log N ( t ) t 1/2 τ m 2τ m time t 4.1: λ decay rate λ = 1 τ m (4.8) A B b Γ = h τ m = hλ (4.9) A B + b (4.10) Q Q = M(B)+M(b) M(A) (4.11)
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1 4 4.1 t N(t) t t +dt dn(t) N(t) dn(t) = λn(t)dt (4.1) dn(t) dt = λn(t) (4.2) t =0 N 0 = N(0) 4.1 N(t) =N 0 e λt (4.3) log N(t) = log N 0 λt (4.4) mean life half-life t N(t) τ m =1/λ 1/e τ m 1/2 t 1/2 T 1/2 : N(t + τ m ) = 1 N(t + t 1/2 ) = 1 (4.5) N(t) e N(t) 2 e e= (4.6) t 1/2 = τ m log e 2=0.693 τ m (4.7) 55
2 log N ( t ) t 1/2 τ m 2τ m time t 4.1: λ decay rate λ = 1 τ m (4.8) A B b Γ = h τ m = hλ (4.9) A B + b (4.10) Q Q = M(B)+M(b) M(A) (4.11) Q Q = T B + T b (4.12) A T B + T b Q 4.2 exp (iht/ h) E R E = E R + iγ 2 (4.13)
3 count Γ Q T B + T b 4.2: exp (i Ēh ) [ ( t ER = exp i h + iγ )] = exp 2 h ( i E ) R h t exp ( Γ ) 2 h (4.14) ( exp i Ē ) 2 h t = exp ( Γ h ) t = exp ( λt) (4.15) (4.2) (4.9) Planck [1] h = (82) Js (4.16) = (26) MeV s τ m Γ 4.3 A =8 8 Be 8 Be J π =0 + Γ =8.8 ± 1.7 ev τ m =(7.5 ± 1.4) s J π =2 + Γ =1.50 ± 0.02 MeV τ m =(4.39 ± 0.06) s J π =4 + Γ 3.5 MeV τ m s A = B β +
4 Li β β 8 5B α [ MeV ] 4 4 2He + 2He α α 8 4Be : 8 Be disintegration proton decay
5 β β e ν e β + e + ν e β + EC: electron capture K β (A, Z) (A, Z +1)+e + ν e β + (A, Z) (A, Z 1) + e + + ν e (4.17) (A, Z)+e (A, Z 1) + ν e β β n p + e + ν e β + p n + e + + ν e (4.18) p + e n + ν e Q β Q β (A, Z) = M(A, Z) M(A, Z +1) = B(A, Z +1) B(A, Z)+(m n m H ) β + Q β +(A, Z) = M(A, Z) M(A, Z 1) 2m e = B(A, Z 1) B(A, Z) (m n m H ) 2m e (4.19) Q EC (A, Z) = M(A, Z) M(A, Z 1) = B(A, Z 1) B(A, Z) (m n m H ) β + 2m e (4.17) 2m e Q Q β + Q EC > 0 >Q β A =56 56 Fe 56 Mn β 56 Fe 56 Co β + /EC 56 Fe
6 Q β h 56 25Mn β EC β 78.8 d 56 27Co Q β Q EC 0 [ MeV ] 56 26Fe 4.4: 56 Mn β 56 Co β + /EC Q Q β Q EC β + 2m e β β s Q 4.2 β +
![8 d 56 27Co Q β Q EC 0 [ MeV ] 56 26Fe](/docs-images/41/22686483/images/page_6.jpg "4.4: 56 Mn β 56 Co β + /EC Q Q β Q EC")
7 separation energy S n S p mass excess S n (A, Z) = M(A 1,Z)+m n M(A, Z) = M(A 1,Z)+ M(1, 0) M(A, Z) = B(A, Z) B(A 1,Z) S p (A, Z) = M(A 1,Z 1) + m H M(A, Z) = M(A 1,Z 1) + M(1, 1) M(A, Z) = M(A, Z) B(A 1,Z 1) (4.20) S 2n (A, Z) = M(A 2,Z)+2m n M(A, Z) = M(A 2,Z)+2 M(1, 0) M(A, Z) = B(A, Z) B(A 2,Z) S 2p (A, Z) = M(A 2,Z 2) + 2m H M(A, Z) = M(A 2,Z 2) + 2 M(1, 1) M(A, Z) = B(A, Z) B(A 2,Z 2) (4.21) 0 S 2p S p drip line 0 proton drip line 0 neutron drip line Coulomb
8 Z =9 15 MeV 19 F N =10 Z =9 15 separation energies Sx [ MeV ] S 2p S p S n F isotopes S 2n neutron number N 4.5: Z =9 A =5 A =8 8 Be A =8 A =5 A =5 5 He 5 Li 4 He A =5 5 He Q =0.89 MeV 5 Li Q =1.97 MeV 5 He 4 He + p Γ 0.60 MeV (4.22) 5 Li 4 He + n Γ 1.5 MeV s
9 B ( A,Z ) / A [ MeV ] He He Li Be B C O N 1 0 H mass number A 4.6: Z /2 1/ [ MeV ] 4 2He + n 5 2He 3/2 5 3Li 3/2 4 2He + p 4.7: A =5 pairing energy J π =0 + P n (A, Z) = 1 4 ( 1)A Z+1 [ S n (A +1,Z)+S n (A 1,Z) 2S n (A, Z)] P p (A, Z) = 1 4 ( 1)Z+1 [ S p (A +1,Z +1)+S p (A 1,Z 1) 2S p (A, Z)] (4.23)
![6: Z 8 10 8 6 1/2 1/2 4 2 0 [ MeV ] 4 2He + n 5 2He 3/2 5 3Li 3/2 4 2He + p 4.](/docs-images/41/22686483/images/page_9.jpg "7: A =5 pairing energy J π =0 + P n (A, Z) = 1 4 ( 1)A Z+1 [ S n (A +1,Z)+S n (A 1,Z) 2S n")
10 A 200 α S α (A, Z) = M(A 4,Z 2) + M(4, 2) M(A, Z) = B(A, Z) B(A 4,Z 2) B(4, 2) (4.24) M(4, 2) = M( 4 He) Q Q α (A, Z) = S α (A, Z) (4.25) B(4, 2) = B( 4 He) = MeV (4.26) 4.6 S α (A, Z) < Q α (A, Z) = S α (A, Z) > 0 A Po 210 Pb 214 Po 210 Pb + α (4.27) 214 Po S = 210 Pb α 214 Po 2 (4.28) spectroscopic factor Coulomb 4.9
11 proton number Z neutron number N 4.8: S α (A, Z) < 0 Coulomb potential 0 S α α r potential quantum mechanical penetration of the α wave function through the Coulomb barrier nuclear potential 4.9: Coulomb
12 66 4 Coulomb R V (r) Coulomb V (r) > 0 Coulomb 4.9 S α (> 0) V (r) ( S α ) > 0 L =0 s Schrödinger Coulomb [ 8m exp h V (r) E dr ] (4.29) V (r) 4.9 E = S α V (r) E 0 Coulomb 210 Po µs y 232 Th y 25
![Coulomb [ 8m exp h V (r) E dr ] (4.29) V (r) 4.](/docs-images/41/22686483/images/page_12.jpg "9 E = S α V (r) E 0 Coulomb 210 Po 0.")
13 (A, Z) (A 1,Z 1 )+(A 2,Z 2 ) { A = A1 + A 2 Z = Z 1 + Z 2 (4.30) Q Q = B(A 1,Z 1 )+B(A 2,Z 2 ) B(A, Z) (4.31) A 1 /A = Z 1 /Z A 2 /A = Z 2 /Z A 1 = A 2 Q Q >0 Z 2 /A Z2 /A > 0.35 (4.32) 2b surf /b Coul 50 Z 2 /A > half life [ y ] Th 230 spontaneous fission U Pu Cm Z = 90 Thorium Z = 92 Uranium Z = 94 Plutonium 246 Z = 96 Curium 252 Cf 10 0 Z = 98 Californium Z = 100 Fermium Fm Z 2 / A 4.10: 90 Z 100
![10 half life [ y ] 10 20 232 Th 230 spontaneous fission 234 10 15 238 U 236 232 242 10 10 238 Pu 244 240 236 Cm Z = 90 Thorium 246 242](/docs-images/41/22686483/images/page_13.jpg "10 5 244 240 Z = 92 Uranium 250 248 Z = 94 Plutonium 246 Z = 96 Curium 252 Cf 10 0 Z = 98 Californium 254 254 Z = 100 Fermium Fm 10-5")
14 MeV M(Eλ) = ρ(r) r λ Y λµ ( r)dr 1 (4.33) M(Mλ) = j(r) (r ) r λ Y λµ ( r)dr c(λ +1) M(Eλ) ρ(r) M(Mλ) c 1/2 J 1 J 2 hcq T (E(M)λ) = B(E(M)λ) = 8π(λ +1) q 2λ+1 λ[(2λ + 1)!!] 2 h B(E(M)) (4.34) 1 2J 1 +1 J 2 M(E(M)λ) 2 B(E(M)λ) λ J 1 J 2 λ J 1 + J 2 (4.35) Eλ ( 1) λ Mλ ( 1) λ+1 λ E1 M2 E3 E M1 E2 M3 M3
![T (E(M)λ) = B(E(M)λ) = 8π(λ +1) q 2λ+1 λ[(2λ + 1)!!] 2 h B(E(M)) (4.](/docs-images/41/22686483/images/page_14.jpg "34) 1 2J 1 +1 J 2 M(E(M)λ) 2 B(E(M)λ) λ J 1 J 2 λ J 1 + J 2 (4.")
15 s [4] proton number Z neutron number N 4.11:
16 70 4 [ 5-20 ] [4]
![[4]](/docs-images/41/22686483/images/page_16.jpg)
17 D.E. Groom et al., European Physical Journal C15 (2000) 1, available on the Particle Data Group WWW page (URL ) 2. Table of Isotopes, Eighth Edition, R.B. Firestone, Ed. V.S. Shirley, (John Wiley and Sons, Inc., New York, 1996) 3. Ajzenberg-Selove, Nucl. Phys. A490 (1988) 1 4. H. Koura, M. Uno, T. Tachibana and M. Yamada, Nucl. Phys. A674 (2000) 47, Nuclear mass formula with shell energies obtained by a new method and its application to superheavy elements 5. P.E. Austein, Atomic Data and Nuclear Data Tables, 39 (1988) 185, An Overview of the atomic mass prediction 6. A. Pape and M.S. Antony, Atomic Data and Nuclear Data Tables, 39 (1988) 201, Masses of proton-rich T z < 0 nuclei via the isobaric mass equation 7. G. Dussel, E. Caurier and A.P. Zucker, Atomic Data and Nuclear Data Tables, 39 (1988) 205, Mass predictions based on α-line systematics 8. P. Möller and J.R. Nix, Atomic Data and Nuclear Data Tables, 39 (1988) 213, Nuclear masses from a unified macroscopic-microscopic model 9. P.Möller, W.D. Myers, W.J. Swiatecki and J.Treiner, Atomic Data and Nuclear Data Tables, 39 (1988) 225, Nuclear mass formula with a finite-range droplet model and a folded-yukawa single-particle potential 10. E. Comay, I. Kelson and A. Zidon, Atomic Data and Nuclear Data Tables, 39 (1988) 235, Mass predictions by modifed ensemble averaging 11. L. Satpathy and R.C. Nayak, Atomic Data and Nuclear Data Tables, 39 (1988) 241, Masses of atomic nuclei in the infinite nuclear matter model 12. T. Tachibana, M. Uno, M. Yamada and S. Yamada, Atomic Data and Nuclear Data Tables, 39 (1988) 251, Empirical mass formula with proton-neuton interaction 13. L. Spanier and S.A.E. Johansson, Atomic Data and Nuclear Data Tables, 39 (1988) 259, A modified Bethe-Weizsäcker mass formula with deformation and shell corrections and few free parameters 14. J. Jänecke and P.J. Masson, Atomic Data and Nuclear Data Tables, 39 (1988) 265, Mass predictions from the Garvey-Kelson mass relations 15. P.J. Masson and J. Jänecke, Atomic Data and Nuclear Data Tables, 39 (1988)
18 , Masses from an inhomogeneous partial differential equation with higher order isospin contributions 16. A.H. Wapstra, G. Audi and R. Heokstra, Atomic Data and Nuclear Data Tables, 39 (1988) 281, Atomic masses from (mainly) experimental data 17. P. Möller, J.R. Nix, W.D. Myers and W.J. Swiatecki, Atomic Data and Nuclear Data Tables, 59 (1995) 185, Nuclear ground-state masses and deformations 18. Y. Aboussir, J.M. Pearson, A.K. Dutta and F. Tondeur, Atomic Data and Nuclear Data Tables, 61 (1995) 127, Nuclear mass formula via an approximation to the Hartree-Fockmethod 19. G.A. Lalazissis, S. Raman an P. Ring, Atomic Data and Nuclear Data Tables, 71 (1999) 1, Ground-state properties of even-even nuclei in the relativistic mean-field theory 20. R.C. Nayakand L. Satpathy, Atomic Data and Nuclear Data Tables, 73 (1999) 213, Mass predictions in the infinite nuclear matter model
42 3 u = (37) MeV/c 2 (3.4) [1] u amu m p m n [1] m H [2] m p = (4) MeV/c 2 = (13) u m n = (4) MeV/c 2 =
![42 3 u = (37) MeV/c 2 (3.4) [1] u amu m p m n [1] m H [2] m p = (4) MeV/c 2 = (13) u m n = (4) MeV/c 2 =](/thumbs/73/68712188.jpg "42 3 u = (37) MeV/c 2 (3.4) [1] u amu m p m n [1] m H [2] m p = (4) MeV/c 2 = (13) u m n = (4) MeV/c 2 =")
3 3.1 3.1.1 kg m s J = kg m 2 s 2 MeV MeV [1] 1MeV=1 6 ev = 1.62 176 462 (63) 1 13 J (3.1) [1] 1MeV/c 2 =1.782 661 731 (7) 1 3 kg (3.2) c =1 MeV (atomic mass unit) 12 C u = 1 12 M(12 C) (3.3) 41 42 3 u
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71 7 3,000 1 MeV t = 1 MeV = c 1 MeV c 200 MeV fm 1 MeV 3.0 10 8 10 15 fm/s 0.67 10 21 s (1) 1fm t = 1fm c 1fm 3.0 10 8 10 15 fm/s 0.33 10 23 s (2) 10 22 s 7.1 ( ) a + b + B(+X +...) (3) a b B( X,...)
6. [1] (cal) (J) (kwh) ( 1 1 100 1 ( 3 t N(t) dt dn ( ) dn N dt N 0 = λ dt (3.1) N(t) = N 0 e λt (3.2) λ (decay constant), λ [λ] = 1/s 1947 2
![6. [1] (cal) (J) (kwh) ( 1 1 100 1 ( 3 t N(t) dt dn ( ) dn N dt N 0 = λ dt (3.1) N(t) = N 0 e λt (3.2) λ (decay constant), λ [λ] = 1/s 1947 2](/thumbs/41/22727315.jpg "6. [1] (cal) (J) (kwh) ( 1 1 100 1 ( 3 t N(t) dt dn ( ) dn N dt N 0 = λ dt (3.1) N(t) = N 0 e λt (3.2) λ (decay constant), λ [λ] = 1/s 1947 2")
filename=decay-text141118.tex made by R.Okamoto, Emeritus Prof., Kyushu Inst.Tech. * 1, 320 265 radioactive ray ( parent nucleus) ( daughter nucleus) disintegration, decay 2 1. 2. 4 ( 4 He) 3. 4. X 5.,
1. 2. 3. 4. 3.2 1. 2. 3. 4 4.1 1. σ f n λ f λ f = 1 nσ f. (4.1) 2. E n, m 1 generation,t g v t g = λ f v = 1 (4.2) vnσ f E = 1 2 mv2 2E v = m t g = 1
2003.3.14 1 nuclear weapon 2 1942 1942 1943 1945.7.15 8. 6 8. 9 2 3 3.1 239, 1 1. 2. 3. 4. 3.2 1. 2. 3. 4 4.1 1. σ f n λ f λ f = 1 nσ f. (4.1) 2. E n, m 1 generation,t g v t g = λ f v = 1 (4.2) vnσ f E
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)
W 1983 W ± Z cm 10 cm 50 MeV TAC - ADC ADC [ (µs)] = [] (2.08 ± 0.36) 10 6 s 3 χ µ + µ 8 = (1.20 ± 0.1) 10 5 (Ge
![W 1983 W ± Z cm 10 cm 50 MeV TAC - ADC ADC [ (µs)] = [] (2.08 ± 0.36) 10 6 s 3 χ µ + µ 8 = (1.20 ± 0.1) 10 5 (Ge](/thumbs/91/105929864.jpg "W 1983 W ± Z cm 10 cm 50 MeV TAC - ADC ADC [ (µs)] = [] (2.08 ± 0.36) 10 6 s 3 χ µ + µ 8 = (1.20 ± 0.1) 10 5 (Ge")
22 2 24 W 1983 W ± Z 0 3 10 cm 10 cm 50 MeV TAC - ADC 65000 18 ADC [ (µs)] = 0.0207[] 0.0151 (2.08 ± 0.36) 10 6 s 3 χ 2 2 1 20 µ + µ 8 = (1.20 ± 0.1) 10 5 (GeV) 2 G µ ( hc) 3 1 1 7 1.1.............................
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δf = δn I [ ( FI (N I ) N I ) T,V δn I [ ( FI N I ( ) F N T,V ( ) FII (N N I ) + N I ) ( ) FII T,V N II T,V T,V ] ] = 0 = 0 (8.2) = µ (8.3) G
![δf = δn I [ ( FI (N I ) N I ) T,V δn I [ ( FI N I ( ) F N T,V ( ) FII (N N I ) + N I ) ( ) FII T,V N II T,V T,V ] ] = 0 = 0 (8.2) = µ (8.3) G](/thumbs/91/106215968.jpg "δf = δn I [ ( FI (N I ) N I ) T,V δn I [ ( FI N I ( ) F N T,V ( ) FII (N N I ) + N I ) ( ) FII T,V N II T,V T,V ] ] = 0 = 0 (8.2) = µ (8.3) G")
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