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
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2 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 (GeV) 2 G µ ( hc) 3 1
3 β NIM Discriminator Coincidence Delay TPHC ADC MCA TAC ADC
4 µ + µ
5 1.1 β β β β β [19] µ µ µ [18] () TAC (ADC) TAC () µs10.45µs) () () p p p p
6 5.17 p p A χ 2 p µ + µ µ + µ ()
7 5.1 ROOT ROOT p ROOT µ + µ
8 1 10 cm TAC(-) PC β β β W. A. Pauli E. Fermi 4 4-7
9 1.1: β β 1.25 V-A β µ µ G. Puppi V-A 1935 π β β W 1983 W Z 0 8
10 1.2: β 1.3: β 9
11 1.2 β β β Z N 1 β A Z (A, Z) (A, Z + 1) + e + ν e (1.1) n p + e + ν e (1.2) 1.4: β β + (A, Z) (A, Z 1) + e + + ν e (1.3) p n + e + + ν e (1.4) 10
12 1.5: β + 11
13 : [19] 1911 Hess ev 12
14 + + + (2.1) + (2.2) K (2.3) K + (2.4) 1 cm cm m = MeV [7] 1/2 ±1 µ + µ µ e + e + ν µ (2.5) µ + e + + ν e + µ 13
15 2.2: µ µ m µ c 2 = m e c 2 + m ν c 2 + m ν c 2 + E e + E ν + E ν (2.6) 0 = P µ = P e + P ν + P ν (2.7) (2.7) 3 4 E e E ν E ν P e P ν P ν 12 E 2 = p 2 +m 2 0 E e 055 MeV E e = (m µ m e ) 2 (m ν m ν ) 2 2m µ c 2 (2.8) 14
16 2.2.2 t Ndecay(t) N0 Γ V-A [1] Ndecay(t) = N0(1 e t/ ) (2.9) Γ µ = h τ = G 2 192π 3 ( hc) 6(m µc 2 ) 5 (1 + ϵ) (2.10) G ( hc) 3 = [(GeV ) 2 ] τ m µ () ϵ m µ [7] Γ µ = 2, [s 1 ] m = MeV (2.11) τ = ( ± ) 10 6 s (2.12) a) 100 b) 15
17 K + p + n (2.13) C τ µ = ± µs ( 8.05 )H τ µ = ± µs ( ) [11] Γ tot = Γ tot = h τ µ h τ µ = s 1 for C (2.14) = s 1 for H (2.15) Γ free = h τ µ,free = Γ cap = Γ cap = h τ µ h τ µ Γ tot = Γ cap + Γ free (2.16) = s 1 for C (2.17) = s 1 for H (2.18) ( Γ cap, Γ free ) Γ tot Γ tot = (7.7, 91.9 ) for C (2.19) = (0.001, 99.8 ) for H (2.20) 2.3: µ 16
18 3 3.1 Bethe-Bloch x [g/cm 2 ] [16] de dx = m e ze V n I z 2 e 4 n ln[ m ev 2 ] (MeV/cm) (3.1) 4πϵ 02 V 2 m e I 17
![3.1: [18] 3.](/docs-images/91/105929864/images/19-0.jpg "2 E 0 [MeV] R(E 0 ) [16] R(E 0 ) = E0 E 0")
19 3.1: [18] 3.2 E 0 [MeV] R(E 0 ) [16] R(E 0 ) = E0 E 0 0 ( de dx ) 1 de (cm) (3.2) 18
20 R (cm) µ 粒子の入射時の運動エネルギー (MeV) 3.2: [g/cm 3 ] (CH) n 3.3: () 10 cm 0 50 MeV 19
21 30 3.4: 20
22 cm 2 6 mm cm 2 10 cm H7195 RD NIM Discriminator Le Croy 4608C Coincidence 2 N Delay N-TM205 21
23 4.2.4 TPHC Time to Pulse Height Converter(-) TAC(Time to Amplitude Converter) TAC ORTEC : TAC 22
24 4.2.5 ADC Analog to Digital Converter(-) MCA Multi Channel Analyzer ADC
25 5 5.1 TAC ADC Hz 16 ns 1.2 V Discriminator TAC delay 1246 µs TAC TAC ADC MCA : 24
26 HV 2000 V TAC 10 µs : (ADC) 25
27 time (μs) : channel ADC y(µs) = x (5.1) 26
28 cm 2 6 mm cm 2 10 cm cm 2 6 mm 5.4: Discriminator Coincidence 3 VETO 3 TAC 2 TAC ADC MCA
29 5.5: TAC 5.6: 28
30 5.2.2 測定器の配置 各種設定 各種設定 装置 光電子増倍管の HV Discriminator スレッショルド TAC フルスケール 図 5.7: 検出器の配置 29 値 2000 V 15 mv 10 µs
31 bin ns t = 84 ns ns 51 counts per channel time (sec) : 30
32 counts per channel time (sec) : () 31
33 5.2.4 dn decay (t) = p 0 e t/p 1 + p 2 (5.2) dt 2.5 µs µs counts per channel time (sec) : 2.5µs10.45µs) 32
34 5.1: ROOT 39 χ p ± 70.1 p 1 (2.079 ± 0.357) 10 6 p ± : 0 µs µs 2.5 µs µs /s /s s dn decay(t) dt
35 counts per channel time (sec) : () 34
36 counts per channel time (sec) : () 35
37 5.2.5 ROOT ROOT p 0 p 1 p χ 2 1 χ 2 = p 0 p 1 p 2 ROOT χ 2 : χ 2 = (y i f(x i )) 2 i ( = (y i f(x i )) 2 (5.3) y i ) 2 i y i dn decay(t) = p dt 0 e (t A)/p 1 + p A=0 χ 2 = 1 p 0 p 1 p 2 A = s χ 2 = 1 p 0 p 1 p 2 A = s χ 2 = 1 p 1 A=0 a) p 1 = p 2 = p χ χ^ p0 5.13: p 0 χ 2 = 1 ±13 36
38 b) p 0 = 281.3p 2 = p χ : p 1 χ 2 = 1 ±
39 c) p 0 = 281.3p 1 = p χ 2 40 χ^ p2 5.15: p 2 χ 2 = 1 ±1.39 ROOT 5.3: parameter ROOT 2 p 0 ±70.1 ± 13 p 1 ± ± p 2 ±3.092 ± 1.39 p 1 ROOT 2 7 p 0 p 1 dn decay (t) dt = p 0 e (t )/p 1 + p 2 (5.4) 38
40 t = µs 2.5 µs 5.4: ROOT 39 χ p ± p 1 (2.079 ± 0.357) 10 6 p ± ROOT 5.1 a) p 1 = p 2 = p χ χ^ p0 5.16: p 0 χ 2 = 1 ±
41 b) p 0 = 84.53p 2 = p χ χ^ p1 (μs) 5.17: p 1 χ 2 = 1 ± c) p 0 = 84.53p 1 = p χ 2 χ^ p2 5.18: p 2 40
42 χ 2 = 1 ± : parameter ROOT 2 p 0 ±6.126 ± 4.47 p 1 ± ± p 2 ±3.092 ± 1.39 p 1 ROOT dn decay(t) = p dt 0 e t/p 1 + p ROOT 41
43 dn decay(t) = p dt 0 e (t A)/p 1 +p 2 A = p 0 p 2 p 1 χ 2 A = : A χ 2 p 1 A = A = A = : p 1 ROOT A = 0 A = A = p 1 ± ± ± ±
44 A = ± A = ± dn decay(t) = p dt 0 e (t A)/p 1 + p 2 p 0 e (t A)/p 1 + p 2 t = A p 0 + p 2 p 1 p 0 e (t A)/p 1 + p 2 p 0 e A/p 1 e t/p 1 + p 2 p 0 e t/p 1 + p 2 p 0 p 0 e A/p 1 p 1 p 1 p 2 p 2 Be t/τ t = 0 Be t/τ dt = [B( τ)e t/τ ] 0 = Bτ (5.5) 0 Bτ = B 0 B = B 0 τ Be t/τ = B 0 τ e t/τ B 0 B 0 τ t = t 1 t 2 t2 t 1 Be t/τ dt = [B( τ)e t/τ ] t 2 t 1 = Bτ(e t 1/τ e t 2/τ ) (5.6) Bτ(e t 1/τ e t 2/τ ) = B 0 B = B 0 τ(e t 1 /τ e t 2 /τ ) Be t/τ = B 0 τ(e t 1/τ e t 2/τ ) e t/τ (5.7) B 0 t = t 1 t 2 τ Be t/τ + C t = t 1 t 2 t2 t 1 (Be t/τ + C)dt = [B( τ)e t/τ + Ct] t 2 t 1 = Bτ(e t 1/τ e t 2/τ ) + C(t 2 t 1 ) (5.8) Bτ(e t 1/τ e t 2/τ ) + C(t 2 t 1 ) = D B = D C(t 2 t 1 ) τ(e t 1 /τ e t 2 /τ ) Be t/τ + C = D C(t 2 t 1 ) τ(e t 1/τ e t 2/τ ) e t/τ + C (5.9) D t = t 1 t 2 τ C 43
45 dn decay(t) dt = p 0 p 2 (t 2 t 1 ) p 1 (e t 1 /p 1 e t 2 /p 1 ) e t/p 1 +p 2 5.7: ROOT 39 χ p 0 (4.317 ± ) 10 4 p 1 (2.079 ± 0.356) 10 6 p ± p 0 p 0 = p 0 = = p 0 p 0 = D p B C counts per channel counts per 200 n second time bin τ 44
46 5.3 µ + µ µ + µ dn decay(t) dt : µ + µ µ + dn decay (t) = e t/ dt µ dn decay (t) = e t/ dt µ + + µ dn decay (t) = e t/ e t/ dt 350 counts per channel μ+ μ μ++μ time (s) 5.20: µ + µ 45
47 1000 counts per channel μ+ μ μ++μ time (s) 5.21: µ + µ () 46
48 [1] Γ µ = h G 2 = τ µ 192π 3 ( hc) 6(m µc 2 ) 5 (1 + ϵ) (5.10) τ µ = (2.079 ± 0.357) 10 6 s G ( hc) 3 = (1.20 ± 0.1) 10 5 (GeV) 2 (5.11) 47
49 6 10 cm 50 MeV TAC(-) ADC [ (µs)] = [] τ (2.08 ± 0.36) 10 6 s G = (1.20 ± 0.1) 10 5 (GeV) 2 ( hc) 3 µ + µ µ + µ µ + µ 8 17 () µ 880 ns( 60 ) µ + µ 48
50 ROOT 49
51 [1] B. /K. /C. /F. (, 2001) [2] (, 1998) [3] (, 1992) [4] (, 1994) [5] (, 1997) [6] --(, 1998) [7] Caso et al., Particle Data Group The European Physical Journal C(Springer, 1998), [8] R. Brun et al.,root Users Guide 4.04(CERN LIBRARY, 2005) [9] [10] [11] T. Suzuki and D.F.Measday Total Nuclear Capture Rates For Negative Muons, Phys. Rev. C Vol. 35, No. 6, pp (1987) [12] D.F.Measday The Nuclear Physics of Muon Capture, Phys. Rep. 354, pp (2001) [13] Donald E.Groom Muon Stopping Power And Range Tables 10MeV-100TeV, Atomic Data and Nuclear Data Tables, 78, pp (2001) [14] Shuhei Tsuji et al., Measurements of Muons at Sea Level, J. Phys. G: Nucl. Part. Phys. 24, pp (1998) [15] (2009) [16] (2008) 50
52 [17] (2009) [18] (2008) [19] pict.php?pictno=
25 3 4
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Mｏｔｔ散乱によるParity対称性の破れを検証
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6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2
![6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2](/thumbs/92/109118076.jpg "6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2")
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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
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陽電子科学 第4号 (2015) 3-8
4 (2015) 3 8 Japanese Positron Science Society Positron annihilation age momentum correlation (AMOC) measurement Abstract: Positron annihilation Age-MOmentum Correlation (AMOC) measurement is the coincidence
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- 28 2 15 - γ 1929 γ - SI γ 137 Cs 662 kev γ NaI active target NaI γ NaI 2 NaI γ NaI(Tl) γ 2 NaI γ γ 10 3 4 γ 1 3 2 γ 5 2.1..................................... 5 2.1.1.................... 5 2.1.2..............................
2.1: n = N/V ( ) k F = ( 3π 2 N ) 1/3 = ( 3π 2 n ) 1/3 V (2.5) [ ] a = h2 2m k2 F h2 2ma (1 27 ) (1 8 ) erg, (2.6) /k B 1 11 / K
![2.1: n = N/V ( ) k F = ( 3π 2 N ) 1/3 = ( 3π 2 n ) 1/3 V (2.5) [ ] a = h2 2m k2 F h2 2ma (1 27 ) (1 8 ) erg, (2.6) /k B 1 11 / K](/thumbs/86/94275608.jpg "2.1: n = N/V ( ) k F = ( 3π 2 N ) 1/3 = ( 3π 2 n ) 1/3 V (2.5) [ ] a = h2 2m k2 F h2 2ma (1 27 ) (1 8 ) erg, (2.6) /k B 1 11 / K")
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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 =")
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H 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [
![H 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [](/thumbs/99/141438442.jpg "H 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [")
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