Lesson 8 Beta Decay Betadecay Beta decay is

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 Ge. V/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 antielectron 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 0. 511 Me. V 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*nan 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 an’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 50 -50 split between electron and neutrino. • Define dn/d. E 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 pe

Fermi theory of beta decay(cont)

Calculating dn/d. E 0 • Consider the electron at position (x, y, z) with momentum components (px, py, pz) • Heisenberg tells us that This volume is the unit cell in phase space

Calculating dn/d. E 0 (cont. )�� • The probability of having an electron with momentum pe (between pe and pe+dpe) is proportional to the number of unit cells in phase space occupied.