THE COMMONWEALTH AND INTERNATIONAL LIBRARY Joint Chairmen of the Honorary Editorial Advisory Board SIR ROBERT ROBINSON, O.M., F.R.S., London DEAN ATHELSTAN SPILHAUS, Minnesota Publisher ROBERT MAXWELL, M.c. Elementary Particles This book is sold subject to the condition that it shall not, by way of trade, be lent, re-sold, hired out, or otherwise disposed of with- out the publisher's consent, in any form of binding or cover other than that in which it is published. Elementary Particles by A. A. SOKOLOV Translated from the Russian by WILLIAM E. JONES United Kingdom Atomic Energy Authority Translation Edited by D. TER HAAR PERGAMON PRESS OXFORD · LONDON · EDINBURGH · PARIS · FRANKFURT THE MACMILLAN COMPANY NEW YORK PERGAMON PRESS LTD. Headington Hill Hall, Oxford 4 & 5 Fitzroy Square, London W.l PERGAMON PRESS (SCOTLAND) LTD. 2 & 3 Teviot Place, Edinburgh 1 THE MACMILLAN COMPANY 60 Fifth Avenue, New York 11, New York COLLIER-MACMILLAN CANADA, LTD. 132 Water Street, Gait, Ontario GAUTHIER-VILLARS ED. 55 Quai des Grands-Augustins, Paris 6 PERGAMON PRESS G.m.b.H. Kaiserstrasse 75, Frankfurt am Main Copyright © 1964 PERGAMON PRESS LTD. This translation has been made especially for inclusion in this Library from A. A. Sokolov's book entitled Elementarnye Chastitsy, published in Moscow, 1963, by Izdatel'stvo Moskovskogo Universiteta Library of Congress Catalog Card No. 64-20742 Set in 10 on 12pt. Times and Printed in Great Britain by THE WHITEFRIARS PRESS LTD., LONDON & TONBRIDGE 1 Introduction THE development of modern physics proceeds under the flag of atomic theory. It is well known that the smallest particle of a chemical element is called an atom, which, translated from the Greek means "indivisible". The most recent investigations have revealed the complexity of the atom, which consists of even smaller so-called elementary particles. Originally the term "elementary particle" (just as for the term "atom" at that time) included the concept of indivisibility. However, scientists now- adays have studied more closely the structure of the elementary particles and consequently this indivisibility must nowadays be accepted with a certain amount of arbitrariness. In studying the atom, the principal role is played by four elementary particles: the proton (p), neutron (n), electron (e) and the photon (y). According to the theory of Ivanenko and Heisen- berg, protons and neutrons comprise the nucleus, which represents the densest part of the atom (Fig. 1). Electrons rotate around the nucleus; they are retained in the atom as a result of the Coulomb attraction acting towards the nucleus (Rutherford's planetary model of the atom). Photons are formed in the atom as a result of transition of electrons from a higher energy level to a lower one. As a result of the reverse transition, absorption of photons by the atom occurs. 1 2 Elementary Particles We shall consider first of all these four elementary particles. Their principal characteristics are rest mass, charge and spin. The latter describes, as it were, the rotation of the particles, i.e., their internal properties. In atomic physics, the units chosen for rest mass and charge are the rest mass of the electron m = 0-9 x 10"27 g, and the 0 elementary charge e = 4-8 x 10~10 e.s.u. Spin is measured, as is 0 well known, in units of h. -n -Θ-^ I I I I 1 I Θ Electron Θ Proton -13 .. 10 cm O Neutron 10 cm r Photon FIG. 1. Planetary model of the atom. Then, for the electron ee = -eol se = i; for the proton mp = 1836 m0; ep = e0; Sp = i; for the neutron mn = 1838-6 m0; en = 0; s» = i. Since the electron is a charged particle, the presence of the spin (s) (i.e., the intrinsic angular momentum) leads to the pheno- menon of the magnetic moment of the electron, the component of which in the direction of the spin has a negative sign, since e = -e <0 e o eo , μ = - μο β 2m c 0 Introduction 3 where μ is the Bohr magneton and Planck's constant 0 h = 2nh = 6-62 x 10~27 erg sec The proton and the neutron also possess a magnetic moment, but more will be said of this below. We shall now say something about the photon. It was thought at one time that light is a train of electromagnetic waves and that electrons are corpuscles, i.e., particles. It was then discovered that light also possessed corpuscular properties (according to Einstein's photon theory, the energy of the light quantum of frequency v is ε = Av), which are manifested, for example, in the emission of photons, and that electrons possessed wave character (De Broglie waves, λ = h/m v), which 0 can be detected, in particular, by passing a beam of electrons with velocity v through a crystal (electron diffraction). Nowadays there is a well-developed branch of science, called electron optics, upon which are based the calculations for the construction of electron microscopes. Photons differ from electrons primarily in the absence of rest mass (m = 0) and in the value of the spin (the spin of the photon y is equal to unity). We shall dwell below on the prediction and discovery of new elementary particles. 2 Prediction of the Positron by Dirac and its Experimental Discovery IT IS well known that Dirac developed a wave equation which takes into account not only relativistic but also spin effects. The discovery made by Dirac is of the same extreme importance for science as the discovery of the three basic laws of mechanics and the law of universal gravitation by Newton, Maxwell's basic equations for the electromagnetic field or Einstein's Theory of Relativity. Bohr's semi-classical theory and even Schrödinger's wave equation were only preliminary theories which can be considered as some intermediate stage en route to the theory established by Dirac. Dirac, by means of the wave equation, first succeeded in giving the correct explanation of the fine structure of the spectral lines of hydrogen-like atoms, and also to postulate the theory of splitting of the lines in the emission spectrum of atoms placed in a magnetic field (the anomalous and normal Zeeman effect). At the same time, it can be shown that at first sight Dirac's theory leads to difficulties, associated with the interpretation of negative energies, which would appear to be non-removable. A more detailed analysis of them, however, led to a new funda- 4 Prediction of the Positron by Dirac 5 mental discovery, which underlies the whole of the modern theory of elementary particles. Actually, in relativistic mechanics, the energy E of a free particle is related to its momentum p and its rest mass m by the 0 relationship where c is the velocity of light. This relation permits two equiva- lent solutions: E = ± |E|, |JB| = y/c2p2 + m2 c* 0 one of which corresponds to a positive energy and the other to a negative energy. A state with negative energy can be shown to be AE - I +m C2 n E = 0 ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^Ξ "moc2 FIG. 2. Diagram of the possible energy levels of the free Dirac particle. unreal, since the region of negative energies is extended to infinity (£-» — oo), and thus no stable minimum energy state could exist (Fig. 2). In classical physics, the energy of a particle, as a result of its motion, can be changed only continuously and therefore a transi- tion from a state with a positive energy {E > m c2) to a state with 0 negative energy (E< — m c2) is completely inadmissible, since 0 then the energy is changed discontinuously (AE ^ 2m c2). Thus, 0 having excluded at the initial instant of time states with a negative energy, we need not at all introduce them at a later time, i.e., there are no difficulties with negative energy states. We have a completely different state of affairs in quantum theory, where transitions with discrete energy changes are quite permissible. Then the state with a negative energy cannot be 6 Elementary Particles mechanically eliminated, since the probability of transition between energy levels of +m c2 and -m c2 will differ from zero. 0 0 After the appearance of Dirac's relativistic theory (1928) nobody drew attention to this difficulty at first. The majority of authors suggested that the state with negative energy, just as in classical theory, should be simply rejected. Since this rejection in the quantum theory was mathematically strictly without any foundation, the presence of a state with negative energy was known by the name of the "plus-minus difficulty". For a number of years this problem remained open, and only in 1931 did Dirac find an extremely original solution to it. He suggested that all states with a negative energy are filled with electrons. Therefore, in accordance with Pauli's principle, according to which there can be only one electron in every quan- tum state, electrons with positive energy cannot pass into these occupied states. According to Dirac, empty space should actually be a "sea" of electrons (vacuum), which completely fill the states with negative energy, and at the same time all states with positive energy remain free (Fig. 3). = m0C2 2m0C2 :-m0C FIG. 3. Diagram of the ground state of the electron-positron vacuum. Let us now assume that a gamma-quantum with energy greater than 2m c2, acting on an electron in the vacuum, transfers it to a 0 state of positive energy (Fig. 4). In this case, in place of the absorbed gamma-quantum an electron appears with positive energy and simultaneously a "hole" in the background of the "sea" of electrons with negative energy,