Coulomb potential
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- せせら ふくだ
- 7 years ago
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1 Fe muonic atom X
2 Coulomb potential X muon muonic atom X trigger ADC A muonic atom 39 A A A
3 B Ge 42 B B B
4 µ 200 µ muon atom µ 1/200 µ 2p 1s X µ Fe muonic Fe X NaI 11 X 3
5 E e MeV 1. 1 ρ(r) = ρ(0) (1.1) 1 + exp ((r R) /a) r R r a 2. A r 0 R/A 1 3 r 0 = (fm) 3. a A a= (fm) 4
6 1.1.3 Coulomb potential Coulomb potential 3 Coulomb potential ρ(r) Coulomb potential V c (r) V c (r) = 4πZα dr 1 r r r 2 dr r 2 ρ(r ) (1.2) 0 ρ(r)/ρ(0) r(fm) 1.1: 5
7 V(r)(MeV) r(fm) 1.2: Coulomb potential muon τ = 2.2(µs) µ muonic atom a 0 (µ) = h2 M µ e 2 Z = m e M µ a 0 (e) (1.3) m e /M µ 1/207 1/207 Fe 1s a(1s) 9.8(f m) (1.4) Fe 4.6(fm) (1.5) 6
8 1.3: 2p,1s Fe X ( S) sec sec X X X E1 3d 2p 2p 1s 2p 1s 1s 7
9 1.2.3 Bohr muon v 0 v 0 = (Zα) c Z Zα 1 c Schrödinger Ĥ = h2 2m d 2 Hψ(r) = Eψ(r) (1.6) m + V (r), ψ(r) = R(r)Y dr2 R(r) y(r) r l (θ, ϕ) (1.7) (1.8) d 2 y + 1) = l(l dr2 r 2 + 2m(V (r) E) y (1.9) y = X 1, dy dr = X 2 (1.10) dx 1 dr = F 1(X 1, X 2, r), dx 2 dr = F 2(X 1, X 2, r) (1.11) Schrödinger F! = X 2 (1.12) l(l + 1) F 2 = r 2 + 2m(V (r) E) X 1 (1.13) Runge-Kutta E Fe 2p 1s X ( ) 1.425(MeV) (1.14) ( ) 1.223(MeV) ( a = 0.5, r 0 = 1.2) (1.15) Fe 0.2MeV 8
10 1.2.4 muon muonic atom muonic atom muon ( 9 ) (π ±, K ± ) µ ±, e ±, γ muon 15km π ±, K ± (π ± µ ± ν, K ± µ ± ν) muon π, K (τ µ = 2.2µs, τ π = 26ns, τ K = 12ns,) (1GeV/c muon 10 ) µ muon 9
11 2 2.1 muonic atom X 2.2 muonic atom 2p 1s X 1. 1cm 3 µ 4 A 2. muonic atom 2p 1s 71.6% [2] 3. 1cm keV X 1255keV X I n ( )/(1 /cm 3 ) 4. Ge 5% B 3. I n C 1. X I I = keV X 3. 2π X X 4. X I 1/2 exp( x/l) I l 2.38cm [7],[10] 10
12 x X 1/2 X 2π I ( (cm 3 )) /(100,000,000) I n l = 2.38cm a A 2.1 B 2.2 z y 0 x z a 2 z a 2 a 2 d2 d3 d3 r d1 r y 0 a d2 a s h Ge Ge a 2 x a 2 a 2 2.1: A 11
13 z y 0 x z a 2 z a 2 a 2 d2 r d1 y 0 a d2 a Ge h r s Ge a 2 x a 2 a 2 2.2: B r = 2.3cm, h = 3.3cm, d1 = 1.0cm, d2 = d3 = 2.2cm a, s I n s = 0 a I n w a I n g/cm 3 [10] 12
14 a(cm) I n ( ) w(kg) a(cm) I n ( ) w(kg) : A s = 0 2.2: B s = 0 a I n a I n (w) (w) 13
15 I n a(cm) 2.3: A s = 0 a I n I n a(cm) 2.4: B s = 0 a I n A B I n /w A 2p 1s X c n In I n 14
16 kg I n 28 c n 4 a = 14cm a = 14cm s I n, w s(cm) I n w(kg) : A a = 14cm s I n (w) I n s(cm) 2.5: A a = 14cm s I n s = 2 a = 14cm
17 2.5cm 2.5cm 2.5cm 2.5cm 2.5cm 2.6: 2.5cm 2.3 X X Ge NaI NaI Ge Ge NaI 2.4 NaI NaI muonic atom X S1 S2 S1 S2 NaI S1 16
18 S3 S1 S3 S2 2.5 trigger delay veto signal anti-coincidence discriminater threshold PMT PMT threshold coincidence rate 2.6 ADC ADC 4ch CAMAC gate 2.7 Co S off Co on 11 S1 S3 4 17
19 S1:H6522B S2:H1161 S3:H1161 Scaler(8ch VISUAL SCALER) N-OR MHz Clock Generator N-TM203 Guad Logic FANIN/FANOUT FF1( ) 3ch 4FOLD 1-VETO COINCIDENCE N-TM 103 OCTAL DISCRIMINATOR MODEL 710 DUAL VARIABLE DELAY ( )DLY6 Quad high voltage power supply RPH ch 100ns DELAY KL6015B TDS3012 Clock Generator CG1( ) Dual gate generator GC10( ) Variable attenuator ATT2( ) 12ch Saler 3122 OCTAL TDC TDC7( ) ADC ADC6( ) INTERRUPT REGISTER REG4( ) TOYO CC/NET CRATE CONTROLLER CCN2( ) 2.4: 18
20 S S1 NaI Fe table S2 8.5 Pb wood : 19
21 10.0 S3 S1 Fe S2 Pb Fe 6.5 table Fe Pb Pb Pb wood : 20
22 Pb Pb Fe Pb NaI : NaI 21
23 S2 S S Pb Fe NaI Fe 2.10: Variable Delay 31ns veto Coinci Scaler 5ch S1 Discri Scaler 0ch 200ns Delay HV NaI Discri Delay 200ns S2 Discri ADC 0ch Variable atteuator 1,8,16dB Scaler 1ch ADC 5ch veto Coinci Gate generator wide 750 s 1v Scaler or Gate generator wide 1 s 1v ADC GATE Delay 200ns ADC 1ch Clock Discri CC7700 REQ G-IN PC Delay 100ns Scaler TDC stop start Interrupt resister 100MHz Clock N-TM 203 Delay 0ch 2.11: 22
24 3 60 Co 8 muonic Fe X 8 CAMAC SCALER NIM VISUAL SCALER(VS) 3.1 VS NaI S S1 S2 NaI ClockGenerator 1Hz or 2 SCALER Clock or Clock 1Hz VS Clock Hz 0.006% ADC NaI ch ch Clock TDC 500ch 4100ch 2 TDC > S1, S2 ADC S1 280ch S2 320ch Discriminator threshold S1 ADC > 280 S2 ADC < 320 NaI 3.4 X 533ch
25 3.2 9 SCALER VS VS LAM NaI (TDC > 4000 ) 3.6 Rebin4 p 0 x 2 + p 1 x + p 2 + p 3 exp( (x p 4) 2 fit 3.7 p 5 ) + p 6 exp( (x p 7) 2 p 8 ) (3.1) fit (kev) X 1255keV Rebin8 fit 3.11 Rebin32 χ fit 40 K (1460keV) keV landau 3.9 landau fit χ 2 = 7.06 S1 S1 S2 S1 S3 S3ADC > NaI
26 3.1: 8 X 3/4 13:25:00 3/7 13:02: sec / hour SCALER(CAMAC) VS(NIM) S NaI S S1 S2 coincidence S1 S2 NaI coincidence ClockGenerator CAMAC ( ) VS LAM ( ) : 9 ADC SCALER(CAMAC) VS(NIM) S NaI S S1 S2 coincidence S1 S2 NaI coincidence ClockGenerator CAMAC ( ) VS LAM ( )
27 3.1: X 8 NaI ( ch) 3.2: X 8 S1 TDC > 4000 ( ) 3.3: X 8 S2 TDC >
28 3.4: X 8 NaI 3.5: 3.6: 9 NaI 3.7: 9 fit 3.8: NaI / kev 3.9: landau fit 27
29 3.10: fit Rebin8 3.11: Rebin : S3 NaI 28
30 4 4.1 muonic atom 2p 1s X 1 8 1cm 3 µ µ µ +, e, e +, γ 1 10GeV µ +, µ µ + µ 1.25:1 [12] µ + µ 1 1cm 3 µ A 1/ NaI NIST XCOM [7] 1255keV 1250keV NaI - NaI α c, α a, α p α c = cm 2 /g α a = cm 2 /g (4.1) α p = cm 2 /g 29
31 NaI 1 e αdl (4.2) α = α c + α a + α p,d = (NaI ) = 3.67g/cm 3 [11], L = ( NaI NaI ) L I n 4 1/2 exp( x/l) 1/2 exp( x/l) (1 e αdl ) 1cm keV X NaI 1255keV X I d I d 19.4 (4.3) 60 Co 9 60 Co clock generator 4.1 count 1173keVのピーク 1332keVのピーク CH 4.1: 9 60 Co clock generator (1bin=4CH) fitting 1173keV p 3 exp( (x p 4) 2 p 5 ) (4.4) 30
32 1332keV p 6 exp( (x p 7) 2 ) (4.5) p 8 p 3 p5 π/4, p 6 p8 π/ CH CH 4.3 count count CH CH 4.2: CH 4.3: CH Co < (ADC ) < p p 8 /2 4.4 count CH 4.4: < (ADC ) < p p 8 /2 Entry NaI 60 Co 31
33 ± muonic atom 2p 1s X N t 1255keV 1.8/ ( ) NaI Ge 60 Co fitting p 5, p 8 ( ) 2 σ 1, σ 2 σ 1 = 32.5 ± 0.2(keV) (4.6) σ 2 = 36.3 ± 0.1(keV) (4.7) muonic atom 2p 1s X 1255keV 3.8 1bin=8keV f(x) = c 1 exp( (x c 2 ) 2 /2σ 2 ) (4.8) σ σ 1, σ c 1 2π/8 < Nt < 36.3c 1 2π/8 (4.9) N t 83( ) 7 < c 1 < keV
34 count kev 4.5: keV keV 1bin / c 1 muonic atom 2p 1s X accidental coincidence muonic atom X e X e + µ + e + e γ muonic atom 1255keV X 33
35 muonic atom 1255keV X 1255keV accidental coincidence TDC 4000 clock generator 4.6 TDC keV accidental coincidence 150keV 4.7 count kev 4.6: clock generator accidental coincidence accidental coincidence keV 4.6 muonic atom X 2p 1s 75keV 3p 1s 89keV 4p 1s 94keV 3d 2p 13keV e X keV 34
36 count kev 4.7: keV muonic atom 1255keV X muonic atom 1255keV X 1255keV 1255keV 1255keV e + µ + e + e γ NaI ADC keV NaI NaI NaI 4.2 Ge µ 35
37 µ + e + e [8] muonic atom 2p 1s X accidental coincidence 36
38 Ge scintillator target scintillator 4.8: 1 scintillator target Ge scintillator 4.9: 2 37
39 scintillator target Ge scintillator 4.10: 3 38
40 A muonic atom A.1 muonic atom stopping rate A.2 B A.2 clock generator 100Hz HV discriminator threshold,width A.1 cosmic ray scintillator1 scintillator2 target scintillator3 A.1: stopping rate 39
41 HV scintillator1 amp discriminator CH1 CH1& CH2& CH3 HV scintillator2 amp discriminator CH2 coincedence CH1& CH2 visual scalar CH2& CH3 HV scintillator3 amp discriminator CH3 clock generator A.2: stopping rate HV(V) threshold(mv) width(ns) scintillator scintillator scintillator A.1: HV,discriminator threshold,width 11.10cm 5cm 10cm 20cm 4 A.3 20cm 20cm 10cm Fe 5cm A.3: 40
42 A.3 (s) CH1&CH2&CH3, CH1&CH2, CH2&CH3 visual scalar A.2 (s) CH1&CH2&CH CH1&CH CH2&CH A.2: (s) CH1&CH2&CH3, CH1&CH2, CH2&CH3 A (A.1) cm ( ) 4 1 1cm 3 µ µ + 41
43 B Ge B.1 Ge Ge 1255keV X 1171keV 1332keV 60 Co B.2 B.1 60 Co Ge 60 Co Ge 検 出 器 pre-amp Signal 電 源 kromek Baias-Supply Shaping-Amp MCA TC INH 950A inhibit -5V/sで-3000Vに GAIN 1V TIME CONSTANT 25μs B.1: Ge Baias 5V/s V Shaping-Amp GAIN TIME CONSTANT 1V,25µs B.2 60 Co Ge d Ge di Ge r di = 0.5cm, r = 2.3cm 42
44 60 Co d di Ge r B.2: Ge 60 Co B.1 60 Co Ge d 10cm,20cm,30cm Ge 1173keV,1332keV B.3 B.1 d =10cm d =20cm d =30cm (s) keV keV B.1: d 10cm,20cm,30cm Ge 1173keV,1332keV 60 Co 1171keV 1332keV kBq,134.80kBq 60 Co kBq,80.53kBq ( ) = ( ) ( ) ( ) 1 2 (1 d + di (d + di)2 + r ) (B.1) 2 B.1 B.2 43
45 d =10cm d =20cm d =30cm 1173keV (%) keV (%) B.2: d 10cm,20cm,30cm 1173keV,1332keV B keV 1332keV γ X 5% 7% 44
46 1 TA TA P3 1 EPR muon 1 45
47 [1] VAL L. FITCH AND JAMES RAINWATER, Studies of X-Rays from Mu-Mesonic Atoms (PHYSICAL REVIEW 1953) [2] D.F. Measday, The nuclear physics of muon capture (Physics Reports ) [3], ( 1994) [4], - - ( 2004) [5] International Atomic Energy Agency (IAEA), Generic procedures for assessment and response during a radiological emergency(iaea- TECDOC-1162) (IAEA 2000) [6] William R Leo, Techniques for Nuclear and Particle Physics Experiments: A How-to Approach (Springer 1994) [7] National Institute of Standerds and Technology (NIST), XCOM: Photon Cross Sections Database ( [8] 2006 P3µ, µ X (2006 P3 ) [9], [ ] ( ) ( 2004) [10], ( [11] (NIHS), (ICSC) - - ( [12], 20 ( 1978) 46
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スライド 1
実験 III 素粒子テーマ 素粒子物理学とは 物質の究極の構造 ( 素粒子 ), 素粒子間に働く力 ( 相互作用 ) 時空の構造, 対称性を探求する分野です 担当教員 : 佐藤 TA: 和田 内山連絡先 : 自然学系棟 D208 (x4270) ksato@hep.px.tsukuba.ac.jp 実験スケジュール 第 1 回 : 素粒子物理概説,μ 粒子寿命測定法, 同軸ケーブルとインピーダンス,NIMモジュールの機能.
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スライド 1
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