Introduction to Nuclear Physics 1. Atomic Structure and the Periodic Table According to the Bohr-Rutherford model of the atom, also called the “solar system model,”the atom consists of a central nucleus surrounded by electrons in orbits around the nucleus. The nucleus is.

• Introduction Nuclear and particle physics are essentially at the forefront of nowadays understanding of physics. Except for the astrophysical sciences it is here where one is at the edge of conceptual knowledge. In contrast, for problems of solid or applied physics we known.
• This physics textbook is designed to support my personal teaching activities at Duke University, in particular teaching its Physics 141/142, 151/152, or 161/162 series (Introductory Physics for life science majors, engineers, or potential physics majors, respectively). It is freely available in its.
• Update the second edition of his classic text Introductory Nuclear Physics (New York: Wiley, 1955). As the project evolved, it became clear that, owing to other commitments, Professor Halliday would be able to devote only limited time to the project and he therefore volunteered to remove himself from active participa.
• The realm of atomic and nuclear physics Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. Atomic physics (or atom physics) is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around.

Introductory Nuclear Physics Notes Pdf

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1Introduction toNuclear Physics All phenomena in the universe are believed to arise from the actionsof just three fundamental forces: gravitation and the less familiarstrong force and electroweak force. The complex interplay betweenthese last two forces defines the structure of matter, and nowhere arethe myriad manifestations of this interplay more evident than in thenucleus of the atom. Much of the substance of the universe exists in theform of atomic nuclei arranged in different ways. Within ordinarynuclei, the weak gravitational attraction between the constituentparticles is overwhelmed by the incomparably more powerful strongnuclear force, but gravitation's effect is large indeed in neutron stars-bizarre astrophysical objects whose properties are very much likethose of gigantic nuclei. Studies of the nucleus can thus be viewed as a link between theworlds of the infinitesimal and the astronomical. Collectively, thevarious nuclei can be regarded as a laboratory for investigating thefundamental forces that have governed our universe since its origin inthe big bang. Indeed, as this report illustrates, the study of nuclearphysics is becoming ever more deeply connected with that of cosmol-ogy as well as elementary-particle physics. Before venturing into these exciting realms, we will quickly surveythe field of nuclear physics at an elementary level in order to learn thelanguage. Although nuclear physics has the reputation of being adifficult subject, the basic concepts are relatively few and simple.9

10 NUCLEAR PHYSICS10-2 m10-14 m~ Raspberry_---~ Nucleus-i Quark-___,-_-_____· ~,~Proms_. ~,-__Nuc:-_- ~. ~ -_-_-10 m-15 mFIGURE l.l Approximate dimensions for the structure of matter from raspberries toquarks (the cellular and molecular levels of structure have been omitted).THE ATOMIC NUCLEUS The atomic nucleus is an extremely dense, roughly spherical objectconsisting primarily of protons and neutrons packed fairly closelytogether (see Figure 1.1~. Protons and neutrons are collectively callednucleons, and for many years it was thought that nucleons were trulyelementary particles. We now know, however, that they are notelementary but have an internal structure consisting of smaller parti

INTRODUCTION TO NUCLEAR PHYSICS 11cles and that there are other particles in the atomic nucleus along withthem. These aspects of the nucleus are discussed below. Protons andneutrons are very similar, having almost identical physical properties.An important difference, however, lies in their electric charge: protonshave a unit positive charge, and neutrons have no charge. They areotherwise so similar that their interconversion in the decay of radio-active nuclei is a common occurrence. The character of the nucleus provides the diversity of the chemicalelements, of which 109 are now known, including a number ofman-made ones. (The cosmic origin of the elements is a differentquestion-one that is addressed by the specialized field of nuclearastrophysics.) Each element has a unique proton number, Z. Thisdefines its chemical identity, because the proton number (equal to thenumber of unit electric charges in the nucleus) is balanced, in a neutralatom, by the electron number, and the chemical properties of anyelement depend exclusively on its orbital electrons. The smallest andlightest atom, hydrogen, has one proton and therefore one electron; thelargest and heaviest naturally occurring atom, uranium, has 92 protonsand 92 electrons. In a rough sense, this is all there is to the diversity ofthe chemical elements and the fantastic variety of forms inanimateand animate that they give rise to through the interactions of theirelectron clouds. To explain the stability of the elements, however, and to studynuclear physics, we must also take into account the neutron number,N. of each nucleus. This number can vary considerably for the nucleiof a given element. The nucleus of ordinary hydrogen, for example, hasone proton and no neutrons, the latter fact making it unique among allnuclei. But a hydrogen nucleus can also exist in a form that has oneproton and one neutron (Z = 1, N = 1~; this nucleus is called adeuteron, and the atom, with its one electron, is called deuterium.Chemically, however, it is still hydrogen, as is the even heavier,radioactive form tritium, which has one proton and two neutrons (Z =1, N = 21; a tritium nucleus is called a triton. These separate nuclei of a single chemical element, differing only inneutron number, are the isotopes of that element. Every element has atleast several isotopes stable and unstable (radioactiveWand some ofthe heavier elements have already been shown to have more than 35.Although the chemical properties of the isotopes of a given element arethe same, their nuclear properties can be so different that it is importantto identify every known or possible isotope of the element unambigu-ously. The simplest way is to use the name of the element and its massnumber, A, which is just the sum of its proton and neutron numbers:

12 NUCLEAR PHYSICSA = Z + N. Because different combinations of Z and N can give thesame value of A, nuclei of different elements can have the same massnumber (chlorine-37 and argon-37, for example). To emphasize theuniqueness of every such separately identifiable type of nucleus,scientists refer to them as nuclides. There are about 300 naturally occurring stable nuclides of thechemical elements and about 2400 radioactive (i.e., spontaneouslydecaying) ones. Of the latter, the great majority do not exist naturallybut have been made artificially in particle accelerators or nuclearreactors. These machines of modern physics can also create experi-mental conditions that are drastically unlike those ordinarily existingon Earth but that are similar, perhaps, to those characteristic of lesshospitable corners of the universe. Thus they enable us, in our effortsto understand the laws of nature, to extend our intellectual grasp intodomains that would otherwise be inaccessible. Experimental and theoretical investigations of the broad range ofnuclides available to us represent the scope of nuclear physics. In thestudy of nuclear spectroscopy, for example, experimentalists performmany kinds of measurements in order to characterize the behavior ofthe nuclides in detail and to find patterns and symmetries that will allowthe huge amounts of information to be ordered and interpreted in termsof unifying principles. The theorists, on the other hand, search forthese unifying principles through calculations based on the availablefacts and the fundamental laws of nature. Their aim is not only toexplain all the known facts of nuclear physics but to predict new oneswhose experimental verification will confirm the correctness of thetheory and extend the bounds of its applicability. A similar approach applies to the study of nuclear reactions, inwhich experimentalists and theorists seek to understand the changingnature and mechanisms of collisions between projectile and targetnuclei at the ever-increasing energies provided by modern accelera-tors. The many ways in which target nuclei can respond to theperturbations produced by energetic projectile beams provide a richfund of experimental data from which new insights into nuclearstructure and the laws of nature can be gained. In extreme cases, newstates of nuclear matter may be found.THE NUCLEAR MANY-BODY PROBLEM The essential challenge of nuclear physics is to explain the nucleus asa many-body system of strongly interacting particles. In physics, threeor more mutually interacting objects whether nucleons or stars are

INTRODUCTION TO NUCLEAR PHYSICS 13considered to be 'many' because of the tremendous mathematicaldifficulties associated with solving the equations that describe theirmotions. With each object affecting the motions of all the othersthrough the interactions that exist among them, and with all themotions and hence all the interactions changing constantly, the prob-lem very quickly assumes staggering proportions. In fact, this many-body problem is now just barely soluble, with the largest computers,for three bodies. For four or more, however, it remains generallyinsoluble, in practice, except by methods relying on various approxi-mations that simplify the mathematics. What nuclear physicists try to do-within the constraints imposed bythe many-body problem is to understand the structure of nuclei interms of their constituent particles, the dynamics of nuclei in terms ofthe motions of these particles, and the fundamental interactions amongparticles that govern these motions. Experimentally, they study theseconcepts through nuclear spectroscopy and the analysis of nuclearreactions of many kinds. Theoretically, they construct simplifyingmathematical models to make the many-body problem tractable. These nuclear models are of different kinds. Independent-particlemodels allow the motion of a single nucleon to be examined in terms ofa steady, average force field produced by all the other nucleons. Thebest-known independent-particle model is the shell model, so calledbecause it entails the construction of 'shells' of nucleons analogous tothose of the electrons in the theory of atomic structure. At the otherextreme, collective models view the nucleons in a nucleus as moving inconcert (collectively) in ways that may be simple or complex- just asthe molecules in a flowing liquid may move smoothly or turbulently. Infact, the best-known collective model, the liquid-drop model, is basedon analogies with the behavior of an ordinary drop of liquid. The above descriptions are necessarily oversimplified. The actualmodels in question, as well as related ones, are very sophisticated, andtheir success in explaining most of what we know about nuclearstructure and dynamics is remarkable. As we try to push this knowl-edge to ever deeper levels, however, we must take increasinglydetailed account of specific nucleon-nucleon interactions. Doing sobrings out the other half of the essential challenge of nuclear physics:that nucleons are strongly interacting particles.THE FUNDAMENTAL FORCES In nature, the so-called strong force holds atomic nuclei togetherdespite the very substantial electrostatic repulsion between all the

14 NUCLEAR PHYSICSpositively charged protons. The distance over which the strong force isexerted, however, is extremely short: about 10- ~5 meter, or 1femtometer-commonly called 1 fermi (fm) after the great nuclearphysicist Enrico Fermi. A fermi is short indeed, being roughly thediameter of a single nucleon. The time required for light to traverse thisincredibly short distance is itself infinitesimal: only 3 x 10-24 second.As we will see, the characteristic duration of many events taking placein the nucleus is not much longer than that: about 10-23 to 10-22second, corresponding to a distance traveled, at the speed of light, ofonly about 3 to 30 fm. This is the domain- incomprehensibly remote from our everydayexperience-of the strong force, which dominates the nucleus. Nucle-ons within the nucleus are strongly attracted to one another by thestrong force as they move about within the confines of the nuclearvolume. If they try to approach each other too closely, however, thestrong force suddenly becomes repulsive and prevents this fromhappening. It is as though each nucleon had an impenetrable shieldaround it, preventing direct contact with another nucleon. The behav-ior of the strong force is thus very complex, and this makes the analysisof multiple nucleon-nucleon interactions (the nuclear many-body prob-lem) much more challenging. At the opposite extreme of the fundamental forces is gravitation, along-range force whose inherent strength is only about 10-38 times thatof the strong force. Since the gravitational force between any twoobjects depends on their masses, and since the mass of a nucleon isextremely small (about 10-24 g), the erects of gravitation in atomicnuclei are not even close to being measurable. Nonetheless, theuniverse as a whole contains so many atoms, in the form of hugelymassive objects (stars, quasars, galaxies), that gravitation is thedominant force in its structure and evolution. And because gravitationis extremely important in neutron stars, as mentioned earlier, thesesupermassive nuclei are all the more interesting to nuclear astrophys-icists. Lying between gravitation and the strong force, but much closer tothe latter in inherent strength, is the electroweak force. This rathercomplex force manifests itself in two ways that are so different thatuntil the late 1960s they were believed to be separate fundamentalforces just as electricity and magnetism, a century ago, were thoughtto be separate forces rather than two aspects of the one force,electromagnetism. Now we know that electromagnetism itself is but apart of the electroweak force; it is therefore no longer considered to bea separate fundamental force of nature.

INTRODUCTION TO NUCLEAR PHYSICS 15 Electromagnetism is the force that exists between any two electri-cally charged or magnetized objects. Like gravitation, its influence canextend over great distances, and it decreases rapidly in strength as thedistance between the objects increases. Its inherent strength is rela-tively large, however, being about 0.7 percent of that of the strongforce at separation distances of about 1 fm. Electromagnetism is thebasis of light and all similar forms of radiation (x rays, ultraviolet andinfrared radiation, and radio waves, for example). All such radiationpropagates through space via oscillating electric and magnetic fieldsand is emitted and absorbed by objects in the form of tiny bundles ofenergy called photons. In some radioactive decay processes, extremelyenergetic photons called gamma rays are emitted by the nuclei as theychange to states of lower total energy. A photon is considered to be thefundamental unit of electromagnetic radiation: a quantum. This pro-found idea revolutionary in its time but now commonplace lies atthe heart of quantum mechanics, the physical theory that underlies allphenomena at the submicroscopic level of molecules, atoms, nuclei,and elementary particles. The other manifestation of the electroweak force is the weak force,which is responsible for the decay of many radioactive nuclides and ofmany unstable particles, as well as for all interactions involving theparticles called neutrinos, which we discuss below. The weak force innuclei is feeble compared with the electromagnetic and strong forces,being only about 10-5 times as strong as the latter, but it is stillextremely strong compared with gravitation. The distance over whichit is effective is even shorter than that of the strong force: about 10-'8m, or 0.001 fm roughly 1/1000 the diameter of a nucleon. The weakforce governs processes that are relatively slow on the nuclear timescale, taking about 10- ~° second or more to occur. As short as this timemay seem, it is about one trillion times longer than the time required forprocesses governed by the strong force. The prediction in 1967 and its subsequent experimental confirma-tion that the electromagnetic and weak forces are but two aspects ofa single, more fundamental force, the electroweak force, were tri-umphs of physics that greatly expanded our understanding of the lawsof nature. However, because these two component forces are sodifferent in the ways in which they are revealed to us (their essentialsimilarities start to become clear only at extremely high energies, farbeyond those of conventional nuclear physics), it is usually convenientto discuss them separately, just as we often discuss electricity andmagnetism separately. Thus they are still often described as thougheach were fundamental. In this book, we will let the circumstances

16 NUCLEAR PHYSICSdecide how they should be discussed: as electromagnetic and weak, oras electroweak. For the remainder of this chapter, we will discuss themseparately. The fundamental forces are often called fundamental interactions,because the forces exist only by virtue of interactions that occurbetween particles. These interactions, in turn, are mediated by theexchange of other particles between the interacting particles. This mayseem like Chinese boxes, but as far as we know, it stops right there: inthe realm of elementary-particle physics, which we must now brieflyintroduce in order to see where the foundations of nuclear physics lie.THE ELEMENTARY PARTICLES The experimental study of elementary-particle physics also knownby the inexact name high-energy physics~iverged from that ofnuclear physics around 1950, when developing accelerator technologymade it relatively easy to search for other and ultimately morebasic 'elementary' particles than the proton or the neutron. Anenormous variety of subnuclear particles has by now been discoveredand characterized, some of which are truly elementary (as far as we cantell in 1984), but most of which are not. Along with the discovery of these particles came major theoreticaladvances, such as the electroweak synthesis mentioned above, andmathematical theories attempting to classify and explain the seeminglyarbitrary proliferation of particles (several hundred by now) as accel-erator energies were pushed ever higher. Chief among these theories,because of their great power and generality, are the quantum fieldtheories of the fundamental interactions. All such theories are relativ-istic, i.e., they incorporate relativity into a quantum-mechanical frame-work suitable to the problem at hand. They thus represent the deepestlevel of understanding of which we are currently capable. We will return to these theories shortly, but first let us see whatclasses of particles have emerged from the seeming chaos. This isessential for two reasons. First, the nucleus as we now perceive it doesnot consist of just protons and neutrons, and these are not evenelementary particles to begin with. To understand the atomic nucleusproperly, therefore, we must take into account all the other particlesthat exist there under various conditions, as well as the compositionsof the nucleons and of these other particles. Second, the theoreticalframework for much of nuclear physics is now deeply rooted in thequantum field theories of the fundamental interactions, which are thedomain of particle physics. Aspects of the two fields are rapidly

INTRODUCTION TO NUCLEAR PHYSICS 17converging, after their long separation, and it is no longer possible toinvestigate many fundamental problems of nuclear physics except inthe context of the elementary particles. Much of the material in thisbook, in fact, deals with the ways in which this new view of nuclearphysics has come about and the ways in which it will accelerate in thefuture. Physicists now believe that there are three classes of elementaryparticles leptons, quarks, and elementary vector bosons and thatevery particle, elementary or not, has a corresponding antiparticle.Here we must make a short digression into the subject of antimatter.An antiparticle differs from its ordinary particle only in having someopposite elementary properties, such as electric charge. Thus, theantiparticle of the electron is the positively charged positron; theantinucleons are the negatively charged antiproton and the neutralantineutron. The antiparticle of an antiparticle is the original particle;some neutral particles, such as the photon, are considered to be theirown antiparticles. In general, when a particle and its correspondingantiparticle meet, they can annihilate each other (vanish completely) ina burst of pure energy, in accord with the Einstein mass-energyequivalence formula, E = mc2. Antiparticles are routinely observedand used in many kinds of nuclear- and particle-physics experiments,so they are by no means hypothetical. In the ensuing discussions of thevarious classes of particles, it should be remembered that for everyparticle mentioned there is also an antiparticle.Leptons Leptons are weakly interacting particles, i.e., they experience theweak interaction but not the strong interaction; they are considered tobe pointlike, structureless entities. The most familiar lepton is theelectron, a very light particle (about 1/1800 the mass of a nucleon) withunit negative charge; it therefore also experiences the electromagneticinteraction. The muon is identical to the electron, as far as we know,except for being about 200 times heavier.* The tan particle, or taNon,is a recently discovered lepton that is also identical to the electronexcept for being about 3500 times heavier (making it almost twice as *The muon is still occasionally called a mu meson its original name which can beconfusing because the term 'meson' is now restricted to a very different kind ofparticle; thus a 'mu meson' is not a meson in the modern sense.

18 NUCLEAR PHYSICSheavy as a nucleon). The very existence of these 'heavy electrons'and 'very heavy electrons' is a major puzzle for physicists. Associated with each of the three charged leptons is a lepton calleda neutrino: thus there is an electron neutrino, a muon neutrino, and atauon neutrino. Neutrinos are electrically neutral and therefore do notexperience the electromagnetic interaction. They have generally beenassumed to have zero rest mass (see page 31 for an explanation of thisterm) and must therefore move at the speed of light, according torelativity, but the question of their mass is currently controversial. Ifthe electron neutrino, in particular, does have any mass, it is very slightindeed. The possible existence of such a mass, however, has greatcosmological significance: because there are so many neutrinos in theuniverse, left over from the big bang, their combined mass might exerta gravitational effect great enough to slow down and perhaps halt thepresent outward expansion of the universe. Neutrinos and antineutrinos are commonly produced in the radioac-tive process called beta decay (a weak-interaction process). Here aneutron in a nucleus emits an electron (often called a beta particle) andan antineutrino, becoming a proton in the process. Similarly, a protonin a nucleus may beta-decay to emit a positron and a neutrino,becoming a neutron in the process. Neutrinos and antineutrinos thusplay an important role in nuclear physics. Unfortunately, they areextremely difficult to detect, because in addition to being neutral, theyhave the capability of passing through immense distances of solidmatter without being stopped. With extremely large detectors andmuch patience, however, it is possible to observe small numbers ofthem. We have now seen that there are three pairs, or families, of chargedand neutral weakly interacting leptons, for a total of six; there aretherefore also six antileptons. Let us next look at the quarks, of whichthere are also three pairs-but there the similarity ends.Quarks Quarks are particles that interact both strongly and weakly. Theywere postulated theoretically in 1964 in an effort to unscramble theprofusion of known particles, but experimental confirmation of theirexistence was relatively slow in coming. This difficulty was due to thequarks' most striking single characteristic: they apparently cannot beproduced as free particles under any ordinary conditions. They seeminstead always to exist as bound combinations of three quarks, threeantiquarks, or a quark-antiquark pair. Thus, although they are believed

INTRODUCTION TO NUCLEAR PHYSICS 19to be truly elementary particles, they can be studied-so far-onlywithin the confines of composite particles (which are themselves ofteninside a nucleus). This apparent inability of quarks, under ordinaryconditions, to escape from their bound state is called quark confine-ment. There are six basic kinds of quarks, classified in three pairs, orfamilies; their names are up and down, strange and charm, and top andbottom. Only the top quark has not yet been shown to exist, butpreliminary evidence for it was reported in the summer of 1984. The sixvarieties named above are called the quark flavors, and each flavor isbelieved-to exist in any of three possible states called colors. (None ofthese names have any connection with their usual meanings in every-day life; they are all fanciful and arbitrary.) Flavor is a property similarto that which distinguishes the three families of leptons (electron,muon, and tauon), whereas color is a property more analogous toelectric charge. Another odd property of quarks is that they have fractional electriccharge; unlike all other charged particles, which have an integral valueof charge, quarks have a charge of either -1/3 or + 2/3. Because freequarks have never been observed, these fractional charges have neverbeen observed either-only inferred. They are consistent, however,with everything we know about quarks and the composite particlesthey constitute. These relatively large composite particles are thehadrons, all of which experience the strong interaction as well as theweak interaction. Although all quarks are charged, not all hadrons arecharged; some are neutral, owing to cancellation of quark charges. There are two distinctly different classes of hadrons: baryons andmesons. Baryons which represent by far the largest single category ofsubnuclear particles-consist of three quarks (antibaryons consist ofthree antiquarks) bound together inside what is referred to as a bag.This is just a simple model (not a real explanation) to account for thenot yet understood phenomenon of quark confinement: the quarks areassumed to be 'trapped' in the bag and cannot get out. Now, finally, we can say what nucleons really are: they are baryons,and they consist of up (u) and down (d) quarks. Protons have the quarkstructure bud, and neutrons have the quark structure add. A largerclass of baryons is that of the hyperons, unstable particles whosedistinguishing characteristic is strangeness, i.e., they all contain atleast one strange (s) quark. In addition, there are dozens of baryonresonances, which are massive, extremely unstable baryons withlifetimes so short (about 10-23 second) that they are not considered tobe true particles.

20 NUCLEAR PHYSICS The other class of hadrons is the mesons, of which there are alsomany kinds. These are unstable particles consisting of a quark-antiquark pair, to which the bag model can also be applied. Like thebaryons, all mesons experience the strong and weak interactions, andthe charged ones also experience the electromagnetic interaction. Themost commonly encountered mesons are pi mesons (pions) and Kmesons (knons); the latter are strange (in the quark sense) particles. All hadrons are subject to the strong force. But the strong force, asit turns out, is merely a vestige of the much stronger force that governsthe interactions among the quarks themselves: the colorforce. The twoforces are actually the same force being manifested in different ways,at different levels of strength. These two manifestations of the force that holds nuclei together areof great importance, because they underlie two distinctly differentlevels of understanding of nuclear phenomena, beyond the simple viewthat encompasses only nucleons as constituents of the nucleus. Thestrong force is related to the presence of large numbers of mesons(especially pions) in the nucleus, and many concepts of nuclear physicscannot be understood unless the nucleus is viewed as consisting ofbaryons and mesons. The color force, on the other hand, is related tothe presence of particles called gluons inside the baryons and mesonsthemselves; this represents a different and much deeper view ofnuclear phenomena-one that is not nearly so well understood, fromeither theoretical arguments or experimental evidence. Gluons belongto the third class of elementary particles, the elementary vectorbosons, which we will examine shortly, after a brief introduction to theconcept of spin. In addition to their mass and charge, all subatomic particles (includ-ing nuclei themselves) possess an intrinsic quality called spin, whichcan be viewed naively in terms of an object spinning about an axis. Thevalues of spin that particles can have are quantized: that is, they arerestricted to integral values (0, 1, 2, . . .) or half-integral values (1/2, 3/2,5/2, . . .) of a basic quantum-mechanical unit of measure. All particlesthat have integral values of spin are called bosons, and all particles thathave half-integral values arefermions. Thus, all particles, regardless ofwhat else they may be called, are also either bosons or fermions.Following the sequence of particles that we have discussed thus far,the classification is as follows: all leptons are fermions; all quarks arefermions; hadrons are divided all baryons are fermions, but allmesons are bosons. In broad terms, fermions are the building-blockparticles that comprise nuclei and atoms, and bosons are the particlesthat mediate the fundamental interactions.

INTRODUCTION TO NUCLEAR PHYSICS 21 The significance of the fermion-boson classification lies in a quan-tum-mechanical law called the Pauli exclusion principle, which isobeyed by fermions but not by bosons. The exclusion principle statesthat in any system of particles, such as a nucleus, no two fermions areallowed to coexist in the identical quantum state (i.e., they cannot haveidentical values of every physical property). This means that all theprotons and all the neutrons in a nucleus must be in different quantumstates, which places restrictions on the kinds of motions that they areable to experience. No such restrictions apply to mesons, however,because they are bosons. This situation has profound consequences inthe study of nuclear physics. Most of the bosons to be discussed in the next section are elementaryparticles unlike mesons and are called vector bosons (because theyhave spin 11.Elementary Vector Bosons Earlier it was mentioned that the fundamental interactions aremediated by the exchange of certain particles between the interactingparticles. These exchange particles are the elementary vector bosons(and some mesons, as mentioned below), whose existence is predictedby the quantum field theories of the respective interactions. Forexample, the theory of the electromagnetic interaction, called quantumelectrodynamics (QED), predicts the photon to be the carrier of theelectromagnetic force. A photon acting as an exchange particle is anexample of a virtual particle, a general term used for particles whoseephemeral existence serves no purpose other than to mediate a forcebetween two material particles: in a sense, the virtual particles movingfrom one material particle to the other are the force between them (seeFigure 1.21. The virtual particle appears spontaneously near one of the particlesand disappears near the other particle. This is a purely quantum-mechanical effect allowed by a fundamental law of nature called theHeisenberg uncertainty principle. * According to this principle, avirtual particle is allowed to exist for a time that is inversely propor-tional to its mass as a material particle. (Under certain conditions, a *Strictly speaking, the Heisenberg uncertainty principle refers to the impossibility ofmeasuring simultaneously and with arbitrarily great precision physical quantities such asthe position and momentum of a particle, but the structure of quantum mechanics leadsto an analogous statement for energy and time.

Krane Introductory Nuclear Physics Pdf

22 NUCLEAR PHYSICS-~ ~ ,->~__-_-, l _~~ ~ _i: ~,'I'-i/FIGURE 1.2 The way in which force is transmitted from one particle to another can bevisualized (crudely) through the example of two roller skaters playing different games ofcatch as they pass each other. Throwing and catching a ball tends to push the skatersapart, but using a boomerang tends to push them together. (After D. Wilkinson, in TheNature of Matter, J. H. Mulvey, ea., Oxford University Press, Oxford, 1981.)

INTROD UCTION TO NUCLEAR PHYSICS 23virtual particle can become a material particle.) The allowed lifetime ofa virtual particle determines the maximum distance that it can traveland, therefore, the maximum range of the force that it mediates.Hence, the greater the mass of the material particle, the shorter thedistance it can travel as a virtual particle, and vice versa. Photons havezero mass, so the range of the electromagnetic force is infinite. By contrast with QED, the theory of the weak interaction (theelectroweak theory, actually) predicts the existence of three differentcarriers of the weak force, all of them extremely massive: about 90 to100 times the mass of a nucleon. These elementary particles are theW+, W-, and Z° bosons, collectively called the intermediate vectorbosons. Their discovery in 1983 dramatically confirmed the validity ofthe electroweak theory. Because of their great mass, these particles arerestricted by the uncertainty principle to lifetimes so short that theycan travel only about 10-~8 m before disappearing. This explains theextremely short range of the weak force. The strong force exists in two guises, as we have seen. Here thefundamental quantum field theory, called quantum chromodynamics(QCD), predicts the existence of no less than eight vector bosons thegluons to mediate the color force between quarks. Experimentalevidence for the gluons has been obtained. Gluons are massless, likephotons, but because of quark confinement, the range of the color forcedoes not extend beyond the confines of the hadrons (the quark bags). In its second, vestigial guise, the strong force is experienced byhadrons (baryons and mesons) and is mediated by mesons by pions atthe largest distances. Here we have a type of particle, the meson(which is a boson, but not an elementary one and not necessarily of thevector kind), that can act as its own exchange particle, i.e., materialmesons can interact through the exchange of virtual mesons. (This isnot a unique case, however, because the gluons, which themselvespossess an intrinsic color, are also self-interacting particles.) The rangeof the strong force very short, yet much longer than that of the weakforce is explained by the mesons' moderate masses, which aretypically less than that of a nucleon and very much less than that of anintermediate vector boson. What is most significant for nuclear physicsis that the nucleons interact via the exchange of virtual mesons, so thenucleus is believed always to contain swarms of these particles amongits nucleons. Thus the traditional picture of the nucleus as consisting simply ofprotons and neutrons has given way to a more complex picture inwhich the strong nucleon-nucleon interactions must be viewed in termsof meson-exchange effects. And even this view is just an approach to

24 NUCLEAR PHYSICSthe deeper understanding of nuclear structure and dynamics that cancome about only through detailed considerations of the quark-gluonnature of the nucleons and mesons themselves. Ultimately, the nucleusmust be explainable in terms of a very complex many-body system ofinteracting quarks and gluons. The experimental and theoretical chal-lenges posed by this goal are enormous, but so are the potentialrewards in terms of our understanding of the nature of nuclear matter.CONSERVATION LAWS AND SYMMETRIES The total amounts of certain quantities in the universe, such aselectric charge, appear to be immutable. Physicists say that thesequantities are conserved, and they express this idea in the form of aconservation law. The law of the conservation of charge, for example,states that the total charge of the universe is a constant-or, simply,'charge is conserved.' This means that no process occurring in anyisolated system can cause a net change in its charge. Individual chargesmay be created or destroyed, but the algebraic sum of all such changesin charge must be zero, thus 'conserving the original charge, whateverit might have been. Another important quantity that is conserved is mass-energy. BeforeEinstein, it was thought that mass and energy were always conservedseparately, but we now know that this is not strictly true: mass andenergy are interconvertible, so it is their sum that is conserved. Mass,in the form of elementary or composite particles, can be created out ofpure energy, or it can be destroyed (annihilated) to yield pure energy;both of these processes are commonplace in nuclear end 'particlephysics. This example illustrates the important point that although anyconserved quantity may change its form, the conservation law is notinvalidated. Energy itself, for instance, can exist in many differentforms-chemical, electrical, mechanical, and nuclear, for example allof which are interconvertible in one way or another without any netgain or loss, provided one accounts for any mass-energy conversioneffects. Such effects are significant only in subatomic processes andare, in fact, the basis of nuclear energy. Two other conserved quantities, linear momentum and angularmomentum, are related to the linear and rotational motions, respec-tively, of any object. Conservation laws for these quantities and theothers mentioned above apply to all processes, at every level of thestructure of matter. However, there are also conservation laws thathave meaning only at the subatomic level of nuclei and particles. Onesuch law is the conservation of baryon number, which states that

INTRODUCTION TO NUCLEAR PHYSICS 25baryons can be created or destroyed only as baryon-antibaryon pairs.All baryons have baryon number + 1, and all antibaryons have baryonnumber -1; these numbers cancel each other in the same way thatopposite electric charges cancel. Thus, a given allowed process maycreate or destroy a number of baryons, but it must also create ordestroy the same number of antibaryons, thereby conserving baryonnumber. Processes that violate this law are assumed to be forbidden-none has ever been observed to occur. There is no conservation law formeson number, so mesons, as well as other bosons, can proliferatewithout such restrictions. A law of nature that predicts which processes are allowed and whichare forbidden with virtual certainty and great generality, and withouthaving to take into account the detailed mechanism by which theprocesses might occur represents a tool of immeasurable value in thephysicist's effort to understand the subtleties and complexities of theuniverse. Conservation laws are therefore often regarded as the mostfundamental of the laws of nature. Like all such laws, however, theyare only as good as the experimental evidence that supports them.Even a single proved example of a violation of a conservation law isenough to invalidate the law for that class of processes, at least andto undermine its theoretical foundation. We will see that violations ofcertain conservation laws do occur, but first let us examine anotherimportant aspect of conservation laws: their connections with thesymmetries of nature. Symmetry of physical form is so common in everything we seearound us and in our own bodies- that we take it for granted as abasic (though clearly not universal) feature of the natural world. Anexample of some geometrical symmetries is shown in Figure 1.3.Underlying these obvious manifestations of symmetry, however, aremuch deeper symmetries. For example, the fundamental symmetry ofspace and time with respect to the linear motions and rotations ofobjects leads directly to the laws of the conservation of linear andangular momentum. Similarly, the mathematical foundations of thequantum field theories imply certain symmetries of nature that aremanifest as various conservation laws in the subatomic domain. One such symmetry, called parity, has to do with the way in whichphysical laws should behave if every particle in the system in questionwere converted to.its mirror image in all three spatial senses (i.e., ifright were exchanged for left, front for back, and up for down).Conservation of parity would require that any kind of experimentconducted on any kind of system should produce identical results whenperformed on the kind of mirror-image system described above. For

26 ~ ~3~ -aFIGURE 1.3 a, ~ woodcut by M. C. Escher, provides an example of complexgeomethca1 symmetries, which underDe many aspects of nuclear structure. Equallyimpotent are dynamical symmetries Lund in the physical laws governing aN naturalphenomena. (By permission of the Escher Foundation, Hags Cemeentemuseum Theague. Reproduction rights arranged courtesy of the Vows OaDer~s, New York SanFranc~co, and Laguna Beach.)

INTRODUCTION TO NUCLEAR PHYSICS 27many years, it was believed that parity was an exact (universal)symmetry of nature. In 1956, however, it was discovered by nuclearand particle physicists that this is not so; parity is not conserved inweak interactions, such as beta decay. However, it is conserved, as faras we know, in all the other fundamental interactions and thusrepresents a simplifying principle of great value in constructing math-ematical theories of nature. A similar, albeit isolated, example of symmetry violation has beenfound for the equally fundamental and useful principle called time-reversal invariance, which is analogous to parity except that it entailsa mirror imaging with respect to the direction of time rather than to theorientation of particles in space. This symmetry has been found to beviolated in the decays of the neutral kaon. No other instances of thebreakdown of time-reversal invariance are known yet but physi-cists are searching carefully for other cases in the hope of gaining abetter insight into the underlying reason for this astonishing flaw in anotherwise perfect symmetry of nature. The implications of such discoveries extend far beyond nuclear orparticle physics; they are connected to basic questions of cosmology,such as the ways in which the primordial symmetry that is believed tohave existed among the fundamental interactions at the instant of thebig bang was then 'broken' to yield the dramatically different inter-actions as we know them now. The efforts of theoretical physicists toconstruct Grand Unified Theories of the fundamental interactions, inwhich these interactions are seen merely as different manifestations ofa single unifying force of nature, depend strongly on experimentalobservations pertaining to symmetries, conservation laws, and theirviolations. A most important observation in this regard would be any evidenceof a violation of the conservation of baryon number, which may not bea universal law after all. Certain of the proposed Grand UnifiedTheories predict, in fact, that such a violation should occur, in the formof spontaneous proton decay not in the sense of a radioactive betadecay, in which a proton would be converted to a neutron (thusconserving baryon number) but rather as an outright disappearance ofa baryon (the proton) as such. Extensive searches have been mountedto find evidence for proton decay, so far without success. Also of great importance would be any violation of the conservationof lepton number. This law, which is also obeyed in all currently knowncases, is analogous to the conservation of baryon number, but with anadded twist: lepton number ~ + 1 for leptons, -1 for antileptons)appears to be conserved not only for leptons as a class but also for each

28 NUCLEAR PHYSICSof the three families of leptons individually (the electron, muon, andtauon, with their respective neutrinos). Any violation of lepton-numberconservation would mean that neutrinos are not, in fact, massless andthat they can oscillate (change from one family to another) during theirflight through space. Exactly these properties are also predicted bycertain of the proposed Grand Unified Theories, and this provides theimpetus for searching for them in various types of nuclear processes.Such searches for violations of conservation laws represent an impor-tant current frontier of nuclear physics as well as of particle physics.ACCELERATORS AND DETECTORS The principal research tools used in nuclear physics are accelera-tors- complex machines that act as powerful microscopes with whichto probe the structure of nuclear matter. Equally indispensable are thesophisticated detectors that record and measure the many kinds ofparticles and the gamma rays emerging from the nuclear collisionsproduced by the accelerator beams.' There are several different kinds of accelerators, differing mainly inthe ways in which they provide energy to the particles, in the energyranges that they can span, and in the trajectories followed by theaccelerated particles. The most common kinds are Van de Graaffelectrostatic accelerators, linear accelerators, cyclotrons, and syn-chrotrons; an example of a modern cyclotron is shown in Figure 1.4.Most of the details of these machines need not concern us here, but asurvey of some basic ideas is necessary for an appreciation of hownuclear physics research is actually done. Additional information onaccelerators in general and on several important accelerators of thefuture can be found in Chapter 10, and a survey of the major operatingaccelerators in the United States is given in Appendix A.Projectiles and Targets The basic principle of all accelerators is the same: a beam ofelectrically charged projectile particles is given a number of pulses ofenergy in the form of an electric or electromagnetic field to boostthe particles' velocity (and hence kinetic energy) to some desired valuebefore they collide with a specified target. Typically, the projectiles areelectrons, protons, or nuclei. The latter are often called ions, becausethey are generally not bare nuclei, i.e., they still retain one or more ofthe orbital electrons from the atoms from which they came. Nuclei ofthe two lightest elements, hydrogen and helium, are called the light

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INTRODUCTION TO NUCLEAR PHYSICS 29FIGURE 1.4 Top view of the main cyclotron of the Indiana University CyclotronFacility, a modern accelerator used for basic nuclear-physics research. The fieldproduced by the four large magnets (note the physicist standing between two of them)confines the projectile particles light ions up to mass number 7 to a series of roughlycircular orbits of ever-increasing size as they are accelerated to energies in the range of40 to 210 MeV. After about 300 orbits, the beam is extracted and directed at targets innearby experimental areas. (Courtesy of the Indiana University Cyclotron Facility.)

30 NUCLEAR PHYSICSions; they include the often-used alpha particle, which is just thenuclide helium-4 (Z = 2, N = 21. Nuclei from those of lithium (A = 6or 7) to those with a mass number of about 40 can be called mediumions, and those with a mass number from about 40 on up through therest of the periodic table are called heavy ions. (This classification isuseful but necessarily somewhat arbitrary; the definition of heavy ion,for example, is sometimes extended all the way down to lithium.) Accelerators can also produce beams of exotic or unstable chargedprojectiles such as muons, mesons, antiprotons, and radioactivenuclides. These are made in reactions occurring at the target of aprimary beam and are then focused into a secondary beam. Evenneutral particles, such as neutrons and neutrinos, can be produced andused as secondary beams. The target struck by the accelerated projectile in a typical nuclear-physics experiment is a small piece of some solid chemical element ofparticular interest, although liquid and gaseous targets can also beused. The objective may be to use the projectiles to raise nuclei in thetarget substance from their lowest-energy ground state to higher-energy excited states in order to gain insight into the structures anddynamics of intact nuclei; in this way one studies nuclear spectros-copy. Alternatively, the objective may be to bombard the target nucleiin such a way that they undergo a nuclear reaction of some kind,possibly disintegrating in the process. The above descriptions pertain to the traditional fixed-target ma-chines (a stationary target being bombarded by a projectile beam), butaccelerators can also be constructed as colliding-beam machines, orcolliders. Here two beams collide violently with each other, nearlyhead-on, in a reaction zone where the beams intersect. Colliders havebeen pioneered by elementary-particle physicists because of the hugeamounts of energy that can be deposited in the collision zone whenboth beams have been accelerated to high velocities. Their use isbecoming increasingly important to nuclear physicists for the samereason, as described in Chapter 7.Energies The kinetic energies to which particles or nuclei are accelerated areexpressed in terms of large multiples of a unit called the electron volt(eV), which is the amount of energy acquired by a single electron (orany other particle with unit electric charge, such as a proton) when itis accelerated through a potential difference of 1 volt (V) as in a 1-V

INTRODUCTION TO NUCLEAR PHYSICS 31battery. The characteristic particle beam energies in modern nuclear-physics accelerators are of the order of mega-electron volts (1 MeV =106 eV) and giga-electron volts (1 GeV = 109 eV). When dealing withaccelerated nuclei, which contain more than one nucleon, it is custom-ary to give the energy per nucleon rather than the total energy of thenucleus. For convenience, not only the energies of particles but also theirmasses are customarily given in terms of electron volts. Any mass canbe expressed in terms of an equivalent energy, in accord with E = mc2.Thus the mass of an electron is 0.511 MeV, and the mass of a protonis 938 MeV. These are the rest masses of these particles, i.e., themasses that they have when they are not moving with respect to someframe of reference (such as the laboratory). When they are moving,however, their kinetic energy is equivalent to additional mass. Thiseffect becomes significant only when their velocity is very close to thespeed of light; then their kinetic energy becomes comparable to orgreater than their rest mass, and they are said to be relativistic particles(or nuclei), because the dynamics of their reactions cannot be accu-rately described without invoking relativity theory. It is convenient to classify nuclear processes in terms of differentenergy regimes of the projectiles, although any such classification, likethat of the projectile masses, is somewhat arbitrary and not likely tofind universal acceptance. Bombarding energies of less than about 10MeV per nucleon, for example, produce a rich variety of low-energyphenomena. It is in this regime (at about 5 MeV per nucleon) that theeffects due to the Coulomb barrier are particularly important; theCoulomb barrier is a manifestation of the electrostatic repulsive forcebetween the positively charged target nucleus and any positivelycharged projectile. For a collision involving the effects of the strongforce to occur, the projectile must be energetic enough to overcome theCoulomb barrier and approach the target closely. Between about 10 and 100 MeV per nucleon is the medium-energyregime, where many studies of nuclear spectroscopy and nuclearreactions are carried out; these are the energies characteristic of themotions of nucleons within a nucleus. In the high-energy regime,between about 100 MeV per nucleon and 1 GeV per nucleon, hightemperatures are produced in the interacting nuclei; also, some of thecollision energy is converted to mass, usually in the form of createdpions, which have a rest mass of 140 MeV. Above about l GeV pernucleon is the relativistic regime, where extreme conditions, such asthe formation of exotic states of nuclear matter, are explored. [It isworth noting here that for electrons the transition to relativistic

32 NUCLEAR PHYSICSbehavior occurs at much lower energies (about 0.5 MeV), owing to theelectron's small rest mass.]Nuclear Interactions The principal kinds of nuclear interactions in collisions are scatter-ing, in which the projectile and target nuclei are unchanged except fortheir energy states; transfer, in which nucleons pass from one nucleusto the other; fusion, in which the two nuclei coalesce to form acompound nucleus; spallation, in which nucleons or nucleon clustersare knocked out of the target nucleus; and disintegration, in which oneor both nuclei are essentially completely torn apart. Not all interactions that occur in collisions are equally probable, soit is important to know what does occur to an appreciable extent andwhat does not-and why. The probability of occurrence of a giveninteraction is expressed by a quantity called its cross section, whichcan be measured experimentally and compared with theoretical pre-dictions. Another quantity whose experimental measurement is important isthe half-life of a radioactive species the time it takes for half of all thenuclei of this nuclide in a sample to decay to some other form or state.Normally, this decay is by the emission of alpha or beta particles orgamma rays; less commonly, it is by spontaneousission, in which anucleus simply splits in two, with the emission of one or moreneutrons. After half of the nuclei have decayed, it will take the samelength of time for half of the remaining nuclei to decay, and so on. Thecharacteristic half-lives of radioactive nuclides vary over an enormousrange of values: from a small fraction of a second to billions of years.Particle Detectors Accelerators would be useless if there were no way to record andmeasure the particles and gamma rays produced in nuclear interac-tions. The detectors that have been invented for this purpose representa dazzling array of ingenious devices, many of which have pushed hightechnology to new limits. Some are designed to detect only a specificparticle whose presence may constitute a signature of a particular kindof event in the experiment in question. They may be designed to detectthis particle only within a certain limited range of angles of emissionwith respect to the beam direction or over all possible angles of. .emission.Other detectors are designed to detect as many kinds of particles as

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INTRODUCTION TO NUCLEAR PHYSICS 33possible, simultaneously again either for limited angles or for allangles. This kind of detector is necessarily complex, owing to the manykinds of particles that must be observed and to the number of particlesactually produced. This latter number, called the multiplicity, is assmall as one or two for many kinds of events, but in the catastrophiccollisions of relativistic heavy ions, it may be several hundred. Yetanother consideration in the design of detectors is whether they are tobe used at a fixed-target accelerator or a collider; the requirements areoften very different. Among the simplest detectors are those in which a visible track is leftin some medium by the passage of a particle. Examples of such visualdetectors are the streamer chamber (in which the medium is a gas), thebubble chamber (liquid), and photographic emulsions (solid). Mostdetectors, however, rely on indirect means for recording the particles,whose properties must be inferred from the data. The operatingprinciples of the great majority of such detectors are based on theinteractions of charged particles with externally applied magnetic fieldsor on the ionization phenomena resulting from their interactions withthe materials in the detectors themselves. The largest of these detectorsystems may consist of thousands of individual modules and are usedin the study of very complex events. Sophisticated, dedicated comput-ers are required to store and analyze the torrents of data from suchinstruments. At the largest accelerators, the efforts of many physicists, engineers,and technicians may be required for many months to plan and executeone major experiment, and months more of intensive effort may berequired to process and analyze the data and interpret their meaning.This is the 'big-science' approach to nuclear-physics research. Ahighly noteworthy feature of nuclear physics, however, is that muchresearch of outstanding value is still done by individuals or smallgroups working with more modest but nonetheless state-of-the-artfacilities in many universities and laboratories throughout the world. Itis the cumulative effort of all these scientists and their colleaguesworking at the accelerators together with that of the nuclear theo-rists that advances our knowledge of nuclear physics.

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Introductory Nuclear Physics Notes Pdf Class 12