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
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1 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. ( m) ( m) 2., 3 1 =reaction-text b.tex 2 ( ) 3 4 ( ) okamoto.ryoji.munakata at gmail.com ( 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
2 : ( 13) 2 13 ( 13) 3 [1] 3, 2
3 1. elastic scattering : (n, n) (a) (b) (c) 2. inelastic scattering : (n, n ) (n, nγ) (a) (b) (c) (d) kev (e) (f) n U U U +n U U + γ U(n, γ) U β Np β Pu ( Pu) (3.1) 3. (absorption): capture reaction nuclear fission (a) (capture): n, γ i. 4 ii. 4 compound nucleus 3
4 iii. 1 1H(n, γ) 2 1H 59 27Co(n, γ) 60 27Co Cd(n, γ) Cd Cd In(n, γ) In Eu(n, γ) Eu Au(n, γ) Au Hg U(n, γ) U Np Pu U(n, γ) 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) MeV: ii. (n, p) 31 15P(n, p) 31 14Si P (c) nuclear fission): (d) : 9 4Be(γ, n) 8 4Be 9 4Be(α, n) 12 6 C 9 4Be(n, 2n) 8 4Be c 2. K i 4
5 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
6 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
7 (b) R R [R] = 1/(cm 3 s) (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 cm 3 /sec F (collision density) cm 3 /sec cm 3 sec [8] p.62 7
8 cross section cm σ 1 barn(b ) 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 %, 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 N i σ i + (5.7) 8
9 N i i σ i i 1 M Σ Σ = ρn a M (ν 1σ 1 + ν 2 σ 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
10 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
11 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 cm 2 = 3 barn) [1] soc, results/2017/ html [2] 1974 [3]
12 [4] D. Jakeman( ) 1975 [5] ( 2 )1985 [6] [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
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Mott Parity P2 Mott target Mott Parity Parity Γ = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 t P P ),,, ( 3 2 1 0 1 γ γ γ γ γ γ ν ν µ µ = = Γ 1 : : : Γ P P P P x x P ν ν µ µ vector axial vector ν ν µ µ γ γ Γ ν γ
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医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009192 このサンプルページの内容は, 第 2 版 1 刷発行時のものです. i 2 t 1. 2. 3 2 3. 6 4. 7 5. n 2 ν 6. 2 7. 2003 ii 2 2013 10 iii 1987
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