Experimental Nuclear Physics, Volume 1: Physics of the Atomic Nucleus [1]

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EXPERIMENTAL NUCLEAR PHYSICS PHYSICS O F ATO M IC NUCLEUS

K. H. MyxMH

3 KCnEPMMEHTAnbHASJ SlflEPHAfl 100 MeV). In partic­ ular, an analysis of the angular distribution of scattered neutrons in (n-p)-interacticn showed that the number of protons scattered in the forward direction is too large to be explained by the lavs of conser­ vation of energy and momentum without any additional assumptions concerning the interaction mechanism. However, the experimental results can be explained by assuming that a neutron and a proton can exchange charge during interaction. In this case, a fast neutron ‘‘acquires" the charge from a proton during interaction and continues to move forward (after undergoing a slight deDeclion during interac­ tion) as a prolcn. This is the charge-exchange interaction which takes place together with '.he usual nuclear interaction. It was naturally assumed that the charge exchange involves an exchange of certain particles, viz. nuclear field quanta, from one nu­ cleon to the other. Such a hypothesis was put forth by the Soviet physicist Tamm in 1934 to explain the nature of nuclear forces. However, Tamm also showed that the light particles kiown at that time, viz. electrons and neutrinos, carnot serve as quanta of nuclear force field. Tamm’s idea was developed in 1935 by the Japanese physicist Yukawa who showed that the short-range character of nuclear forces and some other properties can be explained by assuming that during nucleons exchange neutral or charged particles of mass (200-300)171,. In order that these particles could serve as nuclear quanta, or carriers of nuclear forces, they must have auclear activity, i.e. they must be generated copiously during nudeon-nucleon collisions and strongly absorbed by nuclei.

24

Introduction

Muon, a particle with a mass of 207m, and a lifetime of about 2 X 10'® s was discovered in 1938 during studies of the composition of cosmic rays. An investigation of the properties of the muon revealed th a t it is a nuclear-passive particle and hence cannot be a nuclear quantum. The nuclear passivity and the short lifetime of the muon led to the prediction of heavier particles, viz. pions, in the cosmic radiation. These particles were indeed discovered in 1947 by Powell. An analysis of their properties showed th at they exist in the form of j i +-, ji “- and n°-mesons, have a mass equal to 273m „ zero spin, and a lifetime of about 10'® s.2 These particles were found to interact quite strongly with m atter. Subsequently, it became possible to produce them in large amounts in accelerators and their interaction with nuclei and nucleons was studied at different energies. The results of these investigations indicate that n-mesons are really the quanta of nuclear forces between nucleons. The 1950s were marked by the most significant achievements in the field of detection of particles, and this led to several important discoveries. W ith the help of emulsion cloud and bubble chambers which were invented in this period, new unstable particles were discovered in 1951-54 (first in the cosmic rays and then in accelera­ tors). These include /f-mesons with a mass of 966m„ and hyperons whoso mass is higher than that of a proton. Large-sized liquid scintillators were able to register tho interaction of a neutrino with a proton, thus providing experimental confirmation for the existence of this particle (1953-54). Finally, antiproton (1955) and antineutron (1956) were discovered with the help of Cherenkov and scintillation counters. At the same time, studies were undertaken to determine the structure of nucleons (1955), violation of parity in weak inter­ actions was observed (1957), and the Mossbauer effect was discovered (1958). The most interesting results obtained in the 1960s include the discovery ol resonances, i.e. particles th a t are unstable with regard to strong interaction, the discovery of symmetry in the properties of strongly interacting particles and resonances (19G1) culminating in the prediction of all the properties of Q‘-hyperon which was discov­ ered soon afterwards (1964), the proof for the existence of the muon neutrino v„ which differs from the electron neutrino v , (1962), the discovery of the violation of combined parity in the decay of neutral A'-mesons (1904), tho creation of the quark model of hadrons (1964), the discovery of internucleon potential which is responsible for the violation of parity invarinnee (1964), the synthesis of transuranic elements with Z —104 (1964) and Z = 105 (1968), the creation of a unified theory of weak and electromagnetic interactions (1967), 1 The lifetime of n®-mcsona is about 10*1* s and their mass is approximately equal to 2Mmt .

and the discovery of antihelium-3 (1970). Among the most impor­ tant achievements in the field of experimental techniques during this decsde was the invention of spark and streamer chambers. Among the notable achievements during the 1970s a n the discov­ ery of the last remaining (as it was assumed at that time) metastable antiparti tie iS*-hyperon (1971), investigation of inelastic scaltering of ultrarelativistic electrons by protons which led to the formula­ tion of the parton model of the nucleus, the proof of the existence of neutral currents in weak interactions (1973), the discovery of antitritivm (1973), the discovery of the 106th (1974) and 107th (1976) elements, the discovery of y/t^-particle (19741 and other v-lepton (1977) and the discovery of gluons (1979). The most important theoretical results of the 1970s are the develop­ ment of the unified theory of weak anc electromagnetic interactions, the creation of the four-querk model, and a successful development of quantum chromodynarnica. It is shown in the unified theory of weak and electromagnetic inter­ actions that the role of quanta is shared by four vector bosons, viz. the massless photon, which is the electromagnetic-interaction quan­ tum, heavy charged lV--bosons which are responsible for weak charged currents, and the heavy neutral Z’-boson which causes weak neutral currents. To discover H7*- an! Z*-bosons, the construction of a special accelerator with colliding beams of protons and antiprotors (pp-collider) for large energy was started at CERN. Strong interaction between quarks is described in quantum chromodynamics. Strong-interaction quanta are called gluons. This interaction is sometimes tanned truly strong interaction to distin­ guish it from the strong interaction between nucleons (and other hadrons), in which pions are involved. In this scheme, strong inter­ action is assumed to be a secondary manifestation of truly strong interaction. The 1980s were merked by a splendid confirmation of th apredictions of the theory of electroweak interactions: in 1982-83 at CERN, the a Attempts have been made in recent years to create the so-called grand imificetion" theory, combining strong, electromagnetic and week interactions into a single theory.

Part One Properties of Nuclei and Radioactive Radiation

All atomic nuclei can be divided into two classes: stable and radioactive. Stable nuclei remain unchanged over infinitely long periods of time, while radioactive nuclei undergo spontaneous transforma­ tions. The basic characteristics of a stable nucleus are its mass number A, electric charge Z,mass M (and binding energy AIP), radius R , spin I, magnetic moment ji, quadrupole electric moment Q, isotopic spin T and parity P of the wave-function. Radioactive nuclei are also characterized by the type of radioac­ tive transformation (alpha or beta decay, spontaneous fission, etc.), half-life energy of emitted particles, etc. The nucleus of an atom can be in various energy states. The state with the lowest energy is called the groundstate while all the remain­ ing states are called excited states. The ground state of a stable nucleus is stationary. The excited states of any nucleus (including a stable nucleus) are nonstationary (they undergo gamma transitions, etc.). The characteristics mentioned above can be ascribed to the ground state as well as to any excited energy state of a nucleus. Generally speaking, their values are different for different states (except A and Z which have the same values for all the energy states of a given nucleus). If the characteristics of a nucleus are given without any mention of the state to which they correspond, the ground state is usually meant. In the ideal case, the complete information about a nucleus must describe the structure and the characteristics of all its possible excited states (levels), the methods and probabilities of nuclear tran­ sition from one state to another, the probabilities of radioactive decay of tho nucleus and the properties of the emitted particles, the cross sections and the nature of interactions of the nucleus with other nuclei and elementary particles, etc. Wo shall consider in Chap. 1 only the ground states of nuclei. Chapters 2 and 3 describe the structure and properties of excited states. Chapter 4 and Part Two aro devoted to tho interaction of nuclei with elementary particles and other nuclei.

Chapter I Properties of Stable Nuclei and Nuclear Forces 1.1. Mass Number A and Electric Charge Atomic Nucleus

Z of the

The mass number A of a nucleus is determined by the number of nucleons (protons and neutrons) in it The total number of nucleons in any ordinary nuclear reaction (not involving the creation of antiparlides) remains unchanged (the lav of conservation of the num­ ber of nucleons). Hence the total mass number in such nuclear pro­ cesses is conserved (see Sec. 5.2 for details). A generalization of this statement to all particles and antiparlicles leads to the lair ol conservation of the baryoa charge (see Vol. II). When expressed in atomic mass units (anu), the mass number gives an approximate value (to within 0.1-1 to) if the mass of an atomic nucleus (see Sec. 1.2). The charge Z of in atomic nucleus is defined by the number of protons in it (and lienee by the number of electrons in the atomic shells). This number coincides with the atomic number of the ele­ ment in the Periodic Table. The charge determines the chemical properties of all the isotopes of a given element. The most tccurate measurements of the nuclear charge were made in 1913 by Moseley who established a simple relation between the frequency v of the characteristic X-ray radiation and the charge Z: y"v—aZ—6. Moseley found that the constants a and b do not depend on the element for a given series of radiation. This permitted him to arrange first the elements from t)Ca to >0Zn according to their atomic num­ bers, and then other elements as wbII. Besides, Moseley's method helped in determining the position of certain elements, which had not been disovered by then, in the Periodic Table (lsTc, „Pm, u At, n Fr)* and also confirmed the phenom­ enon of X-captur*. (Ota wen not discovered lor a long time since they only have T -'*’,? ?".•"***•. ifAt end ,,Fr could be discovered only as a result » • detailed Investigation of radioactive tamIUea. As regards ,,Tc and „Pm. they are never encountered In nature since that haU-lWes an leas than the age ol the Earth, and they cannot be formed by radioactive transformations of neighbouring nuclei lamong those found k naltn) since the letter are ruble The elements uTc and „Pm were obtained artlBcnlly In 1937-1MO

as

Pari O ne. P roperties o! Nuclei and Radioactive Radiation

The nuclear charge was directly determined in 1920 by Chadwick from experiments on scattering of a-particles by foils prepared from a metal w ith a given Z (these experiments w ill be described in Chap. 4). The electric charge occupies a special position among other charges (baryon, lepton, strange, etc.). As a m atter of fact, it sort of performs two functions: it is responsible for the strength of electromagnetic interaction (it should be recalled th a t the fine-structure constant a ~ e*lhc) and also participates in the conservation law. The elec­ tric charge is known to be conserved in all types of interactions (strong, electromagnetic, weak) considered in nuclear physics. The law of conservation of electric charge was verified experimen­ tally. The experiment involved an attem pt to register the electro­ magnetic radiation corresponding to a transition of the atomic electrons to the A'-shell in which a vacancy is due to tlw decay of an electron with a violation of the law of conservation of electric charge (for example, according to the scheme e-*- \ e + y). The experiment was conducted in a deep well (about 400 m) with a Nal crystal scintillator which, in the case of A-electron decay, must register an X-ray photon from iodine with energy 33.2 keV. The experiment yielded the following lower bound of the electron lifetime: t , > 5 X 10?1 years. This means th a t the strength of the hypothetic interaction in which the law of conservation of electric charge is violated is smaller than the strength of weak interaction at least by a factor of 1058. The law of conservation of electric charge can be used to find the charge of a nucleus from the charge balance in nuclear reactions or radioacti\e transformations. The electric sharge Z is an integral property of the nucleus and docs not give any information about the distribution of charge over the volume of the nucleus. This information can be obtained from experiments on the scattering of fast electrons by nuclei (see Sec. f.4.6). An idea about the shape of the nucleus can be had by considering another electric property of the nucleus, viz. the quadrupole electric moment (see Sec. 1.7). Since the nuclear charge Z is numerically equal to the number of protons in the nucleus and the mass number A is equal to the total number of nucleons (protons plus neutrons), the number N — A — Z defines the number of neutrons in the nucleus. Nuclei with the same mass number A arc called isobars, those with the same chargo Z are called isotopes, while nuclei containing the same number of neutrons N ~ A — Z arc called isotones. A specific nucleus (atom) with given A and Z is sometimes called a nuclide. We shall denote a nucleus containing A nucleons and Z protons by (A, Z), its mass b y .)/ (A, Z), and the mass of the atom corresponding to it by

CK 1. Piopartlee of Staple Nudal end Nuclow Fowl__________________ » Mki (A, Z). When the chemical symbol of an element has to be Indicated, we shall denote the nuclear and atomic masses by Af (*E) and M ,t (*E). For example, the masses of a nitrogen nucleus and atom will be denoted by M (*JN) and M ,t OJN) respectively.

1.2.

Nuclear and Nucleonic Mass

1.2.1. Mass and Energy. Units of Measurement (he of the most important characteristics of the atomic nucleus is Its mass M. In nuclear physics, the mass of a nucleus (and atom) is measured in atomic mass units. One atomic mass unit (amu) is or.e twelfth of the mass of a neutral “C atom.1 The value of the ato­ mic mass unit can bo easily expressed in grams. For this purpose, ve take the reciprocal of the Avogadro number [NsY1 amu = (1/12)(12/JVa) - 1/8.022 X 10“ - 1.66 X 10-« g. According to Einstein’s relation, each value of mass M in grains his a value of energy M