Chadwick [ 1 ] 1919,, electron number Q kinetic energy [MeV] 8.1: 8.1, 1 internal conversion electron E γ E e =

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1 Chadwick [ 1 ] 1919,, electron number Q kinetic energy [MeV] 8.1: 8.1, 1 internal conversion electron E γ E e = E γ φ φ E e X 153

2 154 8, 3 H 3 He, ( ) 3 H( 1 ) 3 He( 1 )+e ( 1 ) 3 H 1 3 He 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

3 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)

4 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] K( ε ) [arbitrary] kinetic energy [MeV] kinetic energy [MeV] 8.3: Kurie plot β + β 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

5 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 ) kinetic energy [kev] 8.4: Kurie plot, m ν = 0.0 kev, 0. kev, 0.5 kev 0. kev (8.6) ε

6 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)

7 e + + e γ + γ (8.10) 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 z z z Gamow-Teller. l =0 1s 1/

8 160 8 Sm γ Eu 0 Eu Sm Sm ν ν 15 Sm : Goldhaber 15 Eu 15 Sm 15 Sm 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 Eu m 15 Sm (1 ) 15 Sm (1 ) τ m =0.03 ps 15 Sm z Sm Sm 1 Goldhaber Sm O Sm 15 Sm

9 h ν = h γ (8.13) h γ h ν Goldhaber 15 Sm m γ = 1 z h γ = 1 h ν = σ ν p ν p ν = 1 (8.14) 0.67 ± 0.15 h ν = Vylov h ν = 0.93 ± 0.10 [7] β h ν =+1 h e = ±1 v [8] ν ν e e v c + v c

10 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 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) L 1( 1) L =( 1) L 1+L +1 τ J = L 1 L L 1 L 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

11 x x, y y, z z (8.16) r p E J σ B E B E B E B Lee Yang[9] 198 v e σ e 0 e ν σ e p e p ν σ ν J 8.8: 8.8

12 164 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) Co % 60 Ni 4 + (.84) 5 60 Co 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)

13 J θ =0 θ = π 1.3 counting rate H H time [min] 8.11: 60 Co Wu 60 Co θ =0 θ = π 8.11 Counting rate

14 Fermi 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 ( ) ( i σ 1 =, σ = 1 0 i 0 ), σ 3 = ( ) (8.3) Pauli x µ =(x 0, x) x µ =(x 0, x) g µν = g µν = (8.4) 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)

15 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 +

16 168 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 ] Lorentz ψ ψ 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 Fermi Gamow-Teller L =0 π =0 S S =0 Fermi J =0 Fermi Fermi isobaric analog state,

17 8.3 4 Fermi 169 (5.143) O (3.508) He N Li : Fermi Gamow-Teller 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 = : 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)

18 170 8 χ ± Pauli ( ) ( 1 0 χ + =, χ = 0 1 ) (8.8) ± σ ˆp χ ± = ±χ ± (8.9) γ 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

19 8.3 4 Fermi 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 Fermi Gamow-Teller Lee Yang

20 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)

21 8.3 4 Fermi 173 Fermi IAS Fermi T ± Gamow-Teller O M F M GT ft [s] n p ± O 14 N ± 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) 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 - -

22 174 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 ± B ± 0.15 D ± 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

23 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

24 176 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

25 [15] 8.5 L J π log ft Fermi 0 0 no 3 Gamow-Teller 0 1 no ,1, yes ,, 3 no ,3,4 yes , 4, 5 no 1-1 n p 3 H 3 1 He 8.6 J π i J π f log ft F GT s F GT y 6 He 6 Li GT s 14 O 14 N F s 64 Cu 64 Ni GT h 38 Cl 38 Ar h 39 Ar 39 K y 10 Be 10 B y Na Ne y Tc 97 Mo y 40 K 40 Ca y 87 Rb 87 Sr Cd 113 In In 115 Sn y y y

26 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) erg cm 3 (8.63) Hamiltonian G β C V %

27 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)

28 180 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)

29 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

30 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

31 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) 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)

32 184 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

33 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 ±

34 J. Chadwick, Verhandl. Deut. Physik 16 (1919) 383. W. Pauli, Handbuch derphysik, vol. xxiv (1931) 1 3. E. Fermi, Z. Phys. 88 (1934) 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) F. Reines and C.L. Cowan, Jr., Phys. Rev. 90 (1953) 49, Phys. Rev. 113 (1959) M. Goldhaber, L. Grodzins and A.W. Sunyar, Phys. Rev. 109 (1958) Z. Vylov et al, Izv. Akad. Nauk (USSR) ser. fiz. 48 (1984) 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) T.D. Lee and C.N. Yang, Phys. Rev. 104 (1956) C.S. Wu, E. Ambler, R.W. Hayward, D.D. Hoppes and R.F. Hudson, Phys. Rev. 105 (1957) G. Gamow and E. Teller, Phys. Rev. 49 (1936) 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) J.D. Jackson, S.B. Treiman and H.W. Wyld, Phys. Rev. 106 (1957) 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) 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

Einstein 1905 Lorentz Maxwell c E p E 2 (pc) 2 = m 2 c 4 (7.1) m E ( ) E p µ =(p 0,p 1,p 2,p 3 )=(p 0, p )= c, p (7.2) x µ =(x 0,x 1,x 2,x

7 7.1 7.1.1 Einstein 1905 Lorentz Maxwell c E p E 2 (pc) 2 = m 2 c 4 (7.1) m E ( ) E p µ =(p 0,p 1,p 2,p 3 )=(p 0, p )= c, p (7.2) x µ =(x 0,x 1,x 2,x 3 )=(x 0, x )=(ct, x ) (7.3) E/c ct K = E mc 2 (7.4)