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1 71 7 3,000 1 MeV t = 1 MeV = c 1 MeV c 200 MeV fm 1 MeV fm/s s (1) 1fm t = 1fm c 1fm fm/s s (2) s 7.1 ( ) a + b + B(+X +...) (3) a b B( X,...) 2 (a, b)b (4) Q Q (M a + M )c 2 (M b + M B + M X +...)c 2 =( ) ( ) (5) Q>0 Q<0 (decay) a Q >0 ( ) Q>0 (2 ) b(+...) t N(t) dn = λn(t)dt N(t) =N(0)e λt (6)

2 72 7. λ (decay constant) (decay rate) ( 1/e )τ ( )T λ τ = 1 log 2, T = τ log 2 = (7) λ λ 1 (Becquerel):Bq 1 (1 Bq=1 s 1 ) (Curie):Ci -226( 226 Ra)1 1 1 Ci= Bq SI τ τ (N 1 ) τ= 2 α- ( 4 He ) β- () ( ) γ- ( ) ( ) (proton/neutron-decay) () ( ) (fission) (N, Z) (N, Z) ( ) τ tot > (5 = s)

3 7.2. (proton/neutron-decay) 73 Experimental Chart of Nuclides isotopes Half-life Range Unknown <0.1 s s s 100 s - 1 h 1 h - 1 y 1 y - 1 Gy Stable 1: (N) (Z) ( ) (S n,s p > 0 ) τ 1,τ 2,... τ tot ( λ tot ) 1 = , τ tot τ 1 τ 2 (λ tot = λ 1 + λ ) (8) 7.2 (proton/neutron-decay) (N, Z) (separation energy) S p S n S p (N, Z)=[M(N, Z 1) + m p ] M(N, Z) =E B (N, Z) E B (N, Z 1) E B Z N S n (N, Z)=[M(N 1,Z)+m n ] M(N, Z)=E B (N, Z) E B (N 1,Z) E (9) B N Z E B (proton-decay) (N, Z) (N, Z 1) + p (10)

4 74 7. Q p Q p M (N, Z)c 2 [M 1 (N, Z 1) + m p ] c 2 = [Nm n + Zm p M (N, Z)]c 2 +[Nm n +(Z 1)m p M 1 (N, Z 1)]c 2 }{{}}{{} E B (N,Z) E B (N,Z 1) = S p (N, Z) (11) S Q () B-W EB BW (N, Z)=a V a S 2/3 Z 2 a C 1/3 a (N Z) 2 a (12) 2 N Z 2 S p (N, Z)=a V a S 3(N + Z) 1/3 a Z(6N +5Z) C 3(N + Z) 4/3 + a (N Z)(3N + Z) a 2(N + Z) 2 2 S n (N, Z)=a V a S 3(N + Z) 1/3 + a C 3(N + Z) 4/3 a (N Z)(N +3Z) a 2(N + Z) 2 Z 2 (13) S p < 0 S n < 0( Q>0 ) (N, Z) S p (N, Z) =0, S n (N, Z) = 0 (14) Z N (N, Z) Z- N- (drip line) ( (drip )) s 2: (S p =0 S n =0 ) = N + Z ( ) Z 2 / =45

5 7.3. γ- 75 S p < 0 S p α- 7.3 γ- γ- (N, Z) MeV X γ- γ- (electro-magnetic transition) τ( ) s (100 ps 1 fs) (15) (isomer) 3: γ β 60 Co E max =0.31 MeV β β 1.17 MeV 1.33 MeV 2 γ 60 Ni β γ 7.4 β- β- ( ) β - n p + e + ν e Q = MeV β + - p n + e + + ν e Q = MeV p + e n + ν e Q = MeV ν e ν e (neutrino) (antineutrino) 0 ( Q

6 ) 3 β- β - (N, Z) (N 1,Z+1) β + - (N, Z) (N +1,Z 1) β + (Q MeV ) β + β- β- (m e ) (m n m p ) β- β- = N + Z =0 N = Z (16) β - Q β = E B (N 1,Z+1) E B (N, Z) E B N β + - Q β + = E B (N +1,Z 1) E B (N, Z) E B Z =+ E B Z =+ E B N β ± - β- E B Z = 0 (17) B-W E B 2Z Z = a C 1/3 +2a ( 2Z) a = 0 (18) Z Z = ) 2+( ac aa 2/ /3 (19) (N, Z) β- β- (Fermi) ( s) 4 β- ( ) β- γ s( 9 ) 14 C 5,730

7 7.4. β- 77 (m e ) (m n m p ) β- β - Q β E B N + Q 0, Q β 0 =(m β n m p m e )c 2 β + - Q β + E B Z + Q 0 β, Q 0 + β =(m + p m n m e )c 2 β- β- M(N, Z) (N, Z) β- ( = N + Z ) β- (Heisenberg) 4: (a) (N, Z) 3 ( ) (b) 56 Fe β- [N : (even),z : (odd)] [N : (odd),z : (even)] (20) [N : (even),z : (even)] [N : (odd),z : (odd)] β- β-

8 78 7. β- 1 (even-odd/odd-even) 1 ( ) β- 2 (even-even) 1 3 β- 3 (odd-odd) ( M(N, Z) 5 ) β- 4 (odd-odd) β ± N + Z = (even-odd/odd-even) ( β ± ) (even-even/odd-odd) 2 (β ± 2 ) 5 5: Z ( ) β ± 1 N = Z 2 ( ) β ± 2 2 ( ) 5 2 H, 6 Li, 10 B, 14 N 4 60%

9 7.5. α α- α 28 MeV 8 MeV α : 28 MeV < 4 8 MeV = 32 MeV (21) α (N, Z) (N 2,Z 2) + α (22) Q α =[E B (N 2,Z 2) + E B (α)] E B (N, Z) (23) E B (α) Q α > 0 β- (U) (Th) α- β- (decay chain) 6: ( ) ( ) α- β- α, β, γ ( ) ( MeV) α (G.Gamov)

10 80 7. α ( ) ( ) α V α (r) V α (r) ( V 0 ) α (1/r) V α (r) ( ) α-e α > 0 α α ( ) ( ) 1928 α- 7: α- α ( ) α ( ) Q 7.6 (WKB ) 1 WKB WKB λ [ ] 2W (E) λ(e)=λ 0 (E) exp = λ 0 (E)P (E), P(E) exp [ ] 2W (E) (24)

11 7.6. (WKB ) 81 λ 0 (E) E 1 P (E) (transmission coefficient) (penetration factor) W (E) (action integral) W (E)= xf (E) x i (E) p(x, E)dx, p(x, E)= 2M(V (x) E) (25) x i (E) x f (E) V (x) =E (26) (turning point) (imaginary time) H H = p2 2M + V (x) =E( ) (27) V (x) E (28) p 2 =2M(E V (x)) 0 (29) τ τ it p M dx dτ (30) p WKB E τ =1/λ + :α- 6 α ( R) V 0 r<r V (r) = BR (31) r R r α- BR =2(Z 2)e 2 2Ze 2 (Z 1 ) (32) 6 G.Gamov,1928.

12 82 7. α S ( l =0) α- α 5 MeV B (E α B) ( ) µb B W (E α )=R π 4 = const. + π 2µ 2 E α 2 BR (33) E α µ α E α α α µ 4 ( 4) 4+( 4) m Nc 2 4m N c 2 m α (34) α m α BR =2Ze 2 ( ) log τ = log λ const. + 2πe2 Z 2mα Eα (35) (WKB λ 0 (E) ) τ Z/ E α α- α 2πe 2 ( ) Z 2mα Eα 2π e2 c 2mα c 2 Z Eα 2π 1 Z 2 3, 700 Eα 4.0 Z (36) 137 Eα U(Z = 92) E α =5 MeV 10 MeV log 10 τ =0.434 logτ 21 (α- Z) : 1 V (r) =B 1 2 µω2 x 2 (37) ( ) () W (E)= π(b E) ω ( (barrier) )(B E) (38)

13 7.7. (fission) (fission) E B / (parent nucleus) (daughter nucleus) (N, Z) (N 1,Z 1 ) (N N 1,Z Z 1 ) 7 (N, Z) (N 1,Z 1 )+(N N 1,Z Z 1 ) (39) Q fission =[E B (N 1,Z 1 )+E B (N N 1,Z Z 1 )] E B (N, Z) (40) (symmetric fission) N 1 N 2, Z 1 Z 2 (41) E B / 1 MeV 200 MeV ev/ B-W ( N Q fission =2 E B 2, Z ) E B (N, Z) 2 ( ) ] [ 2/3 a S [ 2/3 2 + a C 2 = a S 2/3 (1 2 1/3 )+a C Z 2 Z 2 1/3 2 1/3 (1 2 2/3 ) ( Z 2 ) 2 / ( ) ] 1/3 2 (42) Q fission > 0 (43) f Z2 > 21/3 1 as 17.4 (44) 1 2 2/3 a C f ( ) (fissility parameter) β- > (binary fission) 3

14 U 146 Q 177 MeV, f = Z (45) ( R)[] (a = R(1 + ɛ),b= R(1 ɛ/2))[b] E B = a S (1+ 2/3 2 ) 5 ɛ (46) E B = a C Z 2 1/3 ( 1 1 ) 5 ɛ ɛ E B = (2a ɛ2 S 2/3 Z 2 ) a C 5 1/3 (47) (48) E B > 0 ( ) Z 2 > 2a S a C 49 (49) [D] E B 170 MeV (Ze/2) 2 /r

15 7.7. (fission) 85 8: WKB log τ = log λ const. + 2π B E ω (50) ω ( ω 1 MeV ) (fission barrier) (B E) MeV ( ) U Th MeV α, β-

16 ( ) ( ) µb B W (E α )=R π 4 2 E α (51) E α B ( ) 2. ( ) W (E) = π(b E) ω (52) ( ) 3. β- Z = ) 2+( ac aa 2/ /3 (53) 4. f Z2 > 21/ /3 as a C 17.4 (54)

23 1 Section ( ) ( ) ( 46 ) , 238( 235,238 U) 232( 232 Th) 40( 40 K, % ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4

23 1 Section ( ) ( ) ( 46 ) , 238( 235,238 U) 232( 232 Th) 40( 40 K, % ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4 23 1 Section 1.1 1 ( ) ( ) ( 46 ) 2 3 235, 238( 235,238 U) 232( 232 Th) 40( 40 K, 0.0118% ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4 2 ( )2 4( 4 He) 12 3 16 12 56( 56 Fe) 4 56( 56 Ni)