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- ともみ しどり
- 5 years ago
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1 III
2 2
3 i (Gamma-Ray Burst : GRB) 10 msec 100 sec GRB erg erg GRB GRB GRB GRB 2007 Ikaros (Interplanetary Kite craft Accelerated by Radiation Of the Sun) (GAmma-ray burst Polarimeter : GAP) (Pre-flight Model : PM) (Flight Model : FM) 7 X 8 X 200 MeV proton/cm 2 /s GRB GRB 40% 2 75% 5 GRB
4
5 iii i GRB GRB GRB GRB GRB Ikaros X X X
6 iv β β GAP (M) (η) (MDP) EGS EGS ( ) GEANT4 MEGAlib MEGAlib Body EGS MEGAlib GAP
7 v EGS MEGAlib GAP GAP X GAP GRB CXB CsI Ge CsI Xe GAP
8 vi 10.1 GAP GRB A 103 A A
9 1 1 (Gamma-Ray Burst : GRB) 10 msec 100 sec GRB erg erg GRB GRB 100 sec 1967 GRB GRB X GRB GRB GRB (shell) GRB GRB GRB Ikaros (Interplanetary Kite craft Accelerated by Radiation Of the Sun) (GAmma-ray burst Polarimeter : GAP) (Pre-flight Model : PM) (Flight Model : FM)
10 2 1 X X X 80% GRB
11 3 2 GRB 2.1 GRB (Gamma-Ray Burst :GRB ) 10 msec 100 sec GRB erg erg GRB 1967 VELA VELA 16 GRB 1973 GRB Ic GRB GRB 2.1 CGRO BATSE (Burst And Transient Source Exeperiment) 2.2 BATSE GRB 2 GRB 2 GRB 2 GRB GRB GRB 25% 0.3 BATSE GRB 2.3 BATSE 2704 GRB GRB GRB 1973 X BeppoSAX X GRB BeppoSAX
12 4 2 GRB 2.1 CGRO BATSE GRB 2.2 CGRO BATSE 1234 GRB X X X X GRB 2.4 GRB X GRB GRB GRB GRB GRB
13 2.1 GRB CGRO BATSE 2704 GRB 2.4 BeppoSAX GRB X HETE-2 GRB GRB Z=0.169 ( 20 ) (SN 2003dh) 2.5 GRB SN 2003dh 33 GRB GRB
14 6 2 GRB 2.5 GRB030329/SN 2003dh GRB SN 2003dh GRB GRB BATSE 2.1 [2] ( ) hν N(ν) = N 0 (hν) α exp, hν < (α β)e 0 (2.1) E 0 = N 0 {(α β)e 0 } (α β) (hν) β exp(β α), hν > (α β)e 0 (2.2) E 0 α (β) ( ) exp( hν/kt ) GRB 2.1 GRB 2.1 α 1 β 2 β GRB GRB GRB [1]
15 2.2 GRB GRB GRB 2.2 GRB GRB γ 1 GRB E = erg (shell) shell γ 100 shell shell shell shell 2.7 GRB f 10 2 erg/cm 2 /s d cm GRB GRB
16 8 2 GRB central engine variable wind Inter Stellar Medium internal shock (GRB) external shock (afterglow) 2.7 GRB GRB L γ 4πd 2 f erg/s L g erg/s GRB GRB GRB t 10 R c t cm E L γ t erg (γγ e + e ) f p e + e σ T σ T f p E/m e c 2 E σ T = cm kev cm 2 R cm GRB e + e GRB GRB γ R γ 2
17 2.3 GRB 9 X E b γ b R c t R cγ 2 t 2.8 γ A B 2.8 t R/cγ 2 << R/c γ 1 ( ) γ 1 R t R/c A B t R/cγ 2 A C t R/cγ 2 v = c(1 γ 2 ) 1/2 c(1 γ 2 /2) A C A cr/v R R/γ 2 γ 2(β B+1) γ 4 γ > GRB GRB GRB RHESSI GRB RHESSI kev 20 MeV GRB ± 20 %
18 10 2 GRB INTEGRAL SPI GRB041219a SPI kev 10 MeV GRB GRB GAP GRB 2.9 RHESSI 3 kev-20 MeV 2.10 RHESSI 80 ± 20 % 2.11 INTEGRAL SPI
19 2.3 GRB GRB GRB shell GRB shell 1/γ shell GRB /γ 1/γ 2.3.2
20 12 2 GRB
21 13 3 Ikaros 50 cm (INterplanetary Kite-craft Accelerated by Radiation Of the Sun:Ikaros) Ikaros 3.1 Ikaros Ikaros GAP GAP 3.2 Ikaros 200 GAP 1 GRB
22 14 3 Ikaros 3.1 Ikaros GAP 3.2 GAP
23 Π 4.1 Π I pol I I pol : I : (4.1) Z X-Y X Y X Y I X I Y X I pol I unpol Y X X X X Y 4.2 I X unpol = I Y unpol = 1 2 I unpol (4.2) 4.3 I X pol = I pol (4.3) I Y pol = 0
24 16 4 X-Y X Y I max = I X = 1 2 I unpol + I pol (4.4) I min = I Y = 1 2 I unpol Π = I max I min I max + I min (4.5) Π = 1 Π = X K E e = hν E b (4.6) E b X X [8] θ 4.1 X ( ) Z ν ν E e p e θ φ θ c φ c
25 4.2 X x z θ phi hν = E e + hν (4.7) hν c = p e cos θ e + hν cos θ c (4.8) p e sin θ e cos φ e + hν c p e sin θ e sin φ e + hν c sin θ cos φ = 0 (4.9) sin θ sin φ = 0 (4.10) p e E e (p e c) 2 = E e (E e + 2m e c 2 ) hν hν = 1 + hν (4.11) mc 2 (1 cos θ) E e = h(ν ν ) = m e c 2 2ν 2 cos 2 θ e (hν + m e c 2 ) 2 (hν) 2 cos 2 (4.12) θ e dσ/dω 4.14 dσ dω = r2 0 E 2 2 E 2 ( E E + E E 2 sin2 θ cos 2 φ E E = 1 + E (1 cos θ) m e c2 E = hν, E = hν, r 0 = e m e c 2 ) (4.13)
26 18 4 dσ dω = 1 sin 2 θ cos 2 φ r γ(1 cos θ) 2 [ 1 + γ 2 (1 cosθ) 2 ] 2(1 sin 2 θ cos 2 φ){1 + γ(1 cos θ)} γ = E m e c 2 (4.14) γ dσ dω = r2 0(1 sin 2 θ cos 2 φ), E m e c 2 (4.15) keV 100keV 500keV 2MeV 10MeV keV 100keV 500keV 2MeV 10MeV x axis 0 y axis z axis x axis 4.2 θ 4.3 θ = 90 φ 4.2 θ 1keV( ) θ θ = 0, 180 z θ = 90, 270 x γ γ > θ = 90 φ φ 10.9 θ = 90 φ 4.3 θ = 90 1 cos 2 φ φ sin (x ) σ 4.14 dω [{ 1 σ = 3 8γ σ 0 2(γ + 1) γ 2 } log(2γ + 1) γ 1 2(2γ + 1) 2 ] (4.16)
27 4.2 X 19 σ 0 = 8πr2 0 3 = [cm 2 ], γ = E m e c 2 σ 0 σ MeV MeV X 4.17 I = I 0 e µx (4.17) I : I 0 : µ : 1/cm x : cm σ σ = µ ρ (4.18) I = I 0 e σρx (4.19) I : I 0 : ρ : g/cm 3 σ : cm 2 /g x : cm
28 ρx σρx g/cm 2 [24] ( ) A x B y 1 y 2 y n
29 [8] 4.1 g cm 2 ( MeV ) Be C Al Cu Pb Air , A + x B + y 1 + y y n (4.20) A(x, y 1 y 2 y n )B (4.21) A x B y
30 22 4 A(x, x)a A(x, x )A A(x, y)b A(x, f) (p, p),(p, n),(p, p ),(p, α), (p, γ),(p, 2n),(p, pn) (p, n), (p, pn) X Y Y Q E er E e = E er E b (4.22) E b K L M
31 beta kev MeV X 1 ns X K K X L K L K α K X X X X X β u κ 1 n β c [ (n β)(1 β 2 ] ) E(r, t) = q κ 3 R 2 + q c [ n ] κ 3 (n β) β R (4.23) B(r, t) = [n E(r, t)] (4.24) [] R
32 R β 1 E rad = [ q Rc 2 n (n u) ] (4.25) 4.6 B rad = [n E rad ] (4.26) E rad = B rad = q u sin Θ (4.27) Rc2 4.6 S = c 4π E2 rad = c q 2 u 2 4π R 2 sin Θ (4.28) c4
33 dw dtdω = q2 u 2 4πc 3 sin2 Θ (4.29) P = dw dt = q2 u 2 4πc 2 sin 2 Θ dω (4.30) (4.31) = q2 u 2 4πc (1 µ2 ) dµ P = 2q2 u 2 3c X 4.7 X
34 B m q d dt (γmc2 ) = qv E = 0 d dt (γmv) = q c v B (4.32) 2 γ = const v = const 1 v = v + v dv dt = 0 (4.33) v dt = q γmc v B (4.34)
35 ω B = qb γmc (4.35) v = γ2 v v = v ω B P = 2q2 3c 3 γ4 q2 B 2 γ 2 m 2 c 2 v2 (4.36) /γ 1 γ S = a θ = 2a γ v = v θ s = v t v B α γm v t = q c v B (4.37) θ s = qb sin α γmcv (4.38) a = v ω B sin α (4.39)
36 s 2v γω B sin α (4.40) t 1 2 t 2 t A 1 1 t A 2 2 t A 1 t A 2 R t A 1 = R c (4.41) t A 2 = (t 2 t 1 ) + R c (t 2 t 1 )v c (4.42) (4.43) t A = t A 2 t A 1 = (t 2 t 1 ) (t 2 t 1 )v c = (t 2 t 1 ) ( ) 1 v c 2 s = v(t 2 t 1 ) t 2 t 1 = ω B sin αγ (4.44) (4.45) t A = t A 2 t A 1 = v 1 v c = 1 1 γ γ 2 = t A 1 γ 3 ω B sin α ω c 1 t 2 γω B sin α ( 1 v c ) (4.46) 2 1 γω B sin α 2γ 2 (4.47) ω c γ 3 ω B sin α (4.48)
37 β ( ν ) (A, Z) (A, Z + 1) + e + ν (4.49) β + ( ν ) (A, Z) (A, Z 1) + e + + ν (4.50) ( K ) K X (A, Z) + e (A, Z 1) + ν (4.51)
38
39 31 5 X MeV 2m e c cm 1 ns
40
41 ev 1 ev 10 PN PN p n ( ) PN X /cm 3 (high purity germanium detector:hpge ) cm
42 ORTEC GEM (NaI) (CsI) (Z) Z NaI CsI CsI NaI NaI 5.1 [8] ( ) ( )
43 5.4 GAP [g/cm 3 ] [nm] [µs] [ /MeV] NaI(Tl) CsI(Tl) (64 ) (36 ) BGO GSO (90 ) (10 ) (NE102A) GAP GRB 100 kev CsI (Tl) 5.9 θ = 90
44 φ 5.9 GAP θ = 90 φ (M) 5.9 CsI φ 5.10 φ M 100% N max N min 10.2 M N max N min N max + N min = (5.1) M 100%
45 θ φ M 5.3 Π = M M 1 00% (5.2) (η) η CsI CsI CsI CsI GRB (MDP) (Minimum Detectable Polarization:MDP) (M η) MDP
46 38 5 (a) M (b) η 5.11 η M MDP 10.3 [23] MDP (%) = n σ 2(S + B) M 100% S T (5.3) n σ : M 100% : S : [photon/sec] B : [count/sec] T : [sec] 3σ MDP GRB F [photon/cm 2 /sec] A [cm 2 ] η MDP (%) = 3 2 ηaf + B M 100% ηaf T (5.4)
47 EGS EGS5 EGS5 (Electron Gamma Shower Version 5) EGS5 pegs5 (Preprocessor for EGS) EGS5 1 kev kev GeV 1 kev GeV EGS γ EGS5 1 kev ( ) EGS5 CGVIEW CGVIEW EGS Combinational Geometry (CG) CG
48 EGS EGS CG (Body) ( 6.2) 1. (RPP) x,y,z 2. (SPH) 3. (RCC) 4. (TRC) 5. (TOR) (n : x/y/z = 1/2/3) Body + OR + Body Body
49 6.2 GEANT4 MEGAlib EGS5 Body Body Body + Body AND Body Body OR Body EGS pegs5 CsI EGS5 (C 5 H 8 O 2 ) n 6.2 GEANT4 MEGAlib MEGAlib MEGAlib (MEdium Energy Gamma-ray Astronomy library) MEGAlib Geant3 MGeant/MGGPOD Geant4
50 42 6 C++ ROOT MEGAlib ACT NCT NuSTAR GRI X MEGAllib Geomega (Geometry for MEGAlib) Geomega filename.setup MEGAlib GEomega MEGAlib Body Geomega 1. (BRIK) xyz 2. (SPHERE) θ φ 3. (TUBE) φ 4. (CONE) 5. (TRD1) x y z 6. (TRD2) x y x 7. z (TRAP) z z θ φ xy 8. z (GTRA) TRAP 9. z (PCON)
51 Z z Geomega Geomega Body xyz MEGAlib EGS5 Body MEGAlib EGS5 MEGAlib 5 cm 5 cm 5 cm 0.5 cm CsI kev Z 5.0 cm 5.0 cm ( )
52 CsI CsI plastic scintillator spectrum count MEGAlib EGS energy(mev) 6.3 MEGAlib EGS5 100 kev 100 kev E = 100 kev E < 100 kev MEGAlib EGS5 (E = 100 kev) (E < 100 kev) % 57.05% CsI MEGAlib EGS5 100 CsI 6.5
53 CsI scintillator spectrum (CsI1+CsI2+CsI3+CsI4) box_csi_sum_err.qdp count MEGAlib EGS energy(mev) 6.4 MEGAlib EGS5 CsI 100 kev CsI 6.2 CsI 10 5 CsI E = 100 kev CsI E < 100keV CsI 5cm 5cm CsI CsI MEGAlib EGS5 E = 100 kev CsI CsI CsI CsI E < 100 kev CsI CsI CsI CsI χ 2 ν = 1.77 CsI χ 2 ν = σ EGE5 MEGAlib ( MEGAlib EGS5 ) NIST XCOM (Photon Cross Sections Database)
54 46 6 plastic spectrum MEGAlib/EGS5 pla_mgg_par_egs.qdp ratio energy(mev) CO= 1.000, WV= 94.21, N= EGS5 MEGAlib CsI spectrum MEGAlib/EGS5 CsI_mgg_par_egs.qdp ratio energy(mev) CO= , WV= 65.26, N= CsI EGS5 MEGAlib 6.1 I = I 0 e σρx (6.1) I : I 0 : ρ : g/cm 3 σ : cm 2 /g x : cm (C 5 H 8 O 2 ) n XCOM 6.7 XCOM 100 kev
55 CrossSection (cm 2 /g) CrossSection (PlasticScintillator C 5 H 8 O 2 ) Total Attenuation Thomson scatter Compton scatter Photoelectric absorption energy(mev) 6.7 XCOM cm 2 /g ρ g/cm 3 x 5 cm 43.80% 56.20% MEGAlib 56.12% EGS % cm 5 cm MEGAlib EGS5 1σ 0.42%
56 GAP GAP GAP EGS5 EGS5 3.5 cm CsI EGS5 CsI H 2 EGS5 EGS
57 MEGAlib MEGAlib Z (PCON) CsI MEGAlib GAP 100 kev Z x y 14cm 14cm CsI GAP EGS5 GAP CsI CsI CsI GAP LD MEGAlib root (totalhit == 2) EGS5
58 CsI CsI plastic scintillator GAP coincodence event count MEGAlib EGS energy(mev) 6.9 MEGAlib EGS5 CsI scintillator GAP coincidence event MEGAlib EGS5 count energy(mev) 6.10 MEGAlib EGS5 CsI CsI
59 CsI MEGAlib EGS5 (E = 100 kev) 0 0 (E < 100 kev) CsI12 (E = 100 kev) 0 0 CsI12 (E < 100 kev) CsI CsI CsI kev 99 kev 100 kev 100 kev EGS5 EGS5 CsI MEGAlib
60
61 53 7 GAP X (Cosmic X-ray Background; CXB) GRB 7.1 GAP X (R.Giacconi) 1962 X X X X 10 2 kev X X X X 3 kev 300 kev X (AGN) X 300 kev 10 MeV X 1a [21] [11] 7.1 CXB 3 kev<e <500 kev HEAO MeV<E <30 MeV COMPTEL SAS χ N(E) photon/cm 2 /sec/sr
62 54 7 GAP 300 kev 3 kev 300 kev 7.74 photon/cm 2 /sec/sr kev 100 GeV X 8 χ [11] ( N(E) = 7.877E 1.29 exp ( = 60 ) ( ) 6.5 E + 60 E ), 3 60 kev (7.1) ( ) ( ) E 60 ( ) ( E 60 ) 2.05, > 60 kev (7.2) EGS5 GAP 0.5 mm 0.5 mm mm kev 200 kev 0.5 mm CXB 7.4 CsI CsI
63 7.1 GAP 55 Pb Attenuation Pb transmission factor µ/ρ (cm 2 /g) energy(kev) transmission factor energy(kev) kev 400 KeV mm 30 kev 400 kev CXB trans PB photon/cm 2 /s/kev/sr energy(kev) 7.4 CXB 0.5 mm CsI 1 GAP 4π CXB 3 kev 300 kev 8.5 cm 4π cm 18 cm 4π 10 6 CXB
64 56 7 GAP CXB CXB 3 kev 300 kev 7.74 photon/cm 2 /s/sr π 2π photon/s 0.5 mm CXB 3 kev 300 kev photon/cm 2 /s/sr 2π 4.92/times10 2 photon/s photon/s CXB B = B + B + B (7.3) = = count/sec/12csi CXB 0.5 mm count/s count/s 47.1 (47.1) MeV MeV N C (E) =
65 7.1 GAP proton/m 2 /sr/sec/mev 1 GeV 2π P C = N C (E) de π 0 sin θ dθ 2π =2.26 proton/cm 2 /s = proton/cm 2 /year 0 dφ [proton/m 2 /sec] (7.4) 10 8 proton/cm
66 58 7 GAP 100 MeV/nucleon [22] N S (E) = 10 4 E 4 proton/cm 2 /sec/sr/gev (7.5) km km 7.7 θ 7.6 θ sin θ tan θ = R r (7.6) 7.7 = π Ω = ( ) 2 R r θ 0 sin θ dθ 2π 0 dφ (7.7)
67 7.2 GAP P S = N S (E) de θ 0 2π sin θ dθ 0 = proton/cm 2 /s = proton/cm 2 /year dφ proton/cm 2 /s (7.8) GAP 2 mm 0.5 mm 2 mm 20 MeV 2 mm 0.5 mm 25 MeV CsI MeV UD ( ) 7.2 GAP GRB GAP GAP GAP CsI MEGAlib 7.8
68 60 7 GAP 7.8 GAP GAP 30 cm 30 cm 100 kev 10 6 GAP 30 cm 30 cm 100 kev 10 6 GAP 0.5 mm 30 cm 30 cm 100 kev kev 500 kev GRB CsI 12 CsI GAP 0.5 mm GAP GAP CsI kev 300 kev 500 kev GRB GRB E 1 5 : 5 : kev 300 kev 500 kev N 1
69 7.2 GAP keV Al_block scatter incident Xray=100%polarized,10 6 photon/900cm 2 300keV Al_block scatter incident Xray=100%polarized,10 6 photon/900cm 2 count CsI number GAP only Al_block Al_block(GAPwithPb) (a) 100 kev X count GAP only Al_block 5 10 CsI number Al_block(GAPwithPb) (b) 300 kev X count keV Al_block scatter incidnet Xray=100%polarized,10 6 photon/900cm 2 GAP only Al_block 5 10 CsI number Al_block(GAPwithPb) (c) 500 kev X 7.9 CsI GAP X X GAP 0.5 mm X N 2 N 3 GRB 7.9 N = 15N 1 + 5N 2 + 3N 3 23 (7.9) (7.10)
70 62 7 GAP 7.2 GAP X X 0.5 mm GAP 100 kev 300 kev 500 kev GAP GAP GAP GAP GAP GRB 7.15 N = ( ) GRB 23 (7.11) (7.12) = GRB CXB CXB GRB MEGAlib 7.8 GRB CXB10 kev 30 kev 50 kev GRB CsI 12 CsI 7.3 GRB 100 kev 500 kev CXB 10 kev 30 kev 50 kev 500 kev CXB 300 : 340 : 30 : 8 N 1 N 2 N 3 N N = 300N N N 3 + 8N (7.13) (7.14)
71 7.2 GAP CXB 10 kev 30 kev 50 kev GAP X X 0.5 mm GAP 10 kev 30 kev 50 kev GAP GAP GAP GAP GAP CXB 7.15 N = ( ) GRB (7.15) 678 (7.16) = CXB X X CsI 8
72
73 65 8 ( ) CsI CsI CsI EGS5 8.1 A x B y A + x B + y A (x,y) B A (p,n) B x A (p,xn) B Z A A A x+1 Z A (p, xn) Z+1 B A (p,xn) B β + β β + β β β + (4 ) (p, xn) β CsI(Tl) Cs I Tl (p,xn)
74 Cs
75 I
76 Tl
77 8.2 CsI CsI (p,xn) (p,xn) (p,xn) GAP kev 100 kev CsI (Tl) GAP (7 ) /cm MeV Ge CsI (Tl) (ORTEC EG&G GEM20) GEM P P 56.1 mm 57.5 mm to 3 mm 1.27 mm 700 µm
78 ORTEC GEM20 Ge CsI CsI 8.6 Count Cd109 88keV Co57 122keV Co57 136keV mix_cal_source spectrum livetime=116sec Cs keV Co keV Co keV K keV Count ch Background spectrum livetime=10797sec bgd_csi.qdp Pb Kα keV Pb Kα keV Pb Kβ keV Pb Kβ keV K keV ch CsI 40 19K 40 19K 0.012% MeV MeV X
79 8.2 CsI Cd 57Co 137Cs 60Co 88.03keV keV keV 662keV 1173keV 1333keV 8.7 channel = 2 Energy (8.1) calibrate Channel = 2.00 energy Channel Energy 8.7
80 CsI CsI 25 Ge t= CsI spectrum (each 15000sec) count/sec t: time since measurement (sec) t=0 t=15000 t=30000 t=45000 t=60000 t= energy(kev) t= CsI kev kev kev 500 kev kev EGS5
81 8.2 CsI 73 CsI spectrum (each 15000sec) CsI spectrum (each 15000sec) count/sec Xe 122 Xe 125 Xe 123 Xe energy(kev) 121 I 125 Xe count/sec Xe 127 Cs 129 Cs energy(kev) kev 250 kev 250 kev 500 kev kev 500 kev I kev 84.3 % Xe kev 2.69 % Xe kev 48.9 % kev 14.9 % kev 8.56 % Xe kev 54.0 % kev 30.1 % Cs kev 58.4 % Cs kev 22.5 % CsI CsI 0 kev 500 kev CsI 7
82 74 8 experiment first data & simulation count experiment first data simulation data energy(kev) naomi 7 Jan : CsI 149 kev kev kev kev kev kev kev CsI
83 8.2 CsI dn p dt = N t fσ λn p (8.2) N p : t /cm 3 N t : /cm 3 f : proton/cm 2 /s (σ) : b (1b = cm 2 ) λ : cm T : s (T = ln2 λ ) N p = N tfσ ( 1 e λt) λ (8.3) N p = N tfσ λ (8.4) Xe Xe 149 kev Xe Xe 149 kev 149 kev Xe Xe 149 kev
84 ( ) (E E 0 ) 2 F (E) = N exp 2σ 2 + const (8.5) F (R) dx = 2π N σ (8.6) first data const+gauss fit count/sec F(x)=GN*exp( (x GC) 2 /2GW 2 ) + CO CO=1.492 GC=149.1 GW= GN=6.396 integral count= energy (kev) CO= 1.492, GC= 149.1, GW= , GN= 6.396, WV= N= kev 8.5 (90% ) const E ± σ N χ ν A = A 0 e λt (8.7) A : t A 0 : kev
85 8.2 CsI kev Xe Xe 149 kev ( ) ( ) (t t1 ) (t t2 ) F (t) = N 1 exp + N 2 exp τ 1 τ 2 (8.8) N 1 t 1 τ Xe N 2 t 2 τ Xe 149keV exp+exp fit count/sec F(x)=EN 1 *exp( (x EC 1 )/EW 1 )+EN 2 *exp( (x EC 2 )/EW 2 ) EC 1 =0 EC 2 =0 EW 1 = EW 2 =10802 EN 1 = EN 2 = time since beam stop (sec) EC= 0.000, EW= E+05, EN= E 02, EC= 0.000, EW= E+04 EN= 14.36, WV= 438.2, N= kev 8.6 (90% ) N ± t 1 0 fix τ fix N ± t 2 0 fix τ fix χ ν =keV Xe Xe ± count/s ± count/s
86 Xe 149 kev 149 kev CsI = count/s/csi (8.9) A = λn p (8.10) Xe 149 kev N p = ( ) (8.11) = /CsI = = /cm f e = proton/s/cm2 (8.12) = proton/s/cm Xe I I /cm Xe 8.13 σ σ = λn p N t f(1 e λt ) (8.13) = cm 2 =88.16 mb 2.26 proton/cm 2 /s (7 ) kev
87 8.2 CsI 79 N p = N tfσ λ = /cm 3 (8.14) CsI N p = N tfσ λ = /CsI (8.15) 149 kev A = λn p = Bq/cm 3 (8.16) CsI 149 kev A = λn p = Bq/CsI (8.17) s n/cm 3 Bq/cm produce_n.out Xe123 produced N p and A time (sec) Xe Xe kev kev I 212 kev Xe 149 kev Xe 149 kev 178 kev 330 kev Cs Cs 412 kev
88 keV exp+exp fit 178keV exp fit count/sec F(x)=EN 1 *exp( (x EC 1 )/EW 1 )+EN 2 *exp( (x EC 2 )/EW 2 ) EC 1 =0 EC 2 =0 EW 1 = EW 2 =10802 EN 1 = EN 2 = time since beam stop (sec) 188.5keV exp+exp fit EC= 0.000, EW= E+05, EN= E 02, EC= 0.000, EW= E+04 EN= 14.36, WV= 438.2, N= count/sec F(x)=EN*exp( (x EC)/EW) EC=0 EW=10802 EN= time since beam stop (sec) 212keV exp+exp fit EC= 0.000, EW= E+04, EN= count/sec F(x)=EN*exp( (x EC)/EW) EC=0 EW=87773 EN= time since beam stop (sec) 243.5keV exp+exp fit EC= 0.000, EW= E+04, EN= 4.524, WV= 833.1, N= count/sec F(x)=EN*exp( (x EC)/EW) EC=0 EW=11010 EN= time since beam stop (sec) 330keV exp+exp fit EC= 0.000, EW= E+04, EN= 45.42, WV= E+13, N= count/sec F(x)=EN*exp( (x EC)/EW) EC=0 EW= time since beam stop (sec) T0_412inte_2.qdp 412keV exp+exp fit EN= EC= 0.000, EW= E+04, EN= 2.292, WV= 817.3, N= count/sec F(x)=EN*exp( (x EC)/EW) time since beam stop (sec) EC=0 EW=10802 EN= EC= 0.000, EW= E+04, EN= 2.428, WV= 2191., N= count/sec F(x)=EN 1 *exp( (x EC 1 )/EW 1 )+EN 2 *exp( (x EC 2 )/EW 2 ) EC 1 =0 EC 2 =0 EW 1 =32460 EW 2 = EN 1 = EN 2 = time since beam stop (sec) EC= 0.000, EW= E+04, EN= 6.806, EC= 0.000, EW= E+05 EN=
89 8.2 CsI Xe 149 kev Xe 178 kev Xe 330 kev Ge /cm σ mb 28.10[mb] 16.94[mb] /cm Bq/cm Xe 149 kev Cs 412 kev Cs 412 kev Ge /cm σ mb 162.2[mb] 80.10[mb] /cm Bq/cm CsI CsI EGS5 CsI 7.8 CsI 149 kev 178 kev 330 kev 412 kev 106 CsI CsI 149 kev kev kev kev
90 82 8 CsI CsI GAP CsI CsI 149 kev kev kev kev proton/cm 2 /s CsI X 10 3 Bq/CsI CsI 10 3 counts/csi/s CsI CsI X CsI 10 4 Bq/cm proton/cm 2 /s CsI 10 2 Bq/cm 3
91 83 9 GAP X (EXM-101A5B) X GAP 9.1 GAP GAP GAP PM PM EGS5?? 9.2 ( KEK ) ( Photon Factory:PF )BL14A GAP KEK-PF-BL14A 5keV 80keV X 80 kev X 1 mm 82.3%
92 84 第9章 シミュレーションと実験の比較 実験のセットアップ 偏光度の測定 KEK での 80 kev 単色 X 線の偏光度を知るために 山形大学のプロペラ検出器を用いて偏 光度の測定を行った プロペラ検出器は図 に示すような構造をしており 散乱体から十 分に離れた場所に小さな CdTe 検出器を配置することで 90 方向の散乱光だけを集めること ができる そのためこの検出器はのモジュレーションはとても大きい 0deg Photo diode E 90deg scatter CdTe scatter CdTe 図 9.1 山形大学のプロペラ検出器 散乱体から十分離れたところに小さな検出器を置くこ とで 90circ 方向の散乱光のみを観測し モジュレーションファクタの高い検出器になって いる この検出器のモジュレーションふファクタは山形大学での EGS4 でのシミュレーション結 果より であると報告されている 実験でのモジュレーションカーブは図 となり a + b sin(c x + d) でフィットした結果モジュレーションファクタは ± 1.57 となった 1.2 M=0.811+/ Modified Count Angle[degree] 図 9.2 山形大学のプロペラ検出器によるモジュレーションカーブ a + b sin(cx + d) に よりフィットした結果モジュレーションファクタは ± となった よって KEK 実験における光源の偏光度は Π = 82.3% ± である
93 X 109 Cd kev CsI 109 Cd kev GAP 30 Ch 1 0 ch 0 kev 9.1 E = Ch kev (9.1) CsI 109 Cd kev 88.0 kev 241 Am 59.5 kev 4.15 Ch Ch Ch E = 5.75 Ch 1.69 kev (9.2) 80 kev X CsI CsI 80 kev (Lower Discriminate level : LD) (Upper Discriminate level : UD) (Ch) CsI (Ch) LD UD LD UD GAP X GAP X, CsI CsI
94 cm 37 CsI CsI 9.4 GAP X CsI CsI CsI LD UD 9.2 LD UD kev (kev) CsI (kev) LD UD LD UD csi 9.2 KEK GAP 80 kev 10 6 CsI 9.2 CsI cm x kev 10 5 CsI 9.2 CsI GAP X CsI 9.2 CsI
95 cm x 0 X GAP 10 30
96 GAP X M=0.446+/ Experiment M=0.574+/ simulation Counts count CsI ID CsI ID 9.5 GAP X CsI 9.6 EGS5 GAP Π = M experiment M 100% 77.7% ± 4.89% GAP 2 cm X M=0.262+/ Experiment M=0.273+/ simulation Relative Count count CsI ID CsI ID 9.7 GAP 2 cm 37 X CsI 9.8 EGS5 GAP 2 cm x 0 22 X x % ± 12.0%
97 GAP ( ) Experiment simulation Counts count incident 0deg incident 10deg incident 20deg incident 30deg 5 10 CsI ID 9.9 GAP CsI ID 9.10 GAP
98
99 GAP 5 M η GAP M η EGS5 50 kev 300 kev 10 kev CsI CsI GRB GAP GAP CsI φ f(φ) = a + b sin(c φ + d) (10.1) M = (10.2) = b a 12 CsI GAP ( CsI )
100 92 10 GAP Mfactor GAP efficiency Mfactor efficiency energy(kev) 10.1 GAP energy(kev) 10.2 GAP GAP X (CXB) GRB CXB GAP CsI GRB 10.1 X GAP 10.1 GAP photon (or proton) /cm 2 /sec count/sec/12csi X (CXB) (3 kev kev) 2.27 (20 MeV - 1 GeV) 0 CXB CXB GRB GRB CsI
101 10.3 GRB GRB GRB GAP 1 2 GRB 10.3 MDP MDP GAP M η GRB F T 10.2 B MDP GRB MDP GRB BATSE 1972 GRB GRB MDP MDP (%) = 3 2 ηaf + B M 100% ηaf T (10.3) M 100% : F : GRB photon/cm 2 /s A : cm 2 η : B : count/s T : s GRB 100 kev dn de = αe 1 photon/cm 2 /s/kev (10.4) BATSE GRB erg/cm 2 GRB erg/photon s photon/cm 2 /s BATSE 50 kev 300 kev GRB E <E> 50 E 1 de = 500 <E> E 1 de (10.5) < E >= kev = erg BATSE 50 kev 300 kev α = GRB T photon/cm2 /s (10.6)
102 94 10 MDP MηF ηf kev MηF = E2 E 1 M(E)η(E) dn de de = α ( ) E + 10 M(E)η(E) log E (10.7) ηf = E2 E 1 η(e) dn de de = α ( ) E + 10 η(e) log E (10.8) 1972 GRB MDP BATSE % 9 GAP 2π ± MDP GAP MDP GRB GRB/yr field of view = 90 o field of view = 30 o GRB observation rate MDP 10.3 GAP GRB GRB GRB GAP GAP 30
103 GRB GRB 40% 1.5 GRB 70% 4 GRB 10.4 GAP GRB GAP BATSE GRB BATSE 2 1 photon/cm 2 /s BATSE 2 50 s 50 photon/cm 2 GRB E 1 CsI π = GRB 8823 photon EGS5 40% 75% GAP 8823 GAP 30 GRB CXB count/s/12csi 50 1 CsI 227 count % polarized incident=0deg 40% polarized incident=30deg count CsI ID count CsI ID % GRB 40% GRB 30 GRB CXB GRB CXB
104 % polarized incident=0deg 75% polarized incident=30deg count CsI ID count CsI ID % GRB 75% GRB 30 GRB CXB CXB CXB CXB 10.3 GRB GRB GRB BATSE GRB 50 photon 50% photon photon 1 CXB CXB 1 GRB 100 photon/cm GRB GAP 2π 9 KEK Π = M experiment M 100% M sin
105 % polarized incident=30deg x10 4 photon count CsI ID GRB 100 photon/cm 2 CXB 100 photon/cm2 GRB 50% 10 dσ dω = r2 0(1 sin 2 θ cos 2 φ), E m e c 2 (10.9) GAP 10.7 θ = 90 1 cos 2 φ sin 10.7 θ = 90 φ θ sin 10.7 X CsI θ = 90
106 98 10 h GAP GRB GRB 40% 100 photon/cm 2 GRB GRB CXB count % polarized incident=30deg x10 4 photon 5 10 CsI ID count % polarized incident=30deg 10 6 photon 5 10 CsI ID % 100 photon/cm 2 GRB GAP 30 CXB % GAP 30 naomi 29 Jan : χ 2 ν 1 N N (y i y(x i )) 2 σ 2 i=1 i (10.10) N= χ 2 ν 1 12 N (y i ay(x i )) 2 i=1 y i (10.11)
107 a χ 2 ν 10.9 a a = a χ 2 ν χ 2 ν a 10.9 a a a 1σ a 11 1σ = 0.68 χ 2 ν χ2 ν a (10.12) % = 37.5% (10.13) (10.14) % = 42.5% Π = 40% ± 2.5%
108
109 EGS5 MEGAlib GAP CsI X GRB CXB CXB X X GAP GAP GRB photon/cm 2 GRB GRB 40% 6% 40% GRB GAP 30 GRB 40% 2 75% 5
110
111 103 A A.1 y KŒn y' v K'Œn o x o' ƒæ' x' A.1 (K ) x v (K ) K u K dx = γ(dx + vdt ) dy = dy dz = dz (A.1) dt = γ (dt + v c 2 dx )
112 104 A u x = u y = u z = u x + v 1 + vu x γ γ c 2 u y ( 1 + vu x c 2 u z ( 1 + vu x c 2 ) ) (A.2) K K v u v u u u = u = u + v 1 + vu γ ( c 2 u 1 + vu c 2 ) (A.3) K θ K θ u u tan θ = u u = u sin θ γ(u cos θ + v) (A.4) u u cos θ cos θ = u u = 1 u u cos θ + v 1 + vu cos θ c2 (A.5)
113 A A.2 A.4 A.5 u = u = c tan θ = sin θ ( γ cos θ + v ) (A.6) c cos θ = cos θ + v c 1 + v c cos θ (A.7) sin θ = sin θ γ (1 + v ) (A.8) c cos θ K θ = π/2 tan θ = c γv cos θ = v c sin θ = 1 γ (A.9) (A.10) (A.11) γ 1 θ A.11 θ = 1 (A.12) γ K K 1/γ ƒæ `1/ƒÁ K'Œn A.2 KŒn K K
114
115 107 M1 GAP GAP
116
117 109 [1] 2006 [2] Band, D.L. et al., 1993, ApJ [3] 2007 [4] Lazzati, D., 2003, astro-ph v1 [5] Waxman, E., 2003, Nature [6] Lazzati, D., Rossi, E., Ghisellini, G. & Rees, M.J., 2003, astro-ph v3 [7] Rybicki, G.B., Lightman, A.P., 1979, WILEY INTER SCIENCE, Radiative Processes in Astrophysics [8] KNOLL, F.C., 2001,, 3 [9] 2000 [10] GAPOM X 2003 [11] Gruber, D.E. et al., 1999, ApJ 520, [12] Rees, M.J., Meszaros, P., 1992, MNRAS 258 L41 [13] Piran, T., 1998, Phys.Rept [14] X 2001 [15] [16] [17] RHESSI X 2005 [18] X 2003 [19] MSGC 2000 [20] R.Silberberg and C.H.Tsao The Astrophysical Journal Supplement Series(1977) [21] ( ) [22] NASA Ames/Stanford 1975 Summer Study [23] R.Novick Space Science Rev. 18(1975) pp Stellar and solar X-ray polarimetry
118 110 [24] R.M.Sternheimer Physical Review, vol. 115, Issue 1, pp Range-Energy Relations for Protons in Be, C, Al, Cu, Pb, and Air
Mｏｔｔ散乱によるParity対称性の破れを検証
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
(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x
![(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x](/thumbs/104/162595168.jpg "(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x")
Compton Scattering Beaming exp [i k x ωt] k λ k π/λ ω πν k ω/c k x ωt ω k α c, k k x ωt η αβ k α x β diag + ++ x β ct, x O O x O O v k α k α β, γ k γ k βk, k γ k + βk k γ k k, k γ k + βk 3 k k 4 k 3 k
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B07557 0 0 (AGN) AGN AGN X X AGN AGN Geant4 AGN X X X (AGN) AGN AGN X AGN. AGN AGN Seyfert Seyfert Seyfert AGN 94 Carl Seyfert Seyfert Seyfert z < 0. Seyfert I II I 000 km/s 00 km/s II AGN (BLR) (NLR)
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.............................
V(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H
199 1 1 199 1 1. Vx) m e V cos x π x π Vx) = x < π, x > π V i) x = Vx) V 1 x /)) n n d f dξ ξ d f dξ + n f = H n ξ) ii) H n ξ) = 1) n expξ ) dn dξ n exp ξ )) H n ξ)h m ξ) exp ξ )dξ = π n n!δ n,m x = Vx)
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Λ (Λ ) Λ (Ge) Hyperball γ ΛN J-PARC Λ dead time J-PARC flash ADC 1 dead time ( ) 1 µsec 3
19 Λ (Λ ) Λ (Ge) Hyperball γ ΛN J-PARC Λ dead time J-PARC flash ADC 1 dead time ( ) 1 µsec 3 1 1 1.1 γ ΛN................. 1 1.2 KEK J-PARC................................ 2 1.2.1 J-PARC....................................
http://www.ns.kogakuin.ac.jp/~ft13389/lecture/physics1a2b/ pdf I 1 1 1.1 ( ) 1. 30 m µm 2. 20 cm km 3. 10 m 2 cm 2 4. 5 cm 3 km 3 5. 1 6. 1 7. 1 1.2 ( ) 1. 1 m + 10 cm 2. 1 hr + 6400 sec 3. 3.0 10 5 kg
(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0
1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45
ma22-9 u ( v w) = u v w sin θê = v w sin θ u cos φ = = 2.3 ( a b) ( c d) = ( a c)( b d) ( a d)( b c) ( a b) ( c d) = (a 2 b 3 a 3 b 2 )(c 2 d 3 c 3 d
A 2. x F (t) =f sin ωt x(0) = ẋ(0) = 0 ω θ sin θ θ 3! θ3 v = f mω cos ωt x = f mω (t sin ωt) ω t 0 = f ( cos ωt) mω x ma2-2 t ω x f (t mω ω (ωt ) 6 (ωt)3 = f 6m ωt3 2.2 u ( v w) = v ( w u) = w ( u v) ma22-9
= hυ = h c λ υ λ (ev) = 1240 λ W=NE = Nhc λ W= N 2 10-16 λ / / Φe = dqe dt J/s Φ = km Φe(λ)v(λ)dλ THBV3_0101JA Qe = Φedt (W s) Q = Φdt lm s Ee = dφe ds E = dφ ds Φ Φ THBV3_0102JA Me = dφe ds M = dφ ds
Part () () Γ Part ,
Contents a 6 6 6 6 6 6 6 7 7. 8.. 8.. 8.3. 8 Part. 9. 9.. 9.. 3. 3.. 3.. 3 4. 5 4.. 5 4.. 9 4.3. 3 Part. 6 5. () 6 5.. () 7 5.. 9 5.3. Γ 3 6. 3 6.. 3 6.. 3 6.3. 33 Part 3. 34 7. 34 7.. 34 7.. 34 8. 35
B 1 B.1.......................... 1 B.1.1................. 1 B.1.2................. 2 B.2........................... 5 B.2.1.......................... 5 B.2.2.................. 6 B.2.3..................
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")
1 6 6.1 (??) (P = ρ rad /3) ρ rad T 4 d(ρv ) + PdV = 0 (6.1) dρ rad ρ rad + 4 da a = 0 (6.2) dt T + da a = 0 T 1 a (6.3) ( ) n ρ m = n (m + 12 ) m v2 = n (m + 32 ) T, P = nt (6.4) (6.1) d [(nm + 32 ] )a
(e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a
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0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()
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d M d t = γ M H + α M d M d t M γ [ 1/ ( Oe sec) ] α γ γ = gµ B h g g µ B h / π γ g = γ = 1.76 10 [ 7 1/ ( Oe sec) ] α α = λ γ λ λ λ α γ α α H α = γ H ω ω H α α H K K H K / M 1 1 > 0 α 1 M > 0 γ α γ =
18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α
18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α 2 ), ϕ(t) = B 1 cos(ω 1 t + α 1 ) + B 2 cos(ω 2 t
25 3 4
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![3-2 PET ( : CYRIC ) ( 0 ) (3-1 ) PET PET [min] 11 C 13 N 15 O 18 F 68 Ga [MeV] [mm] [MeV]](/thumbs/91/106519999.jpg "3-2 PET ( : CYRIC ) ( 0 ) (3-1 ) PET PET [min] 11 C 13 N 15 O 18 F 68 Ga [MeV] [mm] [MeV]")
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positron 1930 Dirac 1933 Anderson m 22Na(hl=2.6years), 58Co(hl=71days), 64Cu(hl=12hour) 68Ge(hl=288days) MeV : thermalization m psec 100
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.1, θ, ϕ d = A, t dt + B, t dtd + C, t d + D, t dθ +in θdϕ.1.1 t { = f1,t t = f,t { D, t = B, t =.1. t A, tdt e φ,t dt, C, td e λ,t d.1.3,t, t d = e φ,t dt + e λ,t d + dθ +in θdϕ.1.4 { = f1,t t = f,t {
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