Beta decay, theory

Bogumil Jeziorski received his M.S. degree in chemistry from the University of Warsaw in 1969. He conducted his graduate work also in Warsaw under the supervision of W. Kolos. After a postdoctoral position at the University of Utah, he was a research associate at the University of Florida and a Visiting Professor at the University of Waterloo, University of Delaware and University of Nijmegen. Since 1990 he has been a Professor of Chemistry at the University of Warsaw. His research has been mainly on the coupled-cluster theory of electronic correlation and on the perturbation theory of intermolecular forces. His other research interests include chemical effects in nuclear beta decay, theory of muonic molecules and relativistic and radiative effects in molecules. 

Notice we have replaced v by P, which is the designation of the antineutrino. Beta-decay theory has shown that antineutrinos P are emitted in electron decay, and "regular" neutrinos V in positron decay. We can consider the particles identical cf. 10.4. Because of the extremely low probability of interaction or neutrinos with matter, they are unfortunately often omitted in writing /3-decay reactions. 

Beta-decay theory is quite complicated and involves the weak nuclear interaction force, which is less imderstood than the strong interaction. The theory for j3-decay derived by Fermi in 1934 leads to the expression... 

Perturbation theory was applied to the ionization of atoms accompanying alpha and beta decay soon after the advent of quantum theory (Migdal, 1941). Migdal concluded that the probability for... 

Millikan s experiment did not prove, of course, that (he charge on the cathode ray. beta ray, photoelectric, or Zeeman particle was e. But if we call all such particles electrons, and assume that they have e/m = 1.76 x Hi" coulombs/kg. and e = 1.60 x 10" coulomb (and hence m =9.1 x 10 " kg), we find that they fit very well into Bohr s theory of the hydrogen atom and successive, more comprehensive atomic theories, into Richardson s equations for thermionic emission, into Fermi s theory of beta decay, and so on. In other words, a whole web of modem theory and experiment defines the electron. The best current value of e = (1.60206 0.00003) x 10 g coulomb. 

Another kind of particle and another kind of interaction were discovered from a detailed study of beta radioactivity in which electrons with a continuous spectrum of energies are emitted by an unstable nucleus. The corresponding interactions could be viewed as being due to the virtual transmutation of a neutron into a proton, an electron, and a new neutral particle of vanishing mass called the neutrino. The theory provided such a successful systematization of beta decay rate data for several nuclei that the existence of the neutrino was well established more than 20 years before its experimental discovery. The beta decay interaction was very weak even compared to the electron-photon interaction. 

The neutrino problem is described in the article on Particles (Subatomic), The double-beta decay event may contribute to the solution of that problem. In their introductory to the aforementioned article, the authors observe, The future of fundamental theories that account for everything from the building blocks of the atom to the architecture of the cosmos hinges on studies of this rarest of all observed radioactive events."... 

Although Sn = 7-9 MeV for most stable nuclei, its value falls to Sn = 2-3 MeV after 10 to 20 neutron captures, depending on the element When it does so, the captures effectively cease, because the ejection of the next neutron by photons is even faster than the rate of neutron captures. This location is called a waiting point because the series of captures must then wait until beta decay has been able to transmute the nucleus to the next higher element, for which the neutrons will have greater binding. The waiting point concept was important to the development of the theory of the r process. 

Italian physicist Enrico Eermi s (1901-1954) 1934 theory of beta decay used the neutrino hypothesis. (This theory, still used for approximate calculations, was only surpassed for more accurate calculations by theories developed in the 1970s.) But did neutrinos really exist In the 1930s, no experiments to detect them were possible. 

Nuclear neutrino research includes neutrino experiments such as SNO, Super-Kamiokande, KamLAND, SAGE, and double-beta decay and theory of neutrino oscillations. 

The assumption that the neutrino has a zero rest mass has been questioned by experimentalists and theorists. A number of experim ts have established an upper limit of the rest mass as < 10 eV. The implications of a finite rest mass are broad as the nature of the neutrino and the theory of beta decay is involved. On an even grander scale, the expansion of the universe depends on the neutrino mass. If the neutrino rest mass is only a few eV, this might result in sufficiently greater gravitational force that could eventually stop the expansion and contraction will begin, see Ch. 17. 

The separation of states of different T implies that one of a set of isobaric nuclei is stable and the others unstable against beta decay. The Wigner theory predicts superallowed decay between the states of a given supermultiplet because no change of spatial wave function is needed. This is found (a) for the positron decay of odd mirror nuclei (b) for transitions between the low states of nuclei with mass number 4 + 2 in which both T= and P = 0 states are found in the (1,0,0) supermultiplet. 

These early results were confirmed in further experiments which measured the lifetime and electron emitting power of /i-mesons captured in different elements the early experiments are listed by Sigurgiersson and Yamakawa. The quantitative interpretation of these experiments has been given by Tiomno and Wheeler. They estimate that the coupling constants for the beta decay process and / -meson capture process, Eq. (50.1b) agree with one another within the limits of error of experiment and theory. 

A theory of the weak interaction was also in its infancy in the 1930s. The weak interaction is responsible for beta decay, in which a radioactive nucleus is transformed into a slightly lighter nucleus with the emission of an electron. However, beta decays posed a problem because they appeared not to conserve energy and momentum. In 1931 Pauli proposed 5ie existence of a neutral particle that might be able to carry off the missing... 

The weak interaction, some lO times weaker than the electrom neUc interaction, occurs between "leptons and in the decay of hadrons. It is responsible for the "beta decay of particles and nuclei. In the current model, the weak interaction is visualized as a force mediated by the exchange of virtual particles, called intermediate vector bosons. The weak interactions are described by "electro-weak theory, which unifies them with the electromagnetic interactions. 

The theory of beta decay developed by Fermi is summarized in Chap. 2. The theoretical relationship describing the dependence of the beta decay constant on beta energy 3 ( b) and atomic number Z is given by Eqs. (2.82) and (2.83) in Chap. 2. For allowed transitions one can approximately write... 

Theory is also used to predict the half-lives and the mean energies of the beta and gamma rays emitted in the beta decay of short-lived fission products (with half-lives of the order of 1 sec.). These are required for decay heat predictions. However, measured data form the major part of the decay data even at short decay times. 

In 1898, in Cambridge, England, a New Zealander, Ernest Rutherford, demonstrated that there were at least two different types of radiation with different penetrating power. He called these alpha and beta radiation. He subsequentiy worked at McGill University in Montreal, Canada, and found more radioactive elements different types of radium and thorium, and actinium. He proposed that these were links in chains of radioactive materials, called the transformation theory. Rutherford and his colleague, Frederic Soddy, described that the rate of decay of radioactive elements were characteristic of the element, and came to be known as half-life. Decay follows the law of probability. Over a given period of time, each atom has a certain probability of decaying, a process that results from the random movements of the subatomic components of the radioactive atoms. This was the first instance in physics of a truly unpredictable phenomenon. The decay of a radioactive atom was probabilistic. 

Kofoed-Hansen O (1965) The coupling constants. In Siegbahn K (ed) Alpha-, beta- and gamma-ray spectroscopy, vol 2. North-HoUand, Amsterdam Konopinski EJ, Rose ME (1965) The theory of nuclear (3-decay. In Siegbahn K (ed) Alpha-, beta- and gamma-ray spectroscopy, vol 2. North-HoUand, Amsterdam... 

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