1 2 1 a(=,incident particle A(target nucleus) b (projectile B( product nucleus, residual nucleus, ) ; a + A B + b a A B b 1: A(a,b)B A=B,a=b 2 1. ( 10 14 m) ( 10 10 m) 2., 3 1 =reaction-text20181101b.tex 2 ( ) 3 4 ( ) okamoto.ryoji.munakata at gmail.com ( at @ 3 parity ( ) ( ) ψ (x, y, z), ψ = ψ(x, y, z) (x, y, z) ( x, y, z) ψ( x, y, z) = ψ(x, y, z) ψ( x, y, z) = ψ(x, y, z) 1
3. 4. 2017 11 23 2: ( 13) 2 13 ( 13) 3 [1] 3, 2
1. elastic scattering : (n, n) (a) (b) (c) 2. inelastic scattering : (n, n ) (n, nγ) (a) (b) (c) (d) kev (e) (f) n + 238 92 U 239 92 U 238 92 U +n 238 92 U 238 92 U + γ 238 92 U(n, γ) 239 92 U β 239 93 Np β 239 94 Pu ( 239 94 Pu) (3.1) 3. (absorption): capture reaction nuclear fission (a) (capture): n, γ i. 4 ii. 4 compound nucleus 3
iii. 1 1H(n, γ) 2 1H 59 27Co(n, γ) 60 27Co 113 48 Cd(n, γ) 114 48 Cd 113 48 Cd 115 49 In(n, γ) 116 49 In 151 63 Eu(n, γ) 152 63 Eu 197 79 Au(n, γ) 198 79 Au 198 80 Hg 238 92 U(n, γ) 239 92 U 239 90 Np 239 94 Pu 235 92 U(n, γ) 236 92 U (b) : (n, p), (n, α), (n, n) i. (n, α) 10 5 B(n, α) 7 3Li + 2.5MeV: 6 3Li(n, α) 3 1H(T) + 4.78MeV: ii. (n, p) 31 15P(n, p) 31 14Si 31 15 P (c) nuclear fission): (d) : 9 4Be(γ, n) 8 4Be 9 4Be(α, n) 12 6 C 9 4Be(n, 2n) 8 4Be 4 1. 2. c 2. K i 4
E ex,i, (i = a, b, A, B) (K a + M a c 2 ) + (K A + M A c 2 ) = (K b + E ex,b + M b c 2 ) + (K B + E ex,b + M B c 2 ) (4.1) (4.1) (K b + E ex,b ) + (K B + E ex,b ) (K a + K A ) = (m a + M A )c 2 (m b + M B )c 2 (4.2) (4.2) Q (4.3 (4.2) Q (m a + M A )c 2 (m b + M B )c 2. (4.3) (K b + E ex,b ) + (K B + E ex,b ) (K a + K A ) = Q (4.4) (4.4) Q (4.3) Q E B (i) [Z i m p + N i m n M i ] c 2, (i = A, a, b, B) Q = [M A + m a M B m b ] c 2 (4.5) = E B (b) + E B (B) E B (A) E B (a). (4.6) Q Q (4.4) E threshold ) E threshold = Q (1 + m a M A ). (4.7) 5
E threshold Q (a+a) Q = 0 3. a, A (4.4 K b + K B = Q (4.8) b, B v b, V B 0 = m b v b + M B V B V B = m b M B v b (4.9) K b = m b vb 2 /2, K B = M b Vb 2 /2 (4.8) (4.9) ( Q = 1 + m ) ( b K b = 1 + M ) b K B (4.10) M B m B (4.10) K b = K B = ( ) M B Q, (4.11) M B + m ( b ) m B Q (4.12) M B + m b (4.11) (4.12) Q 5 1. (a) (intensity, current I [I] = 1/(cm 2 s) N [N] = 1/cm 3 ), S, d reaction rate R total R total [R total ] = 1/s 6
(b) R R [R] = 1/(cm 3 s). 5 2. (a) R total I N S d σ 1 R total = σinsd (5.1) σ = R 1 total INSd, [σ] = s 1 [ cm 2 s ][ 1 ][cm cm 2 ][cm] = [cm2 ]. (5.2) 3 σ σ 3: microscopic 5 [4] p.48 (,reaction rate) [5] p.62 (reaction rate) [7] p.22 p.37 R( r, t) R( r, t)dv R( r, t) [8] pp.57-58 cm 3 /sec F (collision density) cm 3 /sec cm 3 sec [8] p.62 7
cross section 10 12 cm σ 1 barn(b ) 10 24 cm 2, 1 mb( ) 10 3 b. (5.3) (b) R : ( )R R R total Sd = σin. (5.4) 3. () 1 Σ Nσ, [Σ] = [ cm 3 ][cm2 ] = [cm 1 ] (5.5) Σ macroscopic cross section 2 U 235 0.7%, 4% ρ m A ( 1 ρ/m A N a, N Σ = ρn a m A σ (5.6) Σ Σ = N 1 σ 1 + N 2 σ 2 + + N i σ i + (5.7) 8
N i i σ i i 1 M Σ Σ = ρn a M (ν 1σ 1 + ν 2 σ 2 + + ν j σ j + ). (5.8) ν j j 1 σ j H 2 O ν H = 2, ν O = 1 4. I 0 x I(x) dx I I + di di di = σindx I(x) = I 0 e Nσx = I 0 e Σx. (5.9) I(x)/I 0 = e Σx x dx Σ dx dx Ndx 1 σ mean free path l x dx e Σx Σdx l 0 x e Σx Σdx = 1 Σ. (5.10),, 9
6 6.1 (scattering) (absorption) a s σ s σ a σ σ = σ s + σ a (6.1) (elastic scattering) (inelastic scattering) (capture) (nuclear fission) σ el σ in σ s = σ el + σ in (6.2) σ c σ f σ a = σ c + σ f (6.3), l t Σ t = Σ a + Σ s, l t = 1 Σ t, l a = 1 Σ a, l s = 1 Σ s (6.4) 1 l t = 1 l a + 1 l s. (6.5) l c, l f Σ a = Σ c + Σ f, l a = 1 Σ a, l c = 1 Σ c, l f = 1 Σ f, (6.6) 1 l a = 1 l c + 1 l f. (6.7) 6.2 * 7 ( 10
4: E n = (1/2)mv 2 ln E n σ f ln σ f [11] ( 3 3 1/v ln σ f ln v, σ f (πr 2 3 10 24 cm 2 = 3 barn) [1] 2017 11 23 https://www.jiji.com/jc/article?k=2017112300128&g= soc, http://www.kyoto-u.ac.jp/ja/research/research results/2017/ 171123 1.html [2] 1974 [3] 1971 11
[4] D. Jakeman( ) 1975 [5] ( 2 )1985 [6] - 1998. [7], 2003 [8] J. R., A. J. ( ) (,2003 [9] J. R., A. J. ( ) (,2003. [10] 2012 [11] Cross-Section Graphs of JENDL-4.0 http : //wwwndc.jaea.go.jp/j40fig/findex.html 12