Lesson 8 Beta Decay

Beta-decay Beta decay is a term used to describe three types of decay in which a nuclear neutron (proton) changes into a nuclear proton (neutron). The decay modes are  -,  + and electron capture (EC).  - decay involves the change of a nuclear neutron into a proton and is found in nuclei with a larger than stable number of neutrons relative to protons, such as fission fragments. An example of  - decay is

Why do we “need” neutrinos? Conservation of energy Conservation of angular momentum

Beta decay and the weak interaction e - created at the instant of emission by weak interaction Weak interaction force carriers are W  and Z 0. Masses of these particles large (81, 93 GeV/c) and forces are short range (10 -3 fm) n(udd)  p(duu) +  - +  e

A fundamental view of beta decay

Beta decay (cont) In  - decay,  Z = +1,  N =-1,  A =0 Most of the energy emitted in the decay appears in the rest and kinetic energy of the emitted electron (  - ) and the emitted anti- electron neutrino, The decay energy is shared between the emitted electron and neutrino.  - decay is seen in all neutron-rich nuclei The emitted  - are easily stopped by a thin sheet of Al

Beta decay (cont) The second type of beta decay is  + (positron) decay. In this decay,  Z = -1,  N =+1,  A =0, i.e., a nuclear proton changes into a nuclear neutron with the emission of a positron,  +, and an electron neutrino, e An example of this decay is Like  - decay, in  + decay, the decay energy is shared between the residual nucleus, the emitted positron and the electron neutrino.  + decay occurs in nuclei with larger than normal p/n ratios. It is restricted to the lighter elements  + particles annihilate when they contact ordinary matter with the emission of two MeV photons.

Beta decay (cont) The third type of beta decay is electron capture (EC) decay. In EC decay an orbital electron is captured by a nuclear proton changing it into a nuclear neutron with the emission of a electron neutrino. An example of this type of decay is The occurrence of this decay is detected by the emitted X-ray (from the vacancy in the electron shell). It is the preferred decay mode for proton-rich heavy nuclei.

Mass Changes in Beta Decay  - decay  + decay

Mass Changes in Beta Decay EC decay Conclusion: All calculations can be done with atomic masses

Spins in Beta Decay The electron spin and the neutrino spin can either be parallel or anti-parallel. These are called, respectively, Gamow-Teller and Fermi decay modes. In heavy nuclei, G-T decay dominates In mirror nuclei, Fermi decay is the only possible decay mode.

Perturbation Theory Up to now, we have restricted our attention primarily to the solution of problems where things were not changing as a fucntion of time, ie, nuclear structure calculations. Now we shall take up the issue of transitions from one state to another. To do so, we need to introduce an additional concept in quantum mechanics, perturbation theory. A full accounting can be found in any quantum mechanics textbook.

a* n a n is the probability that the system will be in state n corresponding to the wave function  n Now consider a two state system How do we handle this in the Schrodinger equation? Make a n ’s time dependent

Modify the Hamiltonian H=H 0 +H’ For two state system

Weak perturbation, neglect term 1 Matrix element describes the probability that H’ will transform state  2 into state  1

Fermi theory of beta decay Fermi assumed  -decay results from some sort of interaction between the nucleons, the electron and the neutrino. This interaction is different from all other forces and will be called the weak interaction. Its strength will be expressed by a constant like e or G. Call this constant g. (g~10 -6 strong interaction)

Fermi theory of beta decay(cont) Interaction between nucleons, electron and neutrino will be expressed as a perturbation to the total Hamiltonian. Decay probability expressed by matrix element Beta decay energy E 0 divided between electron and neutrino Not all divisions are equally probable (would mean flat beta spectrum)

Fermi theory of beta decay(cont) How do we do the counting? First guess is split between electron and neutrino. Define dn/dE 0 as the number of ways the total energy can be divided between electron and neutrino

Fermi theory of beta decay(cont) Probability for emission of electron of momentum p e

Fermi theory of beta decay(cont)

Calculating dn/dE 0 Consider the electron at position (x,y,z) with momentum components (p x,p y,p z ) Heisenberg tells us that This volume is the unit cell in phase space

Calculating dn/dE 0 (cont.) The probability of having an electron with momentum p e (between p e and p e +dp e ) is proportional to the number of unit cells in phase space occupied.

Calculating dn/dE 0 (cont.)

Have neglected the effect of the nuclear charge on the electron energy

Calculating dn/dE 0 (cont.) Add a factor, the Fermi function F(Z,E e )

Kurie Plots

log ft

Allowed vs Superallowed Transitions mirror nuclei Superallowed Allowed non-mirror nuclei

Transition types Fermi vs Gamow-Teller Fermi Gamow-Teller Allowed transitions What is  I?

Transition types(cont.) First forbidden What is  I?

Electron capture decay

Extranuclear effects after EC X-rays vs Auger emission Fluorescence yield

 -delayed radioactivity  -decay followed by another decay fission product examples  -delayed neutron emitters  -delayed fission

Double beta decay