( ) TA 2234 oda@phys.kyushu-u.ac.jp TA (M1) 2161 sumi@epp.phys.kyushu-u.ac.jp TA (M1) 2161 takada@epp.phys.kyushu-u.ac.jp TA (M1) 2254 tanaka@epp.phys.kyushu-u.ac.jp µ ( ) 1 2 1.1............................................... 2 1.2....................................................... 3 1.3 :.......................................... 3 1.4............................................. 3 1.5.................................... 4 2 5 2.1...................................................... 5 2.2...................................................... 5 2.3 β...................................................... 6 3 8 4 9 5 11 5.1.................................................. 11 5.2.................................................. 11 5.3 (PMT).............................................. 12 6 (DAQ:Data Acquisition) 13 6.1 NIM.......................................... 13 6.2 CAMAC....................................... 15 7 16 8 23 9 27 10 27 A UNIX 28 1
1 1 (proton, p) (neutron, n) (uud), (udd) u ( ) d ( ) u d ( ) 1: 2: 1.1 2 1/2 1 0 ( ) 3 1 200 3 1 ( 2) 0 (γ) 0 (g) ( fm) W Z 0 0 β( ) 1 1 3 2
1.2 µ µ + 2 (e ) (e + ) 2 ( (ν e ) (ν e ) (ν µ ) (ν µ )) 3 µ ν µ + e + ν e µ + ν µ + e + + ν e µ ν µ W e ν e 3: (µ ) W 1.3 : 1910 Hess 2 p + Air p, n, π 0, π ±, K ± u d π u s( ) K W π + (u d) µ + + ν µ, π (dū) µ + ν µ, K + (u s) µ + + ν µ, K (sū) µ + ν µ 1.4 1.2 λ t N(t) dt dn dn = λn(t)dt t N(t) = N 0 exp ( λt) 2 e µ τ ν e ν µ ν τ +1 e + µ + τ + ν e ν µ ν τ 1 3
N 0 t = 0 dn dt τ ( τ = t dn ) / ( dt dn ) dt = 1N0 tn 0 λ exp ( λt)dt = dt dt 0 (1.1) 0 dn dt = N 0 λ exp ( λt) (1.1) = N 0 τ 0 0 λte λt dt = 1 λ exp ( t/τ) (1.2) 1/e 1/2 1.5 µ µ + p ν µ + n (1.3) λ (1.3) λ t µ N(t) = N 0 exp ( λt) exp ( λ t) = N 0 exp ( ( λ + λ ) t ) τ τ = 1 λ + λ < 1 λ µ (τ µ = 2197 ns) τ µ (Al) = 864 ns Phys. Rev. C 35, 2212 (1987)) (background) 3 (1.4) dn vis dt = N exp ( t/τ µ ) + N + exp ( t/τ µ +) + r bkg (1.5) τ µ + τ µ + τ µ, τ µ + µ, µ + N, N + t = 0 µ, µ + r bkg λ/(λ + λ ) = τ µ /τ µ + 1 τ µ τ µ + 4
2 2.1 α β γ α β γ α 2 2 4 He α 1 β ( ) α mm γ γ γ 2.2 4 5 α β γ ±1±2±3+4+5 1/2+ 1+ 1/2-1+ 1/2-2- 1/2-1- (1/2-) 14.00674 0.0102% p EC3α EC 99.634 0.366 β - α β - n β - n,β - α, β - n 2 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 230 kev 126.5 ms 19.255 s 20.39 m 5730 y 2.449 s 0.747 s 193 ms 95 ms 0+ (3/2-) 0+ 3/2-0+ 1/2-0+ 1/2+ 0+ 0+ 6 C 4492t 4 3642s +2+4-4 12.0107 0.033% ECp,ECp2α,... EC EC 98.90 1.10 β - β - β - n β - n β - n 2 B7 B8 B9 B10 B11 B12 B13 B14 B15 B16 B17 1.4 MeV 770 ms 0.54 kev 20.20 ms 17.36 ms 13.8 ms 10.5 ms 200 Ps 5.08 ms (3/2-) 2+ 3/2-3+ 3/2-1+ 3/2-2- (0-) (3/2-) 5 B 2075 3 4000 +3 10.811 6.9 10-8 % EC2α 2pα 19.9 80.1 β - 3α β - n β - β - n β - n 2 Be5 Be6 Be7 Be8 Be9 Be10 Be11 Be12 Be13 Be14 92 kev 53.12 d 6.8 ev 1.51E+6 y 13.81 s 23.6 ms 0.9 MeV 4.35 ms 0+ 3/2-0+ 3/2-0+ 1/2+ 0+ (1/2,5/2)+ 0+ 4 Be 1287 2 2471 +2 9.012182 2.38 10-9 % 2p EC 2α 100 β - β - α β - n β - n,β - 2n,... 2 Li4 Li5 Li6 Li7 Li8 Li9 Li10 Li11 Li12 1.5 MeV 838 ms 178.3 ms 1.2 MeV 8.5 ms 2-3/2-1+ 3/2-2+ 3/2-3/2-3 Li 180.5 1 1342 +1 6.941 10 1.86 10-7 % p 7.5 92.5 β - 2α β - n n β - n,β - 2n,... 2 He3 He4 He5 He6 He7 He8 He9 He10 0.60 MeV 806.7 ms 160 kev 119.0 ms 0.30 MeV 0.3 MeV 1/2+ 0+ 3/2-0+ (3/2)- 0+ (1/2-) 0+ 2 He -272.2-268.93-267.96 0 4.002602 8.9% 0.000137 99.999863 n β - n β - n n n -259.34-252.87 H1 H2 H3 H4 H5 H6-240.18 12.33 y +1-1 1/2+ 1+ 1/2+ 2-1.00794 6 8 1 99.985 0.015 β - n1 614.6 s 1/2+ 1 H 91.0% β - 7 2 4 β - n C19 46 ms β - n B18 β - n C20 14 ms 0+ β - n B19 12 14 β - n C21 C22 0+ 16 Decay Q-value Range Q(??) Q(β )>0 Q(β )-S N >0 Q(β )>0 + Q(EC)>0 Stable to Beta Decay Q(EC)>0 Q(EC)-S P >0 Q(P)>0 Naturally Abundant 4: 5
60000 56000 52000 48000 44000 40000 36000 32000 28000 24000 20000 16000 12000 10000 8000 Sp Sn (18800) (4600) 0+ 60 22 Ti Q!" (10400) Sp (14200) Sn 3200 Sp (3+) 200 ms 60 23 V!" Q!" 13800 Sn 16200 0+ 0.57 s 60 24 Cr!" Q!" 6100 7000 1.77 s 51 s Sp Sn 12400 5500 88.5% 3+ 271.8!" 0+ 0 60 25 Mn!" IT 11.5% Sp Sn 13220 8820 A=60 NDS 69, 1(1993) Sp Sn 8274.8 7491.93 Sn Sp 11388.3 9533.5 Sn Sp 10061.0 4479.0 Sn Sp 15000 5121 0+ 2.38 m EC 60 30 Zn Sn Sp (13950) (30) 60 31 Ga Q EC (14190) Sn (18800) 60 33 As Sp (900) 0+ 60 32 Ge Q EC (12200) Q EC (21400) Q p (3300) 6000 5000 4000 3000 2000 1000 Q!" 8500 0+ 1.5#10 6 y 60 26 Fe!" Q!" 237 0.24% 2+ 58.59!" 10.467 m 5+ 0 60 27 Co 5.2714 y!" IT 99.76% Q!" 2823.9 2+ 23.7 m EC 60 29 Cu Q EC 6126.9 Q EC 4158 500 100 0 Evaluator: M.M. King 0+ 60 28 Ni 5: A = 60 60 60 28Ni : 28Ni 2.3 β β β β + (Electron Capture) 3 1 β ( 6) (Z, N) (Z + 1, N 1) + e + ν e n p + e + ν e d u + e + ν e β + ( 7) (Z, N) (Z 1, N + 1) + e + + ν e p n + e + + ν e u d + e + + ν e EC (Z, N) + e (Z 1, N + 1) + ν e p + e n + ν e u + e d + ν e 1: β EC 60 27 Co β 60 28Ni ( 5) β ν e 3 ( 8) 1 3 (uud), (udd) u d + 2 3 e, 1 3e 1 6
n u d d u d u p p u d u u d d n W e W + e + ν e ν e 6: β 7: β + The number of particles [Arbitary Unit] from 90 Y 0 0.5 1 1.5 2 2.5 Kinetic energy [MeV] - β γ 60 from Co 8: 90 Y β 60 Co γ 3 β β 2 γ γ 7
3-3 (Photo Absorption) X ( ) X 3 (Compton Scattering) γ 2 180 ( ) - (Pair Creation) - - 2 511 kev γ γ 3 1 8
4 ( ) S E x ( S = lim E ) = de x 0 x dx Bethe-Bloch de dx = 2πN arem 2 e c 2 ρ Z z 2 [ ( 2me γ 2 v 2 ) ] W max ln 2β 2 A W max = 1 + 2 m e M β 2 2m e c 2 (βγ) 2 1 + (βγ)2 + ( m e M ) 2 I 2 x : [g/cm 2 ] N a : 6.022 10 23 mol 1 r e : 2.818 10 15 m m e : 9.109 10 31 kg c : 299792458 m/s ρ : Z : A : z : e v : β : c β = v/c γ : γ = 1/ 1 β 2 I : 10Z ev W max : M : 0.3 GeV/c 0.4 GeV/c ( 9) 1 ( ) de 3.5 Z ρ dx A MeVcm2 /g (4.1) MIP (Minimum Ionizing Particle) min 9
10 8 1 cm 2 ) de/dx (MeV g 6 5 4 3 2 H 2 liquid He gas Fe Sn Pb Al C 1 0.1 1.0 10 100 1000 10 000 = p/mc 0.1 0.1 1.0 10 100 1000 Muon momentum (GeV/c) 1.0 10 100 1000 Pion momentum (GeV/c) 0.1 1.0 10 100 1000 10 000 Proton momentum (GeV/c) 9: de/dx 10
5 ( 10) 5.1 10: ( ) ( ) ( ) ( ) ns γ 5.2 ( ) 11
5.3 (PMT) Photomultiplier Tube : PMT PMT PMT 11 (cathode) (dynode) ( ) (anode) 3 Dynode Photocathode 11: PMT Anode 12
6 (DAQ:Data Acquisition) DAQ NIM (Nuclear Instrument Module ) CAMAC (Computer Automated Measurement And Control ) NIM CAMAC 6.1 NIM High Voltage Power Supply (HV) HV 0 3.0 kv (2 ma) Discriminator ( ) (threshold) (width) ( 0.8 V NIM ) 12 INPUT threshold OUTPUT width width 12: Discriminator Coincidence ( ) 2 (width) AND Veto 13 INPUT-1 INPUT-2 OUTPUT width width 13: Coincidence 13
Clock generator ( ) ( 0.8 V NIM ) Delay ( ) 14 INPUT OUTPUT delay time 14: Delay Scaler ( ) 14
6.2 CAMAC Crate Controller (CC ) CC Linux CAMAC CAMAC CC PC TDC (Time to Digital Converter ) 15 C027 50 MHz START STOP 20 ns START STOP (20 ns ) Time to Analogue Converter (TAC) 2 16 CC 24 12 11 TAC 1 70 µs 40 ps START STOP t 1 t 2 t 3 15: TDC START STOP t i 50 MHz clock START TAC (START) STOP TAC (STOP) Time The number of clocks=2 20 ns 16: TDC START STOP 20 ns START STOP (20 ns ) Time to Analogue Converter (TAC) 70 µs 40 ps 15
7 1 90 Sr β 60 Co γ β β γ 90 28.8 years Sr - β 0.546 MeV 90 64.1 hours Y 0.01% - β 0.522 MeV 99.99% - β 2.282 MeV γ 1.761 MeV 90 Zr 60 5.271 years Co 99.93% - β 0.318 MeV 0.06% - β 1.491 MeV γ 1.173 MeV γ 1.333 MeV 60 Ni 17: 90 Sr 18: 60 Co 1. PMT HV SHV (HV) (QUAD HIGH VOLTAGE POWER SUPPLY, RPH-033) 1ch 2. PMT A1 BNC T 1 (1CH) 50 Ω A2 DY 50 Ω 3. 1CH 4. 10.0 mv 10.0 ns ( 10 mv ) 5. NIM NIM HV 1ch ON 6. HV 1700 V (VOLT) 1100 V 7. discriminator (8CH DISCRIMINATOR) (V TH ) 100 mv V= discriminator NIM GND( ) 8. 1CH T LEMO discriminator IN( ) OUT( ) 2CH 2CH 9. 6.1 discriminator 20 10. LEMO scaler (8CH VISUAL SCALER, N-OR 425) IN 1 19 16
11. scaler 1 Clock generator 100 Hz NIM 0.01 ( 60.21 ) 12. 90 Sr scaler 1 13. 0.6 mm scaler 1 14. 1 mm 0.6+1 mm 3 mm scaler 1 15. 2 mm scaler 1 16. 1 1 17. 60 Co 3 mm 3 mm + 2 mm 3 mm + 4 mm 3 mm + 6 mm 3 mm + 8 mm 5 scaler 1 1 3 mm 60 Co β γ 18. OFF 19: 20: 19 17
2 NIM 21 #1 #2 #3 21: #1 #2 #3 #1 #1 #2 #2 #1 #2 #2 #3 ( ) ( ) #1 #2 #3 #1 #2 #2 #3 HV #1 #2 #3 1. NIM 2. Clock generator 100 Hz divider 3 discriminator ch1 ch3 IN PMT #1 #3 3. Discriminator ch threshold 100 mv Width #1 #3 70 ns #2 50 ns 70 ns width 4. HV #1 #2 #3 (#1 #2 #3) Coincidence 1 A discriminator #1 OUT 1 ns LEMO B discriminator 18
Coincidence rate [Hz] 20 18 16 14 12 10 8 6 4 2 0 #1 #2 #3 1500 1550 1600 1650 1700 1750 1800 1850 -HV [V] 22: PMT ( HV) 1 (#1 #2 #3) HV #1 HV=1650 V #2 HV=1650 V #3 HV=1750 V 100% 1 16 #1 #2 #2 #3 #3 #1 #2 #3 #2 #3 0 4 14 54 64 70 t [ns] 0 10 50 70 85 t [ns] #1 #2 #3 23: Start #1 #2 #3 24: #2 #3 #1 (#2 #3) #1 (#2 #3) 0 9 19 69 70 79 t [ns] 0 50 t [ns] 25: Stop 26: Start Stop 19
#2 OUT 5 ns LEMO C discriminator #3 OUT 1 ns LEMO A B C IN D OFF OUT 5. HV ch1 ch3 PMT 1700 V 10 mv 1100 V 6. #1 #3 discriminator ch1 ch3 clock generator 7. Discriminator #1 OUT scaler IN 1 #2 OUT IN 2 #3 OUT IN 3 (#1 #2 #3) OUT IN 4 Clock generator NIM IN 5 8. #1 HV 1500 V 1900 V 50 V 1 (#1 #2 #3) 9. 1 HV [V] [Hz=1/s] ( 22) 10. HV ( 22) 11. #2 #3 HV 12. Clock generator discriminator ch1 ch3 #1 #3 13. Start #1 #2 #2 #3 Start #1 #2 #3 (#1 #2 #3) Coincidence 1 A discriminator #1 OUT 1 ns LEMO B #2 OUT 5 ns LEMO VETO discriminator #3 OUT 1 ns LEMO A B IN C D OFF VETO (#1 #2 #3) #2 ( 23) OUT 14. Stop Stop #2 #3 #1 (#1 ) (#1 (#2 #3)) Coincidence 2 A discriminator #2 OUT B #3 OUT 1 ns LEMO A B IN C D OFF N 3 2 1 N 3 (#2 #3) ( 24) N 3 width 75 ns coincidence 2 N 3 3 A discriminator #1 OUT VETO 2 ns LEMO A IN B C D OFF (#1 (#2 #3)) VETO #1 (#2 #3) ns ( 25) Start 15. Start Stop Start delay ( 26) 16. Start Stop TDC CH2 START STOP 17. #1 #3 discriminator ch1 ch3 clock generator 18. Discriminator #1 OUT scaler IN 1 #2 OUT IN 2 #3 OUT IN 3 Start OUT IN 4 Stop OUT IN 5 (Discriminator OUT #1 #2 #3 ) 20
19. CAMAC 1 (CC) 20. ( slc01 slc02 slc03 ) muon_3rd (terminal) CC $ ssh b3muon@ccnet01 $ Linux slc02 ccnet02 slc03 ccnet03 21. Password 22. cd /home/b3muon/camac/program/ $ cd /home/b3muon/camac/program/ 23. TDC $./measure_c027.sh [ ] [1 run ] [run ] /home/b3muon/camac/data/data1/ 24. [1 run ] 1 run 100 20 100 PC data $./measure_c027.sh /home/b3muon/camac/data/data1/ 1 100 25. 3 100 26. [1 run ] 100 run 10000 $./measure_c027.sh /home/b3muon/camac/data/data2/ 100 10000 21
3 1. PC data 2. dat cat 1 $ cd /home/muon_3rd/camac/data/data2/ $ cat *.dat > TDC.data * >.dat cat TDC.data 3. 4 3 Ctrl+c CAMAC ccnet halt TA 22
8 ROOT 1. TDC.data ROOT $ root -l (-l ) ROOT root [] 2. ROOT.q root [].q 3. (start, stop, tdc) root [] double start, stop, tdc; 4. 0 ns 20000 ns 200 root [] TH1D *hist = new TH1D("hist", "hist", 200, 0., 20000.); 5. TDC.data root [] ifstream data("tdc.data"); 6. start stop tdc tdc Start Stop ( ns) root [] while(!data.eof()) {data >> start >> stop >> tdc; if(!data.eof()) hist->fill(tdc);}; 7. TDC.data root [] data.close(); 8. root [] hist->draw(); 300 hist hist Entries 10400 Mean 3392 RMS 4420 250 200 150 100 50 0 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 27: 23
9. root [] hist->settitle("muon Lifetime; time[ns]; Counts"); root [] hist->getxaxis()->centertitle(); root [] hist->getyaxis()->centertitle(); root [] hist->draw(); PDF root [] c1->print("hogehoge muon lifetime.pdf"); hogehoge PDF Evince PDF $ evince hogehoge muon lifetime.pdf (F) (P) Canon-LBP5300-CAPT (P) 1. root [] gstyle->setoptfit(1111); 2. f1 root [] TF1 *f1 = new TF1("f1", "[0]*exp(-x/[1])+[2]", 0., 20000.); p 0 exp( t[ns]/p 1 ) + p 2 p 1 ns 3. f1 p 0 300 p 1 2200 p 2 5 root [] f1->setparameters(300., 2200., 5.); 4. p 2 10 root [] f1->setparameter(2, 10.); 5. hist f1 root [] hist->fit("f1"); 6. root [] hist->fit("f1", "R", "", 500., 15000.); 500 15000 7. UnZoom 24
8. 28 ( p1) 1774 ± 36 ns µ µ + τ µ τ µ + τ µ τ µ + (= N i f (t i ) (N i N i ) χ 2 = i{n i f (t i )} 2 /{ N i } 2 ) (the number of degrees of freedom) χ 2 /ndf 1 FCN=234.274 FROM MIGRAD STATUS=CONVERGED 75 CALLS 76 TOTAL EDM=1.05873e-07 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 p0 2.98007e+02 6.68766e+00 3.19047e-02 3.40109e-05 2 p1 1.77393e+03 3.63219e+01 1.61785e-01 1.70901e-05 3 p2 5.65529e+00 2.30900e-01 1.55592e-03 1.64550e-03 300 Muon LifeTime hist Entries 10400 Mean 3392 RMS 4420 2 χ / ndf 234.3 / 197 Prob 0.03561 p0 298 ± 6.7 p1 1774 ± 36.3 p2 5.655 ± 0.231 250 200 Counts 150 100 50 0 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 time [ns] 28: 25
(uud) π + (u d) π (dū) µ + µ 1.5 t = 0 ns µ + N + µ N R = N + /N muon charge ratio muon charge ratio R 1.3 1.5 dn vis dt = N { exp ( t/τµ ) + R exp ( t/τ µ +) } + r bkg (8.1) τ µ + t x N p 0 τ µ + p 1 τ µ p 2 R p 3 r bkg p 4 root [] TF1 *f2 = new TF1("f2", "[0]/[1]*(exp(-x/[2])+[3]*exp(-x/[1]))+[4]", 0., 20000.); τ µ + τ µ R τ µ + τ µ R root [] f2->fixparameter(1, 2197.); root [] f2->fixparameter(2, 864.); root [] f2->fixparameter(3, 1.3); root [] hist->fit("f2"); N (p 0 ) r bkg (p 4 ) root [] hist->fit("f2", "R", "", 500., 20000.); τ µ + (p 1 ) root [] f2->releaseparameter(1); root [] hist->fit("f2", "R", "", 500., 20000.); 40 ns τ µ + 2197 ns? 2% R (p 3 ) τ µ + R root [] f2->releaseparameter(3); root [] hist->fit("f2", "R", "", 500., 20000.); R 1.3? τ µ + R? τ µ (p 2 ) root [] f2->releaseparameter(2); root [] hist->fit("f2", "R", "", 500., 20000.); 864 ns? τ µ + R τ µ 200 100 26
9 ( ) ( A4 5 ) 2014 PDG (Particle Data Group) τ µ = 2196.9811 ± 0.0022 ns 4 (= ) 1 2 4 ( ) 5 2 10 1. 2. 3. 4. PMT SHV 5. 0 6. 7. 8. 9. LEMO 27
A UNIX 2: UNIX $ pwd $ cd $ cd $ ls $ ls -a Emacs vi $ mkdir $ cp $ mv $ mv $ rm $ rmdir $ rm -r $ find -name $ find -name * * $ grep -r $ emacs $ vi $ less $ cat 1 2 28