drum.
Washington, too, was quick-tempered and passionate when a boy; but the beauty of his story in this point is, that by adopting good habits and principles he overcame these tendencies of his nature, and he showed that all quick-tempered boys can do the same, if they please. They can govern their tempers; they can adopt good rules of conduct; they can get into the habit of being calm, patient, and just, and thus grow up to honor and usefulness.
There are many other traits of character belonging to Washington that are interesting and worthy of imitation. He was accurate and just
