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Transcript
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 14 C14 N 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) + -+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. e • - 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 + decay,Ne • Like - decay, in Na the is shared between decay energy e 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 MeV photons. 22 22 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 209 209 • The occurrence of this decay by the emitted e Bi Pbisdetected e 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 14 C14 N e Energy [(m(14C) 6melectron ) (m(14 N) 6melectron ) m( )]c 2 Energy [M(14 C) M(14N)]c 2 •+ decay 64 Cu64 Ni e Energy [(m( 64Cu) 29melectron ) (m( 64 Ni) 28melectron ) melectron m( )]c 2 Energy [M( 64 Cu) M( 64Ni) 2melectron ]c 2 Mass Changes in Beta Decay • EC decay 207 Bi e 207Pb 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. 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. H Eˆ H 2 2m 2 V Eˆ i t (x, y,z.t) (x, y,z) (t) 1 2 2 i V 2m t 2 2 V E 2m i E t (t) eiE t / n a11 a2 2 an n n an n 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=H0+H’ For two state system Weak perturbation, neglect term 1 Matrix element 1*H '2d 1 H '2 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 H • Beta decay energy E0 divided between electron and neutrino • Not all divisions are equally probable (would mean flat beta spectrum) f i 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 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 pxx h pyy h pzz h pxxpyypzz h 3 This volume is the unit cell in phase space 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 g M if 2 2 p max 3 7 3 c F(Z ,pe )p (Q Te ) dp 2 e D 2 0 2 2 5 4 e 3 7 g M mc f (ZD ,Q ) 2 ft1/ 2 ln 2 2 3 2 2 7 5 4 e g M mc 1 g2 M 2 Allowed vs Superallowed Transitions Superallowed Allowed mirror nuclei non-mirror nuclei Transition types • Fermi vs Gamow -Teller Ii I f Ii I f 1 •Allowed transitions 0 no What is I? Fermi Gamow-Teller Transition types(cont.) • First forbidden 1 yes What is I? Electron capture decay 2 2 EC g M if T2 2 c 2 3 3 K (0) 2 3 / 2 1 Zme e K (0) 2 4 0 2 K EC 2 g Z M if T2 constan ts K Z 3T2 cons tan ts f (ZD ,Q ) 3 2 Electron capture decay Extranuclear effects after EC • X-rays vs Auger emission • Fluorescence yield X ray X ray Auger -delayed radioactivity • • • • -decay followed by another decay fission product examples -delayed neutron emitters -delayed fission Double beta decay