Lesson 9 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 β-, β+ and electron capture (EC). • β- 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 β- decay is 14 (animation) € C→14 N + β − + ν e 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 Z0. Masses of these particles large (81, 93 GeV/c) and forces are short range (10-3 fm) • n(udd)→p(duu) + β-+ ν e • (Animation) € A fundamental view of beta decay Beta decay (cont) • In β- decay, ΔZ = +1, ΔN =-1, ΔA =0 • Most of the energy emitted in the decay appears in the rest and kinetic energy of the emitted electron (β- ) and the emitted anti-electron neutrino, ν e • The decay energy is shared between the emitted electron and neutrino. • β- decay is seen in all neutron-rich nuclei € stopped by a thin sheet of Al • The emitted β- are easily Beta decay (cont) • • • • • • The second type of beta decay is β+ (positron) decay. In this decay, ΔZ = -1, ΔN =+1, ΔA =0, i.e., a nuclear proton changes into a nuclear neutron with the emission of a positron, β+ , and an electron neutrino, νe 22 22 + An example of this decay is Na→ Ne + β + ν e Like β- decay, in β+ decay, the decay energy is shared between the residual nucleus, the emitted positron and the electron neutrino. € larger than normal p/n ratios. It is β+ decay occurs in nuclei with € elements restricted to the lighter β+ particles annihilate when they contact ordinary matter with the emission of two 0.511 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. e− + 209Bi→209 Pb + ν e • An example of this type of decay is • The occurrence of this decay is detected by the emitted Xray (from the vacancy in the electron shell). € for proton-rich heavy nuclei. • It is the preferred decay mode Mass Changes in Beta Decay • β- decay 14 C→14 N + β − + ν e Energy = [(m(14 C) + 6melectron ) − (m(14 N) + 6melectron ) − m(β − )]c 2 Energy = [M(14 C) − M(14 N)]c 2 •β+ decay € 64 Cu→64 Ni− + β + + ν e Energy = [(m( 64 Cu) + 29melectron ) − (m( 64 Ni) + 28melectron ) − melectron − m(β + )]c 2 Energy = [M( 64 Cu) − M( 64 Ni) − 2melectron ]c 2 € Mass Changes in Beta Decay • EC decay 207 Bi + + e− →207 Pb + ν e Energy = [(m( 207Bi) + 83melectron ) − (m( 207Pb) + 82melectron )]c 2 Energy = [M( 207Bi) − M( 207Pb)]c 2 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, GamowTeller and Fermi decay modes. • In heavy nuclei, G-T decay dominates • In mirror nuclei, Fermi decay is the only possible decay mode. Fermi theory of beta decay • Fermi assumed β-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 Fermi’s golden rule 2π 2 dn λ= M h dE 0 M ≡ matrix⋅ element = ∫ ψ *f Mψ i dτ € ψ f = ψ Rψ eψν M reflects the probability of going from state I to state f (nuclear structure information) € Fermi theory of beta decay(cont) • Probability for emission of electron of momentum pe Fermi theory of beta decay(cont) Calculating dn/dE0 • Consider the electron at position (x,y,z) with momentum components (px,py,pz) • Heisenberg tells us that Δpx Δx = h Δpy Δy = h ΔpzΔz = h Δpx ΔxΔpy ΔyΔpzΔz = h 3 This volume is the unit cell in phase space € Fermi theory of beta decay(cont) • How do we do the counting? First guess is 50-50 split between electron and neutrino. • Define dn/dE0 as the number of ways the total energy can be divided between electron and neutrino • Not all ways are equally probable Calculating dn/dE0 (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. Calculating dn/dE0 (cont.) Calculating dn/dE0 (cont.) • Have neglected the effect of the nuclear charge on the electron energy Calculating dn/dE0 (cont.) • Add a factor, the Fermi function F(Z,Ee) Kurie Plots log ft 2 λ= 2 € g M if 2 p max 3 7 3 2π h c ∫ F(Z 2 e 2 ,pe )p (Q − Te ) dp D 0 2 5 4 e 3 7 g M mc λ= f (ZD ,Q ) 2π h ft1/ 2 = ln 2 2π 3 h7 2 2 5 4 e g M mc f=Fermi integral ∝ 1 2 g M 2 Use of log ft1/2 • Consider the β+ decay of 25Al. t1/2=7.6 s, Eβ+=3.24 MeV log f0t=3.7, log(C)=-0.2 log ft=3.5 Allowed vs Superallowed Transitions Superallowed Allowed mirror nuclei non-mirror nuclei Transition types • Fermi vs Gamow-Teller Ii = I f + l Ii = I f + l + 1 •Allowed transitions € l=0 Δπ = no What is ΔI? € Fermi Gamow-Teller Transition types(cont.) • First forbidden l =1 Δπ = yes What is ΔI? € Electron capture decay 2 2 λEC = g M if Tν2 2 3 3 2π c h ϕ K (0) 2 ⎞ 3 / 2 ⎛ 1 Zme e ϕ K (0) = ⎜ 2 ⎟ π ⎝ 4 πε 0 h ⎠ € 2 € € λK −EC = 3 2 g Z M if Tν2 cons tan ts λK Z 3Tν2 = cons tan ts λβ + f (ZD ,Q ) 2 Electron capture decay Extranuclear effects after EC • X-rays vs Auger emission (animation) • Fluorescence yield λX −ray ω= λX −ray + λAuger € β-delayed radioactivity • • • • β-decay followed by another decay fission product examples β-delayed neutron emitters β-delayed fission Double beta decay