Fe muonic atom X 25 5 21
3 1 4 1.1......................... 4 1.1.1....................... 4 1.1.2.................. 4 1.1.3 Coulomb potential.............. 5 1.2.......................... 6 1.2.1................... 6 1.2.2 X............... 7 1.2.3.................. 8 1.2.4 muon muonic atom..... 9 2 10 2.1.............................. 10 2.2.......................... 10 2.3 X............................ 16 2.4........................... 16 2.5 trigger............................ 17 2.6 ADC............................. 17 2.7.............................. 17 3 23 4 29 4.1.......................... 29 4.2............................... 35 A muonic atom 39 A.1................................ 39 A.2........................... 39 A.3............................ 41 1
B Ge 42 B.1................................ 42 B.2........................... 42 B.3............................ 43 45 46 2
µ 200 µ muon atom µ 1/200 µ 2p 1s X µ Fe muonic Fe X NaI 11 X 3
1 1.1 1.1.1 1.1.2 E e 150 200MeV 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 =1.1 1.3(fm) 3. a A a=0.5 0.6(fm) 4
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
V(r)(MeV) r(fm) 1.2: Coulomb potential 1.2 1.2.1 muon 206.77 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
1.3: 2p,1s Fe 1.2.2 X ( S) 10 13 10 14 sec 2.1 10 6 sec X X X E1 3d 2p 2p 1s 2p 1s 1s 7
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
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
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 3 1 1255keV X 1255keV X I n ( )/(1 /cm 3 ) 4. Ge 5% B 3. I n C 1. X I I = 0 2. 1255keV X 3. 2π X X 4. X I 1/2 exp( x/l) I l 2.38cm [7],[10] 10
x X 1/2 X 2π 5. 2. 4. 6. I ( (cm 3 )) /(100,000,000) I n l = 2.38cm 2.1 2.2 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 0 2 2 s h Ge Ge a 2 x a 2 a 2 2.1: A 11
z y 0 x z a 2 z a 2 a 2 d2 r d1 y 0 a d2 a 0 2 2 Ge h r s Ge a 2 x a 2 a 2 2.2: B 2.1 2.2 r = 2.3cm, h = 3.3cm, d1 = 1.0cm, d2 = d3 = 2.2cm a, s I n s = 0 a I n w 2.1 2.2 a I n 2.3 2.4 7.87g/cm 3 [10] 12
a(cm) I n ( ) w(kg) 10.0 13.8 2.7 10.5 16.4 3.7 11.0 18.8 4.7 11.5 20.9 5.9 12.0 22.9 7.2 12.5 24.6 8.6 13.0 26.2 10.2 13.5 27.6 11.9 14.0 28.9 13.7 14.5 30.1 15.8 15.0 31.2 17.9 15.5 32.1 20.3 16.0 33.0 22.8 16.5 33.9 25.5 17.0 34.7 28.4 17.5 35.3 31.5 18.0 36.0 34.8 18.5 36.6 38.2 19.0 37.1 41.9 19.5 37.6 45.8 20.0 38.1 50.0 20.5 38.5 54.3 21.0 38.9 58.9 21.5 39.3 63.7 22.0 39.7 68.8 22.5 40.0 74.1 23.0 40.3 79.7 23.5 40.5 85.6 24.0 40.8 91.7 24.5 41.0 98.1 25.0 41.2 104.7 a(cm) I n ( ) w(kg) 10.0 12.2 2.5 10.5 14.3 3.2 11.0 16.3 4.1 11.5 18.0 5.1 12.0 19.7 6.2 12.5 21.2 7.5 13.0 22.5 8.9 13.5 23.8 10.4 14.0 24.9 12.0 14.5 25.9 13.8 15.0 27.0 15.8 15.5 27.8 17.9 16.0 28.6 20.2 16.5 29.4 22.6 17.0 30.1 25.2 17.5 30.8 28.0 18.0 31.5 31.0 18.5 32.1 34.2 19.0 32.7 37.6 19.5 33.2 41.2 20.0 33.7 45.0 20.5 34.2 49.1 21.0 34.6 53.3 21.5 35.1 57.8 22.0 35.5 62.5 22.5 35.8 67.5 23.0 36.2 72.7 23.5 36.5 78.2 24.0 36.9 83.9 24.5 37.2 89.9 25.0 37.4 96.1 2.1: A s = 0 2.2: B s = 0 a I n a I n (w) (w) 13
I n a(cm) 2.3: A s = 0 a I n I n a(cm) 2.4: B s = 0 a I n 2.1 2.2 A B I n /w A 2p 1s X c n In 0.716 0.05 4 0.143I n 14
kg I n 28 c n 4 a = 14cm a = 14cm s I n, w 2.3 2.5 s(cm) I n w(kg) -3.0 26.4 11.3-2.5 27.6 11.7-2.0 28.4 12.1-1.5 28.8 12.5-1.0 29.0 12.9-0.5 29.0 13.3 0.0 28.9 13.7 0.5 28.6 14.1 1.0 28.3 14.5 2.3: A a = 14cm s I n (w) I n s(cm) 2.5: A a = 14cm s I n s = 2 a = 14cm 2.6 15
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
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 S1 100000 off Co on 11 S1 S3 4 17
S1:H6522B S2:H1161 S3:H1161 Scaler(8ch VISUAL SCALER) N-OR 426 100MHz 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-033 16ch 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
S3 5.0 14.2 1.0 11.5 1.5 S1 NaI Fe 14.0 2.5 table S2 8.5 Pb wood 5.0 2.4 20.0 14.0 2.7: 19
10.0 S3 S1 Fe 14.2 1.5 1.0 S2 Pb Fe 6.5 table Fe Pb Pb Pb wood 40.0 14.0 2.8: 20
Pb Pb Fe Pb NaI 5.0 15.0 10.0 5.0 20.0 2.9: NaI 21
0.8 1.5 S2 S3 10.0 S1 14.0 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
3 60 Co 8 muonic Fe X 8 CAMAC SCALER NIM VISUAL SCALER(VS) 3.1 VS NaI S2 1 37.8 2.11 S1 S2 NaI ClockGenerator 1Hz or 2 SCALER 250320 250312 Clock or Clock 1Hz VS Clock 0.77986Hz 0.006% ADC NaI 3.1 280ch 400 600ch Clock TDC 500ch 4100ch 2 TDC > 4000 3.2 3.3 S1, S2 ADC S1 280ch S2 320ch Discriminator threshold S1 ADC > 280 S2 ADC < 320 NaI 3.4 X 533ch 3.5 23
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) 3.8 3.10 X 1255keV Rebin8 fit 3.11 Rebin32 χ 2 1.85 0.995 fit 40 K (1460keV) 3.8 800keV landau 3.9 landau fit χ 2 = 7.06 S1 S1 S2 S1 S3 S3ADC > 320 91.14 NaI 3.12 24
3.1: 8 X 3/4 13:25:00 3/7 13:02:00 257820sec / 71.6167hour SCALER(CAMAC) VS(NIM) S1 2281025 2281030 5 NaI 1466528 1469236 2708 S2 1429285 1429436 151 S1 S2 coincidence 2104788 2104837 49 S1 S2 NaI coincidence 49253 49257 4 ClockGenerator 201062 201063 1 CAMAC ( ) VS LAM ( ) 250312 250313 1 3.2: 9 ADC 100000 SCALER(CAMAC) VS(NIM) S1 617333 618254 921 NaI 163530 164411 881 S2 2250 2255 5 S1 S2 coincidence 617092 618063 971 S1 S2 NaI coincidence 100271 100413 142 ClockGenerator 211 211 0 CAMAC ( ) VS LAM ( ) 100000 100594 594 25
3.1: X 8 NaI ( ch) 3.2: X 8 S1 TDC > 4000 ( ) 3.3: X 8 S2 TDC > 4000 26
3.4: X 8 NaI 3.5: 3.6: 9 NaI 3.7: 9 fit 3.8: NaI / kev 3.9: landau fit 27
3.10: fit Rebin8 3.11: Rebin32 3.12: S3 NaI 28
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 1/2.25 1.8 NaI NIST XCOM [7] 1255keV 1250keV NaI - NaI α c, α a, α p α c = 4.846 10 2 cm 2 /g α a = 2.240 10 3 cm 2 /g (4.1) α p = 1.634 10 4 cm 2 /g 29
NaI 1 e αdl (4.2) α = α c + α a + α p,d = (NaI ) = 3.67g/cm 3 [11], L = ( NaI NaI ) L 2.2 2.2 I n 4 1/2 exp( x/l) 1/2 exp( x/l) (1 e αdl ) 1cm 3 1 1255keV 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
1332keV p 6 exp( (x p 7) 2 ) (4.5) p 8 p 3 p5 π/4, p 6 p8 π/4 4.1 50CH 4.2 600CH 4.3 count count CH CH 4.2: 4.1 50CH 4.3: 4.1 600CH 4.2 4.3 60 Co 4.1 0 < (ADC ) < p 7 + 3 p 8 /2 4.4 count CH 4.4: 4.1 0 < (ADC ) < p 7 + 3 p 8 /2 Entry NaI 60 Co 31
10 0.302±0.005 11 muonic atom 2p 1s X N t 1255keV 1.8/1 0.716 19.4 0.302 11 83( ) 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 2 32.5c 1 2π/8 < Nt < 36.3c 1 2π/8 (4.9) N t 83( ) 7 < c 1 < 9 3.8 1255keV 4.5 32
count kev 4.5: 3.8 1255keV 4.5 12255keV 1bin 100 140 1/2 10 12 c 1 muonic atom 2p 1s X accidental coincidence muonic atom X e X e + µ + e + e γ muonic atom 1255keV X 33
muonic atom 1255keV X 1255keV accidental coincidence TDC 4000 clock generator 4.6 TDC 4000 150keV accidental coincidence 150keV 4.7 count kev 4.6: clock generator accidental coincidence 3.8 125796 4.6 648190 3.8 accidental coincidence 3.8 150keV 4.6 muonic atom X 2p 1s 75keV 3p 1s 89keV 4p 1s 94keV 3d 2p 13keV e X 3.8 150keV 34
count kev 4.7: 4.6 150keV muonic atom 1255keV X muonic atom 1255keV X 1255keV 1255keV 1255keV e + µ + e + e γ NaI ADC 3.8 150keV NaI NaI NaI 4.2 Ge µ 35
µ + e + e [8] 1 4.8 2.2 2 4.9 3 4.10 3 muonic atom 2p 1s X accidental coincidence 36
Ge scintillator target scintillator 4.8: 1 scintillator target Ge scintillator 4.9: 2 37
scintillator target Ge scintillator 4.10: 3 38
A muonic atom A.1 muonic atom stopping rate A.2 B.2 3 2 3 A.2 clock generator 100Hz HV discriminator threshold,width A.1 cosmic ray scintillator1 scintillator2 target scintillator3 A.1: stopping rate 39
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) scintillator1 1450 439 70 scintillator1 1450 372 70 scintillator1 1450 483 70 A.1: HV,discriminator threshold,width 11.10cm 5cm 10cm 20cm 4 A.3 20cm 20cm 10cm Fe 5cm A.3: 40
A.3 (s) CH1&CH2&CH3, CH1&CH2, CH2&CH3 visual scalar A.2 (s) 12459.06 67464.29 CH1&CH2&CH3 19794 94223 CH1&CH2 143410 755828 CH2&CH3 66758 157671 A.2: (s) CH1&CH2&CH3, CH1&CH2, CH2&CH3 A.2 1 19794 12459.06 94223 0.19 (A.1) 67464.29 1 1cm 3 0.19 60 60 24 (5 10 20 4) 4 1 1cm 3 µ µ + 41
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 1-3000V Shaping-Amp GAIN TIME CONSTANT 1V,25µs B.2 60 Co Ge d Ge di Ge r di = 0.5cm, r = 2.3cm 42
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) 196 174 180 1173keV 9243 2995 1460 1332keV 9115 2531 1301 B.1: d 10cm,20cm,30cm Ge 1173keV,1332keV 60 Co 1171keV 1332keV 1430 131.97kBq,134.80kBq 60 Co 5.272 2 1430 5.272 365 78.84kBq,80.53kBq ( ) = ( ) ( ) ( ) 1 2 (1 d + di (d + di)2 + r ) (B.1) 2 B.1 B.2 43
d =10cm d =20cm d =30cm 1173keV (%) 5.2 7.0 7.3 1332keV (%) 5.0 5.8 6.3 B.2: d 10cm,20cm,30cm 1173keV,1332keV B.2 1173keV 1332keV γ X 5% 7% 44
1 TA TA P3 1 EPR muon 1 45
[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 354 2001) [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 (http://www.nist.gov/pml/data/xcom/) [8] 2006 P3µ, µ X (2006 P3 ) [9], [ ] ( ) ( 2004) [10], (http://www.rikanenpyo.jp/) [11] (NIHS), (ICSC) - - (http://www.nihs.go.jp/icsc/) [12], 20 ( 1978) 46