Alpha Decay vs Beta Decay – Radioactivity

Alpha decay (or α-decay and also alpha radioactivity) represents the disintegration of a parent nucleus to a daughter through the emission of the nucleus of a helium atom. This transition can be characterized as:

Alpha Decay - Alpha Radioactivity

As can be seen from the figure, alpha particle is emitted in alpha decay. Alpha particles are energetic nuclei of helium. Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus. Alpha particles are relatively large and carry a double positive charge. They are not very penetrating and a piece of paper can stop them. They travel only a few centimeters but deposit all their energies along their short paths.

In practice, this mode of decay has only been observed in nuclides considerably heavier than nickel, with the lightest known alpha emitters being the lightest isotopes (mass numbers 106–110) of tellurium (element 52). In nuclear reactors alpha decay occurs for example in the fuel (alpha decay of heavy nuclei). Alpha particles are commonly emitted by all of the heavy radioactive nuclei occuring in the nature (uranium, thorium or radium), as well as the transuranic elements (neptunium, plutonium or americium).Uranium 238 decay.

Theory of Alpha Decay – Quantum Tunneling

Among the variety of channels in which a nucleus decays, alpha decay has been one of the most studied. The alpha decay channel in heavy and super heavy nuclei has provided information on the fundamental properties of nuclei far from stability, such as their ground state energies and the structure of their nuclear levels.

Alpha decay is a quantum tunneling process. In order to be emitted, the alpha particle must penetrate a potential barrier. This is similar to cluster decay, in which an atomic nucleus emits a small “cluster” of neutrons and protons (e.g. 12C).

The height of the Coulomb barrier for nuclei of A « 200 is about 20-25 MeV. The alpha particles emitted in nuclear decay have typical energies of about 5 MeV. On the one hand an incoming 5 MeV alpha particle is scattered from a heavy nucleus and it cannot penetrate the Coulomb barrier and get sufficiently close to the nucleus to interact via the strong force. On the other hand, a 5 MeV alpha particle bound in a nuclear potential well is able to tunnel that same Coulomb barrier.

alpha decay - quantum tunnelingBy 1928, George Gamow (and independently by Ronald Gurney and Edward Condon) had solved the theory of alpha decay via quantum tunneling. They assumed that the alpha particle and the daughter nucleus exist within the parent nucleus prior to its dissociation, namely the decay of quasistationary states (QS).  A quasistationary state is defined as a long-lived state that eventually decays. Initially, the alpha cluster oscillates in the potential of the daughter nucleus, with the Coulomb potential preventing their separation. The alpha particle is trapped in a potential well by the nucleus. Classically, it is forbidden to escape, but according to the (then) newly discovered principles of quantum mechanics, it has a tiny (but non-zero) probability of “tunneling” through the barrier and appearing on the other side to escape the nucleus. Using the tunneling mechanism, Gamow, Condon and Gurney calculated the penetrability of the tunneling α particle through the Coulomb barrier, finding the lifetimes of some α emitting nuclei. The main success of this model was the reproduction of the semi-empirical Geiger-Nuttall law that expresses the lifetimes of the α emitters in terms of the energies of the released α particles. It must be noted, that other common forms of decay (e.g. beta decay) are governed by the interplay between both the nuclear force and the electromagnetic force.

Special Reference: W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467.

 

Beta decay or β decay represents the disintegration of a parent nucleus to a daughter through the emission of the beta particle. This transition (β decay) can be characterized as:

Beta Decay - Beta Radioactivity - definition

If a nucleus emits a beta particle, it loses an electron (or positron). In this case, the mass number of daughter nucleus remains the same, but daughter nucleus will form different element.

Beta particles are high-energy, high-speed electrons or positrons emitted by certain types of radioactive nuclei such as potassium-40. The beta particles have greater range of penetration than alpha particles, but still much less than gamma rays. The beta particles emitted are a form of ionizing radiation also known as beta rays. There are the following forms of beta decay:

  • Negative Beta Decay – Electron Decay. In electron decay, a neutron-rich nucleus emits a high-energy electron (β particle). The electrons are negatively charged almost massless particles Due to the law of conservation of electric charge, the nuclear charge must increase by one unit. In this case, the process can be represented by: 
  • Positive Beta Decay – Positron Decay. In positron decay, a proton-rich nucleus emits a positron (positrons are antiparticles of electrons, and have the same mass as electrons but positive electric charge), and thereby reduces the nuclear charge by one unit. In this case, the process can be represented by: An annihilation occurs, when a low-energy positron collides with a low-energy electron.
  • Inverse Beta Decay – Electron Capture. Electron capture, known also as inverse beta decay is sometimes included as a type of beta decay, because the basic nuclear process, mediated by the weak interaction, is the same. In this process, a proton-rich nucleus can also reduce its nuclear charge by one unit by absorbing an atomic electron. 

Theory of Beta Decay – Weak Interaction

Beta decay is governed by the weak interaction. During beta decay one of two down quarks changes into an up quark by emitting a W boson (carries away a negative charge). The W boson then decays into a beta particle and an antineutrino. This process is equivalent to the process, in which a neutrino interacts with a neutron.

theory of beta decay - weak interaction

As can be seen from the figure, the weak interaction changes one flavor of quark into another. Note that, the Standard Model counts six flavours of quarks and six flavours of leptons. The weak interaction is the only process in which a quark can change to another quark, or a lepton to another lepton (flavor change). Neither the strong interaction nor electromagnetic permit flavour changing. This fact is crucial in many decays of nuclear particles. In the fusion process, which, for example, powers the Sun, two protons interact via the weak force to form a deuterium nucleus, which reacts further to generate helium. Without the weak interaction, the diproton would decay back into two hydrogen-1 unbound protons through proton emission. As a result, the sun would not burn without it since the weak interaction causes the transmutation p -> n.

In contrast to alpha decay, neither the beta particle nor its associated neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons. The probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. For either electron or positron emission to be energetically possible, the energy release (see below) or Q value must be positive.

 

Energy Spectrum of Beta Decay

In both alpha and gamma decay, the resulting particle (alpha particle or photon) has a narrow energy distribution, since the particle carries the energy from the difference between the initial and final nuclear states. For example, in case of alpha decay, when a parent nucleus breaks down spontaneously to yield a daughter nucleus and an alpha particle, the sum of the mass of the two products does not quite equal the mass of the original nucleus (see Mass Defect). As a result of the law of conservation of energy, this difference appears in the form of the kinetic energy of the alpha particle. Since the same particles appear as products at every breakdown of a particular parent nucleus, the mass-difference should always be the same, and the kinetic energy of the alpha particles should also always be the same. In other words, the beam of alpha particles should be monoenergetic.

It was expected that the same considerations would hold for a parent nucleus breaking down to a daughter nucleus and a beta particle. Because only the electron and the recoiling daughter nucleus were observed beta decay, the process was initially assumed to be a two body process, very much like alpha decay. It would seem reasonable to suppose that the beta particles would form also a monoenergetic beam.

To demonstrate energetics of two-body beta decay, consider the beta decay in which an electron is emitted and the parent nucleus is at rest, conservation of energy requires:

conservation-of-energy-beta-decay

Since the electron is much lighter particle it was expected that it will carry away most of the released energy, which would have a unique value Te-.

Energy spectrum of beta decay
The shape of this energy curve depends on what fraction of the reaction energy (Q value-the amount of energy released by the reaction) is carried by the electron or neutrino.

But the reality was different. The spectrum of beta particles measured by Lise Meitner and Otto Hahn in 1911 and by Jean Danysz in 1913 showed multiple lines on a diffuse background, however. Moreover virtually all of the emitted beta particles have energies below that predicted by energy conservation in two-body decays. The electrons emitted in beta decay have a continuous rather than a discrete spectrumappeared to contradict conservation of energy, under the then-current assumption that beta decay is the simple emission of an electron from a nucleus. When this was first observed, it appeared to threaten the survival of one of the most important conservation laws in physics!

To account for this energy release, Pauli proposed (in 1931) that there was emitted in the decay process another particle, later named by Fermi the neutrino. It was clear, this particle must be highly penetrating and that the conservation of electric charge requires the neutrino to be electrically neutral. This would explain why it was so hard to detect this particle. The term neutrino comes from Italian meaning “little neutral one” and neutrinos are denoted by the Greek letter ν (nu). In the process of beta decay the neutrino carries the missing energy and also in this process the law of conservation of energy remains valid.

 

 

References:

Radiation Protection:

  1. Knoll, Glenn F., Radiation Detection and Measurement 4th Edition, Wiley, 8/2010. ISBN-13: 978-0470131480.
  2. Stabin, Michael G., Radiation Protection and Dosimetry: An Introduction to Health Physics, Springer, 10/2010. ISBN-13: 978-1441923912.
  3. Martin, James E., Physics for Radiation Protection 3rd Edition, Wiley-VCH, 4/2013. ISBN-13: 978-3527411764.
  4. U.S.NRC, NUCLEAR REACTOR CONCEPTS
  5. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Nuclear and Reactor Physics:

  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

See above:

Radioactive Decay