8 8.1 8.1.1 1 Chadwick [ 1 ] 1919,, electron number Q 0.0 0. 0.4 0.6 0.8 1.0 kinetic energy [MeV] 8.1: 8.1, 1 internal conversion electron E γ E e = E γ φ φ E e X 153
154 8, 3 H 3 He, ( ) 3 H( 1 ) 3 He( 1 )+e ( 1 ) 3 H 1 3 He 1 1930 Pauli [ ] m ν m ν =0 3 H 3 He m ν 0.5 kev 0. kev 3 H( 1 ) 3 He( 1 )+e ( 1 )+ν e( 1 ) 1 Fermi
8.1 155 8.1. Fermi Fermi 1934 [3] Fermi g Fermi golden rule ε ε+dε w(ε)dε = g m e 5 c 4 π 3 h 7 M if F (Z, ε)(ε 0 ε) ε ε 1dε (8.1) ε m e c β ± Q Q β = ε 0 1 (8.) M if F (Z, ε) Coulomb β + Z Z F ( Z, ε) (8.1) K(ε) = [ w(ε) ε ε 1 F (Z, ε) ] 1/ = [ ] g m 5 e c 4 1/ M if (ε 0 ε) (8.3) π 3 h 7 K(ε) ε Kurie plot 64 Cu 64 Cu 8. β β + β 64 Cu 64 Zn + e + ν β + 64 Cu 64 Ni + e + + ν (8.4)
156 8 64 Cu 1 β 64 Zn 0 64 Ni 0 β Q( β ) = 579 kev Q( β ) = 653 kev 8.: 64 Cu 5 5 ω( ε ) [arbitrary] 4 3 1 K( ε ) [arbitrary] 4 3 1 0 0.0 0.1 0. 0.3 0.4 0.5 0.6 0.7 kinetic energy [MeV] 0 0.0 0.1 0. 0.3 0.4 0.5 0.6 0.7 kinetic energy [MeV] 8.3: Kurie plot β + β 8.3 64 Cu [4] (8.1) 8.3 (8.3) ε 1 ε 0 λ ε 0 f = ε0 1 λ = g m e 5 c 4 π 3 h 7 M if f (8.5) F (Z, ε)(ε 0 ε) ε ε 1 dε (8.6) Fermi Gamow-Teller
8.1 157 τ m =1/λ t 1/ = log /λ M if g ft ft = log g m e 5 c 4 π 3 h 7 M if (8.7) (8.5) t (8.1) - (8.6) m ν =0 (8.1) (ε 0 ε) m ν : ε 0 ε ε 0 ε : ε 0 ε (ε 0 ε) (m ν /m e ) (8.8) Kurie plot 8.4 K( ε ) 16.6 17.0 17.4 17.8 18. 18.6 kinetic energy [kev] 8.4: Kurie plot, m ν = 0.0 kev, 0. kev, 0.5 kev 0. kev (8.6) ε
158 8 8.1.3 Fermi 0 ν ν γ p e γ n Cd γ γ 8.5: Reines Cowan Reines Cowan 8.5 [ 5] n p + e + ν ν + p n + e + (8.9)
8.1 159 e + + e γ + γ (8.10) 8.1.4 Goldhaber [6] h h = σ p p (8.11) σ p h =1 h = 1 Goldhaber 15 Eu 3 15 Eu m (0 )+e 15 Sm (1 )+ν 15 Sm (1 ) 15 Sm(0 + g.s.)+γ (8.1) z 1. 1 + 0 1 z + 1 1. z z 1 0 3 Gamow-Teller. l =0 1s 1/
160 8 Sm γ 0.046 15 Eu 0 Eu Sm Sm 1 0.963 ν ν 15 Sm 0.1 0 0.0 8.6: Goldhaber 15 Eu 15 Sm 15 Sm 1 + 0 + 1 1 z 1 z m m ν = + 1 m γ = 1 m ν = 1 m γ = +1 m ν m γ m γ =+1 m γ = 1 m ν 3. 15 Eu m 15 Sm (1 ) 15 Sm (1 ) τ m =0.03 ps 15 Sm z 4. 15 Sm 1 0 + 8.6 15 Sm 1 Goldhaber Sm O 3 1 + 0 + 15 Sm 15 Sm
8.1 161 5. h ν = h γ (8.13) h γ h ν Goldhaber 15 Sm 1 0 + m γ = 1 z h γ = 1 h ν = σ ν p ν p ν = 1 (8.14) 0.67 ± 0.15 h ν = 1 0.75 Vylov h ν = 0.93 ± 0.10 [7] β h ν =+1 h e = ±1 v [8] 8.1 8.1 ν ν e e + 1 +1 v c + v c
16 8 8. 8..1 K [9] K π π θ π + + π 0 τ π + + π + + π (8.15) θ τ π + L π 0 π + L 1 L π + π 8.7: π 3π π 0 8.7 θ π π + π 0 L ( 1) 1+1 ( 1) L =( 1) L θ J = L τ 3π π + L 1 π L ( 1) 1+1+1 ( 1) L 1( 1) L =( 1) L 1+L +1 τ J = L 1 L L 1 L +1... L 1 + L 3π Q- L 1,L τ L 1 = L =0 τ J =0 J =0 π J =0 K K π K 3π
8. 163 8.. x x, y y, z z (8.16) r p E J σ B E B E B E B 0 0 1956 Lee Yang[9] 198 v e σ e 0 e ν σ e p e p ν σ ν J 8.8: 8.8
164 8 J p e σ e p e / p e σ ν p ν / p ν 8..3 J p e 1957 [10] 60 Co 60 Ni + e + ν (8.17) 8.9 60 Co 5 + 99 % 60 Ni 4 + (.84) 5 60 Co.506 1.333 4 0.0 0 60 Ni 8.9: 60 Co J J θ p e π θ p ν p ν p e (a) (b) 8.10: 8.10 (a) (b) p e p e, J J (8.18) (a) (b)
8. 165 J θ =0 θ = π 1.3 counting rate 1. 1.1 1.0 0.9 0.8 H H 0.7 0 4 6 8 10 1 14 16 18 time [min] 8.11: 60 Co Wu 60 Co θ =0 θ = π 8.11 Counting rate
166 8 8.3 4 Fermi 8.3.1 Lorentz Fermi 1934 [3] J EM µ J EM µ = ψ e (x) γ µ ψ e (x) (8.19) A µ Hamiltonian H EM (x) =+ej EM µ (x) Aµ (x) = eψ e (x) γ µ ψ e (x) A µ (x) (8.0) ψ e ψ e = ψ e γ 0 γ µ Dirac γ ( ) ( ) I 0 0 σ γ 0 =, γ k k = 0 I σ k (8.1) 0 γ 5 γ 5 = γ 5 = iγ 0 γ 1 γ γ 3 = ( 0 I I 0 ) (8.) I ( ) ( 0 1 0 i σ 1 =, σ = 1 0 i 0 ), σ 3 = ( 1 0 0 1 ) (8.3) Pauli x µ =(x 0, x) x µ =(x 0, x) 1 0 0 0 g µν = g µν = 0 1 0 0 0 0 1 0 (8.4) 0 0 0 1 - Fermi (8.19) V c µ l c µ V c µ (x) = ψ p (x) γ µ ψ n (x) l c µ(x) = ψ e (x) γ µ ψ ν (x) (8.5)
8.3 4 Fermi 167 c W Fermi V c µ l c µ 8.1 e e p e p e γ W e e n ν n ν 8.1: Hamiltonian G β H β (x) = G ] β [l cµ (x) Vµ c (x)+v cµ (x) lµ c (x) = G β [ψ e (x) γ µ ψ ν (x) ψ p (x) γ µ ψ n (x) ] + ψ n (x) γ µ ψ p (x) ψ ν (x) γ µ ψ e (x) (8.6) β 8.13 Hermite β + p e ν n ν e n ν n p p e β decay β decay electron capture 8.13: β β +
168 8 Lorentz Fermi V c µ l c µ ψγ µψ Lorentz (8.6) γ µ γ µ - J =0 Fermi Fermi - Gamow Teller[ 11 ] 1936 - Lorentz ψ ψ 16 8. ψ ψ S ψψ 1 V ψγ µ ψ 4 T ψγ µ γ ν ψ 6 P ψγ 5 ψ 1 A ψγ µ γ 5 ψ 4 γ S-S V -V T -T P-P A-A S-P V -A 8.3. Fermi Gamow-Teller Q- J =0, 1 Fermi Gamow-Teller 8.14 8.15 Fermi Gamow-Teller L =0 π =0 S S =0 Fermi J =0 Fermi Fermi isobaric analog state,
8.3 4 Fermi 169 (5.143) 0 3.948 1 14 O (3.508) 0.313 0 6 He 0.0 14 N 1 0.0 6 Li 1 8.14: Fermi 0 + 0 + Gamow-Teller 0 + 1 + Fermi S=0 p e ν Gamow-Teller S=1 p e ν n S= 0 L = 0 J = 0 n S= 1 L = 0 J = 1 8.15: Fermi Gamow-Teller IAS Gamow-Teller J =1 S =1 S =1 J =1 J J =0 J =0 (Fermi Gamow-Teller ) Lorentz Fermi Gamow-Teller 8. γ γ m p E = p c + m c 4 u ± = E + mc χ ± cσ p E + mc χ ± (8.7)
170 8 χ ± Pauli ( ) ( 1 0 χ + =, χ = 0 1 ) (8.8) ± σ ˆp χ ± = ±χ ± (8.9) γ 0 0 8. γ ( ) I 0 S : 1 = (8.30) 0 I V : γ 0 = T : γ 0 γ 0 = P : γ 5 = γ k γ l = m ( I 0 0 I ( I 0 0 I ( 0 I I 0 ) ) iε klm ( σm 0 0 σ m ) ( ) 0 I A : γ 5 γ 0 = I 0 γ k = ( 0 σk σ k 0 ) γ 0 γ k = γ k γ 0 = ( 0 σk σ k 0 ) γ 5 γ k = ( σk 0 0 σ k ) ) (8.31) (8.3) (8.33) (8.34) Fermi (V ) (S) γ 0 γ 0 Fermi θ θ V : 1+ v c cos θ, S : 1 v c cos θ (8.35) v/c γ
8.3 4 Fermi 171 8.16 Fermi S =0 Fermi Gamow-Teller e ν e e e ν ν ν V S A T 8.16: Fermi Gamow-Teller β Gamow-Teller Gamow-Teller (A) (T : γ k γ l ) A : 1 1 v 3 c cos θ, T : 1+ 1 v cos θ (8.36) 3 c 8.16 Gamow-Teller [1] Fermi Gamow-Teller 8.3.3 Fermi Gamow-Teller Lee Yang
17 8 Hamiltonian H β = G β [( ψ p γ µ ψ n )( ψ e (C V + C V γ 5 ) γ µ ψ ν ) + ) ] (ψ p γ µ γ 5 ψ n )(ψ e (C A + C Aγ 5 ) γ µ γ 5 ψ ν +h.c. (8.37) γ 5 Hamiltonian G β 0 C V = C V, C A = C A (8.38) 0 (m =0,E = cp) u ± = χ cp ± (8.39) σ ˆp χ ± (8.9) 1 (1 γ 1 5) u = u, (1 + γ 5) u = 0 1 (1 γ 5 ) u 1 + = 0 (1 + γ 5 ) u (8.40) + = u + 1 (1 ± γ 5 ) 1 (1 γ 1 5) ψ ν = ψ ν, (1 + γ 5) ψ ν = 0 (8.41) (8.38) Hamiltonian H β = G [( )( ) ] β ψ e γ µ (1 γ 5 ) ψ ν ψ p γ µ (C V C A γ 5 ) ψ n +h.c. (8.4) C V C A C V C A Fermi Gamow-Teller M F M GT ft- ft = ln G β π 3 h 7 m e 5 c 4 1 C V M F + C A M GT (8.43)
8.3 4 Fermi 173 Fermi IAS Fermi T ± Gamow-Teller 8.3 8.3 14 O M F M GT ft [s] n p 1 3 180 ± 50 14 O 14 N 0 315 ± 10 ft- ft(n p) ft( 14 O 14 N) = C V C V +3C A =0.41 ± 0.08 (8.44) C A =1.14 ± 0.16 (8.45) C V Gamow-Teller 14 O G β C V =(1.403 ± 0.003) 10 49 erg cm 3 (8.46) G β G β C V 1eV J p e p ν dω = ξ G β (π) 5 c 5 h 7 (E 0 E e ) p e E e de e dˆp e dˆp ν [ 1+a c p e p ν E e E ν + A cj p e E e + B cj p ν E ν + D c J (p e p ν ) E e E ν ] (8.47) [13] A B D - -
174 8 ξ C A C V ξ = M F C V + M GT C A a = C V C A ξ } A = Re( C A + C V C A ) D = Im(C V C A ) B ξ ξ (8.48) C V C A V A (C A C V ) J p ν p e V + A J p e J p ν Burgy 8.4 [14] 8.4 A 0.114 ± 0.019 B +0.88 ± 0.15 D +0.04 ± 0.05 a 0.09 ± 0.11 D 0 (175 ± 10) A B C V C A C A C V =1.5 ± 0.05 (8.49) a 14 O V A V (C A /C V )A V A V A γ 5 γ µ ψ e γ µ (1 γ 5 ) ψ ν = ψ e (1 + γ 5 ) γ µ ψ ν γ 5 γ µ 1 γ 5
8.4 175 8.4 8.4.1 γ ρ V = g V k t (k) δ(r r k ) j A = g A k t (k) σ k δ(r r k ) (8.50) g V g A 4 t p t n =1 (8.50) 0 p/m [ 1 j V = g V t (k) Mc {p k δ(r r k )+δ(r r k ) p k } k + h ] Mc µ β σ k δ(r r k ) (8.51) 1 ρ A = g A t (k) Mc [ p k σ k δ(r r k )+δ(r r k ) σ k p k ] k j V µ β A =1 µ β µ β = µ p µ n =4.706 (8.5) µ p µ n 8.4. Hamiltonian r ρ j δ(r r k ) 4 C V, C A g V g A
176 8 q 1 = h/p 10 fm exp(iq r) Bessel j λ (qr) r qr 1 M(ρ, λµ) = r λ Y λµ ( r) ρ(r)dr (8.53) M(j, λµ) = r κ [ Y κ ( r) j(r)] λµ dr ρ j [ Y κ ( r) j(r)] λµ Clebsch-Gordan λ = κ 1, κ, κ +1 forbiddenness r r n π n = r + (8.54) π =( 1) n (8.55) n =0 n 1 n (8.53) λ J i J f J i J f λ J i + J f (8.56) 8.5 log ft t f (8.6) 8.6 (8.50) (8.51) M(ρ V,λµ) = g V t (k)r λ k Y λµ ( r k ) (8.57) k M(j A, κλµ) = g A t (k)r κ k [ Y κ ( r k )σ k ] λµ (8.58) M(ρ A,λµ) = g A 1 Mc k t (k)( σ k p k ) r λ k Y λµ ( r k ) (8.59) k
8.4 177 [15] 8.5 L J π log ft Fermi 0 0 no 3 Gamow-Teller 0 1 no 3-6 1 0,1, yes 6-10 1,, 3 no 11-15 3,3,4 yes 16-0 4 3, 4, 5 no 1-1 n p 3 H 3 1 He 8.6 J π i J π f log ft + 1 + + 1 + F GT 3.0 614.8 s F GT 3.0 1.33 y 6 He 6 Li 0 + 1 + GT.8 0.8067 s 14 O 14 N 0 + 0 + F 3.5 71.08 s 64 Cu 64 Ni 1 + 0 + GT 5.0 1.0 h 38 Cl 38 Ar 0 + 9. 1.08 h 39 Ar 39 K 7 3 + 10.1 69 y 10 Be 10 B 0 + 3 + 13.4 1.51 10 6 y Na Ne 3 + 0 + 15.1 6.8 10 3 y + 5 + 97 Tc 97 Mo 9 13.0.6 10 6 y 40 K 40 Ca 4 0 + 19.7 1.430 10 9 y 87 Rb 87 Sr 3 9 + 113 Cd 113 In 1 + 9 + 115 In 115 Sn 9 + 1 + 17.5 4.75 10 10 y 3. 9.3 10 15 y.5 4.41 10 14 y
178 8 8.5 8.5.1 Fermi 8.17 µ µ ± π ± n ν µ e νµ ν e e νµ ν e π 0 e ν e π 0 e ν e p µ µ µ π π 8.17: µ µ ± π ± µ e µ µ Hamiltonian (8.4) H µ = G ] β [(ψ νµ γ µ (1 γ 5 )ψ µ )(ψ n γ µ (C V C A γ 5 )ψ p )+h.c. (8.60) G β µ µ ± Hamiltonian H µ = G ] µ [(ψ e γ µ (1 γ 5 )ψ νe )(ψ νµ γ µ (1 γ 5 )ψ µ )+h.c. (8.61) G µ H µ µ ω(µ e + ν µ + ν e )= G µ m µ 5 c 4 µ 4(π) 3 h 7 (8.6) G µ =(1.435 ± 0.001) 10 49 erg cm 3 (8.63) Hamiltonian G β C V %
8.5 179 Hamiltonian λ = C A /C V eν e J (N) µ = g N ψ p γ µ (1 λγ 5 )ψ n J (e) µ = g e ψ νe γ µ (1 γ 5 )ψ e µν µ J (µ) µ = g µ ψ νµ γ µ (1 γ 5 )ψ µ (8.64) β µ µ µ e + ν µ + ν e (8.64) Hamiltonian 8.7 β J (N)µ J µ (e) G β C V / =g N g e µ J (N)µ J µ (µ) G βc V / =g N g µ µ J (e)µ J µ (µ) G µ / =g µ g e g N g e g µ (8.65) µ λg N g e g µ (8.66) e-µ-τ l c µ = ψ e γ µ (1 γ 5 )ψ νe + ψ µ γ µ (1 γ 5 )ψ νµ + ψ τ γ µ (1 γ 5 )ψ ντ (8.67) µ τ 8.17 π ± h c µ Fermi H W (x) = G F J cµ (x) Jµ c (x) (8.68) J c µ (x) = lc µ + hc µ (8.69)
180 8 G F π ± l cµ h c µ h cµ l c µ µ ± l cµ l c µ h cµ h c µ Fermi 4Fermi 8.5. (8.67)-(8.69) V A G F (Conserved Vector Current : CVC) 8.18 p γ p n π π γ p e ν e p p π 0 e π ν e p p n n 8.18: π + 0 π + Dirac π + π + π + e µ J EM µ = 0 (8.70) t Q = t d 3 x J0 EM = d 3 x k Jk EM = ds k J EM k (8.71)
8.5 181 0 V µ µ V µ = 0 (8.7) n p + e + ν e π π π π 0 + e + ν e (8.73) π J π =0 π (8.73) Fermi 14 O ft- π π π µ + ν µ (8.74) (8.73) 10 8 π 8.18 Gamow-Teller Fermi C A C V Partially Conserved Axial-vector Current : PCAC π (8.74) J π =0 π 0 π π m π c 140 MeV
18 8 p e ν e π n 8.19: π 8.19 π Goldberger Treiman [16] C A C V = gπ g πnn m p + m n (8.75) g π π g πnn π m p m n C A /C V g πnn Goldberger-Treiman g π 10% π
8.6 183 8.6 8.6.1 Fermi µ 8.0 Λ ν µ e ν e p e νe p e νe µ n Λ 8.0: µ Λ J (Λ) µ = g Λ ψ p γ µ (1 λ γ 5 )ψ Λ (8.76) (8.64) 8.0 8.8 µ J (µ)µ J µ (e) g µ g e = G µ / Λ J (N)µ J µ (e) J (Λ)µ J µ (e) g N g e = G µ C V / g Λ g e g e g µ g N g Λ g µ g N % g µ = g N [1 + (0.0 ± 0.00)] (8.77)
184 8 Λ g Λ 0. g N (8.78) Λ g µ = g N + g Λ (8.79) 8.6. J µ (N) = g N ψ p γ µ (1 λγ 5 )ψ n π (8.73) π π 0 + e + ν e ( ) J µ (π) = g π ( µ φ 0 )φ φ 0 ( µ φ ) (8.80) c h φ 0 π 0 φ π ± π (8.73) (CVC) g N g π (PCAC) π π e + ν e 8.19 (8.73) π (8.80) 1
8.6 185 8.6.3 dσ(ν e + e ν e + e ) dω = G µ E ν π c 4 h 4 (8.81) E ν l =0 dσ dω = c h 4E ν M 0 (8.8) M 0 M 0 1 (8.8) (8.81) (8.8) M 0 =1 E ν = ( π c 3 h 3 ) 1/ 300 GeV (8.83) G µ W ± 100 GeV W ± W ±
186 8 8.7 8 1. J. Chadwick, Verhandl. Deut. Physik 16 (1919) 383. W. Pauli, Handbuch derphysik, vol. xxiv (1931) 1 3. E. Fermi, Z. Phys. 88 (1934) 161 4. L.M. Langer, R.D. Moffat and H.C. Price, Phys. Rev. 76 (1949) 175 G.E. Owen and C.S. Cook, Phys. Rev. 76 (1949) 176 C.S. Wu and R.D. Albert, Phys. Rev. 75 (1949) 315 5. F. Reines and C.L. Cowan, Jr., Phys. Rev. 90 (1953) 49, Phys. Rev. 113 (1959) 73 6. M. Goldhaber, L. Grodzins and A.W. Sunyar, Phys. Rev. 109 (1958) 1015 7. Z. Vylov et al, Izv. Akad. Nauk (USSR) ser. fiz. 48 (1984) 1809 8. H. Frauenfelder, R. Bobone, E.V. Goeler, N. Levine, H. Lewis, R. Peacock, A. Rossi and G. DePasquali, Phys. Rev. 106 (1957) 386; Ullman, Fauenfekler, Lipkin and Rossi, Phys. Rev. 1 (1961) 536; A.R. Brosi, A.I. Galonsky, B.H. Ketelle and H.B. Willard, Nucl. Phys. 33 (196) 353 9. T.D. Lee and C.N. Yang, Phys. Rev. 104 (1956) 54 10. C.S. Wu, E. Ambler, R.W. Hayward, D.D. Hoppes and R.F. Hudson, Phys. Rev. 105 (1957) 1413 11. G. Gamow and E. Teller, Phys. Rev. 49 (1936) 895 1. J. Allen, R. Burman, W. Hermannsfeldt, P. Stähelin and T. Braid, Phys. Rev. 116 (1959) 134; C.H. Johnson, F. Pleasonton and T.A. Carlson, Phys. Rev. 13 (1963) 1149 13. J.D. Jackson, S.B. Treiman and H.W. Wyld, Phys. Rev. 106 (1957) 517 14. M.T. Burgy, V.E. Krohn, T.B. Novey, G.R. Ringo and V.L. Telegdi, Phys. Rev. Lett. 1 (1958) 34, Phys. Rev. 10 (1960) 189 15. E.J. Konopinski and G.E. Uhlenbeck, Phys. Rev. 60 (1941) 308, E.J. Konopinski and M.E. Rose, in Alpha-, Beta- and Gamma-Ray Spectroscopy, ed. K. Siegbahn, Vol., (North-Holland, Amsterdam, 1965) 16. M.L. Goldberger and S.B. Treiman, Phys. Rev. 110 (1958) 1178, 1478