入門講座 陽電子寿命測定法 - positron-science.org

1 2 (2014) 21 27 Japanese Positron Science Society .. Positron lifetime measurement technique . Abstract: The basic principles of the positron lifetime measurement technique are described. The topics are as follows: (1) timing measurements of creation and annihilation of positrons, (2) -ray detector, (3) signal processing for the -ray timing, (4) positron lifetime spectrum, (5) data analysis, and (6) fundamental annihi- lation process. Keywords: positron, positron lifetime, measurement method, ray, -ray detector, scintillation detector, life- time spectrum 1.. 106 107 .. 2.. 1 . 2 . 511 keV 3 0 511 keV . 11 12 .. + .. 22. Na 22 Ne + e+ + e (1).. e 22 Ne .. 22 Ne ps .. MeV .. ps . 22 Na .. 22 Na .. 11 11 23 Na.

2 Haruo Saito (Graduate School of Arts and Sciences, the University 1 . of Tokyo), . 153 8902 3 8 1. TEL: 03 5454 6548, E-mail: + .. 1 .. NaI(Tl) g cm 3. BaF2 ns 4% 220 nm . BC-422 ns 25% 1 NE-111A . BC-418 ns 25% 1 Pilot-U . LaBr3 (Ce) 40 ns 160% 200 ps 4%@511 keV . BC .. 22 Na mm 68 Ge mm . 100 ps . RF .. 1 . 3.. BaF2 . g cm 3 . ns . (1) 511 keV NaI(Tl) 4% . (2) 100 ps 220 nm . 2 (quartz-glass) .. 2 .. 2 . 22 Japanese Positron Science Society 2 (2014).. H3378 50 mm 40 mm . 20% BaF2 . 3 250 ps . 1 ns . 4.. 3 BaF2 .. BaF2 30 20 mm .. 1 BC .. 5 .. 20 mm BaF2 511 keV . 60% MeV 40% .. 4 . (Vth = Vmax ) .. cm3 Constant Franction Discriminator (CFD) Constant Fraction Di erential Discriminator (CFDD) .. 1 . % EG&G ORTEC 583 CFDD.

3 CCD CFDD Time-to-Amplitude CMOS Converter (TAC) Multi-Channel Analyzer (MCA) . 5(a) TAC . 2 CFDD MCA. TAC 80 . 90 .. 2000 Analog- Digital Converter (ADC) .. CFDD, TAC, MCA . 4 . 2 (2014) Japanese Positron Science Society 23.. 5 (a) (b) . SN 5(b) . 2 . 3 . 2 . PC 100 .. 100 .. 5.. t = 0 N0 Ii (i = 1, .. , N) N . i i (= 1/ i ) . t N(t) t N(t) . dN(t) . N. = N(t) (2) N(t) = N0 Ii exp( i t) (6). dt i=1. N(t = 0) = N0 . S (t) . N(t) = N0 exp( t) (3).. N N. Ii t S (t) Ii i exp( i t) = exp( ) (7). S (t) . i=1 i=1 i i S (t) N(t) S (t) dN(t)/dt . S (t) N(t) N(t) S (t) N(t) S (t) .. 6 . t t + dt . dN/dt|t=t dt . 115 ps 22 NaCl . 310 ps . 1 dN(t ) 1 t= 1. = t dt = N(t)t + N(t )dt . N0 0 dt N0 t=0 N0 0. 1 1 t= 1. 6.

4 = N0 exp( t) = (4). N0 t=0 .. (7) . 1/e = 1 .. T 1/2 .. (loge 2) = = T 1/2 (5) res . 24 Japanese Positron Science Society 2 (2014).. " # . 2. = exp ( res t)2 + t2 dt (t ). 8 ln(2). " #. 4 ln(2) 2. exp 2 (t + res t)2 (14). res 8 ln(2). " # " #. 2 4 ln(2) 2. = exp ( res t)2 + t2 dt exp (t ). 8 ln(2) 2res t 8 ln(2) 2res (15). erfc . 2. erfc(x) = exp( t2 )dt (16). x .. 6 .. " #. 4t2 . R(t) = exp ln(2) 2 (8). res 100 .. n n . (t) t < 0 0 0 < t ti yi i = 1, .. , N . 1 . i ti .. f (ti , , I ) .. 1 , 2 , .. , k , I1 , I2 , .. , Ik , res . N " #. Ii t S (t) = C (t) exp N. (yi f (ti , , I, res ))2. i=1 i i 2 ( 1 , .. , k , I1 , .. , Ik , res ) =. " # 2i Ii N. t i=1. =C . dt (t t) (t ) exp (9) (17). i=1 i i 2. 2.

5 C . N n n . R . 2 /(N n) reduced- 2 . N " # N. Ii t Ii 1 reduced- 2. S (t) = C dt R(t t) (t ) exp =C Si . i=1 i i . i=1 i . (10) reduced- 2 .. 2/N N . " # 2 N ( 2 ) 2N . t Si = dt R(t t) (t ) exp 100 reduced- 2 . i " . # " # . 4(t t) 2. t = dt exp ln(2) (t . ) exp (11). 2res i . (yi f (ti ))/ i .. " #. 4 ln(2) 2res 2 . Si = dt (t ) exp 2 ((t t) +. 2. t (12). res 4 ln(2) .. ". 4 ln(2) 2 yi (i = 1, .. , N) yi . = dt (t ) exp 2 (t + res t)2. res 8 ln(2) . #. 2res ( t) + t (13). 2 2. 8 ln(2). 2 (2014) Japanese Positron Science Society 25.. yi i . (1) 1 . N.. ( ) =2. ( )2 2i (18) (2) . y i i=1 .. (18) 1 .. 1 .. 1 1 . 7.. 22 Na 105 Bq . (10 Ci) 2 . t t + dt .. 0 t .. C1 . 105 Bq 3 s 100 ps 0 t 0 t 1 ns . n n.)

6 T lim (1 C1 )n = exp( C1 t) (19). n n exp( C1 t) . C1 = 3 104 30 s . 30 20 mm BaF2 30 mm . (15)2/4 (30)2 = 1/16 . (511 keV) C1 = . 2 105 /16 104 cps 2. 2 2 ( MeV) . 8.. C2 = 105 /16 104 cps .. 105/16 1/2 . 2= cps . 10 ps 0 2 . 10 ps 1 3 .. C1 C2 10 ps 3 108 10 11 = 3 10 3 cps 0 1/4 1 . 1/10 3/4 . 2 104 2 . v c .. r02 c 2 = (20). v . SN r0 c v . 0 . 1/4 0 . 2 4 . 1 2 0. 26 Japanese Positron Science Society 2 (2014).. 3 4 370 : 4/3=1110 : 1 .. 4 2 r2 4 2 . 3 = ( 9) 0 = ( 9) 2 = 2 . 3 v 3 | (0)|2 . 1. = 2 (21). 371 para = n v = | (0)|24 2 v (24). = 1 para = 8 109 s 1 . 125 ps . 1 1 1110 1 . 4/3 7 106 s 1 139 ns .. 106 s 1 142 ns . 4 1 0 . 2 2 3 . 3 / 2 = 1/371 .. = n( 2 + 3 )v n 2 v (22) . H. Saito, Y. Nagashima, T.

7 Kurihara, T. Hyodo: Nucl. Instrum. n Methods Phys. Res. Sect. A, 487 (2002) 612.. g cm 3 . mol 10 mol m 6 3 z ek, L. Le st ak, I. Novotn y, I. Proch azka, F. F. Be cv a r, J. C . 6 1023 106 m 3 = 1029 m 3 Sebesta: Nucl. Instrum. Methods Phys. Res. Sect. A, 443. 13 (2000) 557. r0 = 10 15 m .. = n 2 v = n r02 c Positron Solid-State Physics, W. Brandt and A. Dupasquier (Eds.), North-Holland, Amsterdam, 1983. = 13 10 ( 10 15 )2 3 108. 29. = 109 s 1 (23).. S. DeBenedetti and H. C. Corben: Ann. Rev. of Nucl. Sci., 4. 170 ps (1954) 191. (2013 6 28 ).. : .. 3/4 1 .. 3/4 3 .. 2 : 3 =370:1.. 0 1 . 2 (2014) Japanese Positron Science Society 27.