Fundamentals in Nuclear Physics Kenichi Ishikawa () http://ishiken.free.fr/english/lecture.html ishiken@n.t.u-tokyo.ac.jp 1
Nuclear decays and fundamental interactions (II) Weak interaction and beta decay 2
Four fundamental interactions interaction gravity exchanged particle (gauge boson) graviton decay weak W ±, Z 0 beta decay electromagnetic photon gamma decay strong nuclear force gluon pion and other hadrons alpha decay tunnel effect 3
beta decay decay + decay ZN ZN Z+1N +e Z + e 1N +e + + e half life = 5730 years dating 4
Emitted electron (positron) energy has a broad distribution 64 Cu _ 64 + β Cu β 0.2 0.6 1.0 1.4 1.8 0.2 0.6 1.0 1.4 1.8 p (MeV/c) p (MeV/c) β β β 5
beta decay decay + decay ZN ZN Z+1N +e Z + e 1N +e + + e half life = 5730 years dating The existence of the neutrino was predicted by Wolfgang Pauli in 1930 to explain how beta decay could conserve energy, momentum, and angular momentum. Pauli 6
fundamental processes n pe e p ne + e mp = 938.3 MeV/c 2 < mn = 939.6 MeV/c 2 mean life = 881.5 ± 1.5 s - free proton does NOT decay - takes place only in nuclei Feynman diagram p n weak boson W mw = 80.385 GeV/c 2 e ν e cf. mpion = 139.570 MeV/c 2 (±), 134.9766 MeV/c 2 (neutral) 7
Fermi theory of beta decay Decay rate w = 2 ~ h p e H n i 2 dn de Fermi s golden rule Z e k pr 2 e k er 2 H (r 2 r 1 )e k nr 1 e k r 1 dv density of state weak interaction is a short-range force H (r 2 r 1 ) G (r 2 r 1 ) G Electron energy distribution dominated by density of state 8
Density of state assuming plane waves dn / p 2 dpq 2 dq p : electron momentum q : neutrino momentum energy E E = cq E e = p m 2 ec 4 + p 2 c 2 0 = E e + E electron de = de = cdq 5 4 64 Cu neutrino + Q = 0.653 kev dn de / p2 q 2 dp / (E 0 E e ) 2 p 2 dp statistical factor Experiment Experiment Theory n (p) (arb. unit) 3 2 Coulomb repulsion 1 0 0.0 0.5 1.0 p /m e c 1.5 2.0 9
Electron capture (EC) a) b) (,Z) k l m c) (,Z 1) (,Z 1) l m νe 40 r 18 γ followed by characteristic x-ray emission uger effect 40 K 19 10.72%1.5049 MeV EC γ 0+ 1.277 10 9 a radiation from the human body 4-89.28%1.31109 MeV β 40 20Ca 0+ ZN + e Z 1N + e fundamental process: pe n e neutrino energy: E = M(, Z)c 2 M(, Z 1)c 2 atomic mass 10
β + decay and electron capture + decay ZN Z 1N +e + + e M(, Z)c 2 >M(, Z 1)c 2 +2m e c 2 atomic mass electron capture ZN + e Z 1N + e M(, Z)c 2 >M(, Z 1)c 2 Both may not always be energetically possible! 11
By transforming the Feynman diagram... p n W e n pe e p ne + e ν e betabeta+ pe e p n e e + n electron capture (EC) neutrino detection 12
Parity violation... but before that... β Symmetry and conservation law 13
no change under a transformation ny symmetry of a physical law has a corresponding conservation law Noether s theorem symmetry temporal translation spatial translation rotation reflection r -r (P) time reversal (T) charge conjugation (C) gauge invariance conserved quantity energy momentum angular momentum parity T-parity C-parity electric charge Example: Coulomb force V (r) = q 1q 2 4 0 r 2 or V (r 1, r 2 )= q 1 q 2 4 0 r 1 r 2 2 14
example in the classical mechanics Hamilton equations q i = H p i ṗ i = H q i If the Hamiltonian does not explicitly depend on qi (invariant under the spatial translation) ṗ i =0 gauge invariance B =, E = invariant under the gauge transformation p i = const Conservation of momentum t = +, = Invariance of the ction S t Conservation of the electric charge t + j =0 15
Parity reflection ˆ (r) = ( r) parity operator ˆ2 (r) = (r) Eigenvalues ± 1 If the physical law is invariant under the reflection (gravitational, electromagnetic, and strong interaction) i tˆ = H ˆ i tˆ =ˆH ˆH = H ˆ [ˆ, H] =0 Heisenberg s equation of motion i dˆ dt =[ˆ, H] =0 Conservation of parity 16
parity violation nonconservation of parity in the weak interaction Prediction by T.-D. Lee and C. N. Yang in 1956 Experimental verification by C.S. Wu in 1957 4BPBPF 7PK ^ ^ M b by d c e M c Y d n o F 76? anisotropy 7PPP real world in the mirror ol l 2 i m ph M go =FPIFK= ^ ^ M b T cy d c _ c M h _ P asymmetry {a n Low-temperature cryostat Cerium magnesium nitrate crystal PPPPPPPPP)PPPP 8BDDBE 17
parity violation nonconservation of parity in the weak interaction Prediction by T.-D. Lee and C. N. Yang in 1956 Experimental verification by C.S. Wu in 1957 4BPBPF 7PK ^ ^ M b by d c e M c Y d n o F 76? anisotropy 7PPP real world inverted world θ e- ol l 2 i m ph M go =FPIFK= ^ ^ M b T cy d c _ c M h _ P asymmetry {a θ 60 Co 60 Co n Low-temperature cryostat Cerium magnesium nitrate crystal PPPPPPPPP)PPPP 8BDDBE e - 18
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Lee Yang Wu Nobel prize in physics (1957) 20
CP violation Makoto Kobayashi Toshihide Maskawa Nobel prize in physics (2008) 21
CPT theorem CPT Preservation of CPT symmetry by all physical phenomena ny Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry 22