陽電子科学 第4号 (2015)

Transcription

1 PALS as a tool for further insights into the transport of water and solutes during reverse osmosis Doppler Broadening of Annihilation Radiation (Doppler) H.V. HPGe TFA BaF 2 PMT CFD Positron Annihilation Lifetime (PAL) Sample + 22 Na BaF 2 PMT H.V. CFDD Fast Coincidence CFDD PAL Doppler Counts Main Amp. Gate & Delay Generator 10 Biased Amp. TAC ADC 2D-MCA ADC Personal Computer Energy (kev) Positron Age-MOmentum Correlation (AMOC) Time (ns) 4 (2015)

2 4 (2015) PALS as a tool for further insights into the transport of water and solutes during reverse osmosis... Takahiro Fujioka, Long D. Nghiem , Visiting research at Positron Probe Group in AIST The 11th International Workshop on Positron and Positronium Chemistry (PPC11) The International Workshop on Positron Studies of Defects 2014 (PSD-14) : (AMOC) γ : Japanese Positron Science Society

3 O. E. Mogensen 9 (ICPA-9) 62 Yasuyuki Nagashima ( ) (2015) Japanese Positron Science Society 1

4 2 Japanese Positron Science Society 4 (2015)

5 4 (2015) 3 8 Japanese Positron Science Society Positron annihilation age momentum correlation (AMOC) measurement Abstract: Positron annihilation Age-MOmentum Correlation (AMOC) measurement is the coincidence measurement method of positron injection time, positron annihilation time and positron annihilation gamma-rays energy. The methods for measurement and analysis of AMOC will be introduced briefly. Some of the interesting researches also will be introduced. Keywords: positron, annihilation gamma rays, lifetime, Doppler broadening, S parameter, W parameter ) (AMOC) Ge (HPGe) 511 kev (Ps) Ps (p-ps) (o-ps) p-ps 125 ps o-ps 142 ns Ps p-ps o-ps 2 Ps kev p-ps p-ps o-ps Ps *1 2 o-ps Energy (kev) Time (ns) Counts 1 AMOC Tetsuya Hirade (Nuclear Science and Engineering Center, Japan Atomic Energy Agency), TEL: , FAX: , t.hirade@kurenai.waseda.jp *1 free positron Ps free

6 H.V. Doppler HPGe TFA Main Amp. Biased Amp. ADC Sample + 22 Na BaF 2 PMT CFD BaF 2 2D-MCA PMT CFDD Personal Computer 2 H.V. Fast Coincidence Gate & Delay Generator ADC TAC AMOC PAL CFDD Na 22 Na 1.27 MeV Na 2, 3) X 4) 22 Na AMOC 2. AMOC AMOC 22 Na 2 (2D-MCA) 2 22 Na AMOC AMOC 5) 1 1 HPGe 3 HPGe ps 20 ps ev AMOC 2 ns ns μs 5) Fast-Filter Amplifier (Fast Amp.) AMOC Fast Amp. 6) AMOC 1 3 p-ps o-ps (1) A(t) *2 N A(t) I i λ i exp ( λ i t) (1) i=1 N ( ) I i λ i *2 S S (t) A(t) 4 Japanese Positron Science Society 4 (2015)

7 1 AMOC 511 kev (1) AMOC f i (t) = I i λ i exp ( λ i t) Nj=1 I j λ j exp ( λ j t ) (2) f i (t) t i Ps Ps 125 ps p-ps 400 ps ns o-ps 3 p-ps p-ps 3 S S S S S S N N I i λ i exp ( λ i t) S (t) = S i f i (t) = S i Nj=1 I j λ j exp ( λ j t ) (3) i=1 i=1 S (t) 4 AMOC S (t) 1 AMOC PALSfit 7) τ i I i 1 S 4 S (t) I 1 3 λ 1 3 (= 1/τ 1 3 ) S(t) S S p-ps o-ps ns Ps (ns) Ps S(t) 4 (2015) Japanese Positron Science Society 5

8 3 (2) 3 S 1 3 (3) S 1 3 o-ps S S o-ps 6) AMOC AMOC 3. 4 S (t) p-ps o-ps AMOC S (t) AMOC 260 ps 290 ps AMOC 125 ps p-ps 8) o-ps R p- Ps R p-ps o-ps + R (1/4) p-ps + R (3/4) o-ps + R (4) 3 5 p-ps S (t) 6 4-hydroxy-2,2,6,6-tetramethylpiperidine1- oxyl (HTEMPO) o-ps 9) o-ps S (t) o-ps p-ps o-ps p-ps o-ps p-ps (ns) S S 5 Ps o-ps 6 HTEMPO 0.1 M S(t) 9) Reprinted figure with permission. Copyright EDP Sciences Japanese Positron Science Society 4 (2015)

9 7 20K S 13) Reprinted figure with permission. Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. AMOC S (t) (5) N S (t) = S i f i (t). (5) i=1 S S (t) 4. AMOC Ps Ps 1974 Mogensen 10) (spur) Ps 0.5eV 3eV 11) Ps Ps 11) S (t) 7 20 K 12, 13) Ps Ps p-ps S (t) Ps 10) S (t) Ps 7 13) Ps 2 AMOC (5) S S 4 (2015) Japanese Positron Science Society 7

10 AMOC C Fe-0.88 at.% Cu W 5) Reprinted figure with permission from K. Inoue, Y. Nagai, Z. Tang, T. Toyama, Y. Hosoda, A. Tsuto, M. Hasegawa, PHYSICAL REVIEW B 83 (2011) Copyright (2011) by the American Physical Society. 14) W W(t) AMOC 8 5) 5. AMOC AMOC 1) 2 (2014) 21. 2) H. Stall, M. Koch, K. Maier, J. Major: Nucl. Instrum. Methods B (1991) ) R. Suzuki, T. Ohdaira, T. Mikado, G. V. Rao: Mater. Sci. Forum (2001) ) D. Zvezhinskiy, M. Butterling, A. Wagnerc, R. Krause-Rehberg, S. V. Stepanov: Acta Phys. Pol. A 125 (2013) ) K. Inoue, Y. Nagai, Z. Tang, T. Toyama, Y. Hosoda, A. Tsuto, M. Hasegawa: Phys. Rev. B 83 (2011) ) K. Sato, H. Murakami, K. Ito, K. Hirata, Y. Kobayashi: Macromolecules 42 (2009) ) P. Kirkegaard, J. V. Olsen, M. Eldrup, N. J. Pedersen: PALSfit (Risø-R-1652(EN), 2009). 8) T. Hirade: Mater. Sci. Forum 607 (2009) ) H. Schneider, A. Seeger, A. Siegle, H. Stoll, I. Billard, M. Koch, U. Lauff,J.Major:J.Phys.IV3 (1993) C4 69, 10) O. E. Mogensen: J. Chem. Phys. 60 (3) (1974) ) T. Hirade, F. H. J. Maurer, M. Eldrup: Radiat. Phys. Chem. 58 (2000) ) N. Suzuki, T. Hirade, F. Saito, T. Hyodo: Radiat. Phys. Chem. 68 (2003) ) T. Hirade, N. Suzuki, F. Saito, T. Hyodo: Phys. Status Solidi C 4 (2007) ) Matti Valo 1 (2013) 41. ( ) : Japanese Positron Science Society 4 (2015)

11 4 (2015) 9 22 Japanese Positron Science Society Radioisotope-based spin-polarized positron beam Abstract: In this article, I report, the spin polarization of positrons emitted from radioisotopes, the development of spin-polarized positron beams, the fundamental aspects of spin-polarized positron annihilation method, and the investigation of current-induced spin polarization on metal surfaces through the spinpolarized positronium annihilation. Keywords: spin, spin polarized positron, spintronics, magnetism, surface Yang Li 1) 1957 Wu 2) 60 Co β β Wu Hanna Preston 3) 64 Cu β ) Dead Layer 5) 58 Co 22 % Atsuo Kawasuso (Advanced Science Research Center, Atomic Energy Agency), TEL: , FAX , kawasuso.atsuo@jaea.go.jp Japan 70 % 1982 Ni Dead Layer Live Layer 6) ) 8) 27 Si 18 F d 0 d

12 ν e I I-1 1/2 1/2 e + h<0 h>0 2. e + 1/2 1/2 ν e (Radioisotope, RI) RI 22 Na RI RI RI 2.1 β + (β ) RI β + A Z X N Z 1 A N+1 + e+ + ν e (p + n 0 + e + + ν e ) β + (1) A Z X N + e Z 1 A X N+1 + ν e (p + + e n 0 + ν e ) (2) A Z X N Z+1 A N 1 + e + ν e (n 0 p + + e + ν e ) β (3) X (X ) Z A N (A = Z + N) p + n 0 e e + ν e (ν e ) β + (β ) Q Q β + = [ M(X) M(X ) 2m ] c 2 (4) Q β = [ M(X) M(X ) m ] c 2 (5) M m c β + m 2 1 β + Q (E max ) β ± Fermi Fermi V A β ± 1/2 l = 0 β ± 0 1 Fermi Gamow-Teller 1 Gamow-Teller β + π Japanese Positron Science Society 4 (2015)

13 ( ) (+) 1 β Fermi β Yang Li 1) Wu 2) Hanna Preston 3) +1 ±v/c 1 v/c = (n n )/(n + n ) n ( ) RI 4π 2θ 2π(1 cos θ) P + P + = v 1 + cos θ cos θ = 1 (6) c 2 [1 + E/(mc 2 )] 2 2 E E 1 E 2 ( E max ) P + = v 1 + cos θ c 2 E2 1 = 1 [ ( 1 + E/ mc 2 )] 1 + cos θ N(E)dE (7) 2 2 E 1 v N(E) Q RI RI 22 Na 2 22 Na 9) 22 Na 2.6 β % 9.4 % β + 22 Na 3 Ne Ne MeV EC γ 1 β + 1 β Na 9.43% 90.51% 0.06% 2.842MeV 2 22 Na Na (EC) β Ne MeV 22 Na 22 Ne MeV % 1.275MeV β + Q 22 Na 22 Ne + e + + ν e (8) Q = [ M( 22 Na) M( 22 Ne) 2m ] c 2 = 1.82 MeV (9) Q β + 22 Ne (1.275 MeV) E = = MeV 1 1) 3(a) 3(b) (N 0 (E)) 22 Na 68 Ge/ 68 Ga (N S (E)) (N(E)) 10) 22 Na (0.2 MeV) v /c = % (θ = π/2) 35 % (7) N(E) β + β + N 0 (E) A(z) A 0 4 (2015) Japanese Positron Science Society 11

14 1 (E max ) ( E ) ( v /c) N S (E) = 1 2 ds 0 N 0 (E)[A(z)/A 0 ] T S (E, z)dz (10) E max /MeV E /MeV v /c 18 F Na Al Si Ti/ 44 Sc Cu Co Ge/ 68 Ga N 0 (E) 1 d A N A (E) N A (E) = N S (E)T A (E, d A ) (11) T A (E, d A ) 11) T(E, z) = exp [ (z/z 0 ) m] (12) z 0 = ae n / [ ργ(1 + 1/m) ] (13) N0(E) and NS(E) (arb. units) N0(E) and NS(E) (arb. units) N S (E) N S (E) N 0 (E) N(E) Energy (MeV) N 0 (E) N(E) 0.5 (a) (b) Energy (MeV) 3 N(E) (arb. units) N(E) (arb. units) (a) 22 Na (b) 68 Ge/ 68 Ga N 0 (E) N S (E) 1 μm N(E) 12) T S (E, z) d S N S (E) ρ a (= 4.0 μgcm 2 kev n ) n m. (11) ε M (E, d M ) N(E) = N S (E)T A (E, d A )ε M (E, d M ) (14) d M ε M (E, d M ) 12) ε M (E,d M ) dm = P em p(e, z)sinh(z/l)sinh(d M /L)dz ε M (E,d M ) 0 (15) dm = P em p(e, z)exp( z/l)dz 0 (16) P em p(e, z) (= dt(e, z)/dz) L 2 1 μm (7) 53 % ( 68 Ge/ 68 Ga) 42 % ( 22 Na) 10) 12 Japanese Positron Science Society 4 (2015)

15 2 d S : d M : ρ: m, n: (12) (13) P em : L: 68 Ge/ 68 Ga GaN 22 Na NaCl 53 % ( 68 Ge/ 68 Ga) 42 % ( 22 Na) d S /mm ρ /gcm 3 m n 68 Ge/ 68 Ga GaN 22 Na NaCl d M / μm ρ /gcm 3 m n P em L /nm W Na 68 Ge/ 68 Ga R p 13) R p = logz (17) Z = 6 (17) 10 %. ΔP 10 % Bhabha Mott Bhabha EZ/800,RI 1MeV Bhabha 14) 10 kev ev 15, 16) 17) Spin-flipping probability E=0.2MeV 0.5MeV 1.0MeV Energy loss / Scattering (kev) 4 E = 0.2 MeV, 0.5 MeV, 1.0 MeV Bhabha Bhabha 18) 4 18 I 0.2 MeV, 0.5 MeV 1.0 MeV Na 68 Ge/ 68 Ga 0.2 MeV 0.5 MeV kev 19) 0.2 MeV MeV 1000 ΔP 11 % 8% Mott 4 (2015) Japanese Positron Science Society 13

16 ΔP 20) ( ) 2 1 exp( γd) ΔP = 1 (18) γd d γ N k γ = 4 ( e 2 ) 2πN E + 2mc 2 ( ln(2kb) ξS 1 + ξ 2 S 2 ) b = me 2 Z 1/3 Thomas Fermi S 1 = π 2 l=1 ξ = e2 Z c E + mc 2 E 1/2 (E + mc 2 ) 1/2 H (1) 1 [i(l + 1/2)/(kb)] kb(l + 1/2) tan 1 [ (l + 1/2)k/k 0 ](H: ) 5 68 Ge/ 68 Ga 22, 23) k 0 = e 2 Z(E + mc 2 )/( c) 2 S 2 = { tan 1 [ (l + 1/2)k/k 0 ] } 2 (l + 1/2) 3 l=1 0.2 MeV 0.5 MeV 1 μm ΔP 6 22 NaCl 25) 1T 14 Japanese Positron Science Society 4 (2015)

17 7 22 NaCl 68 Ge/ 68 Ga 10, 24) 90 6% 4% 32 % ( 22 Na) 42 % ( 68 Ge/ 68 Ga) RI 21) NaCl 68 Ge/ 68 Ga 10, 22 25) 5 6 1T ) 27, 28) 29) S = 0 M S = 0: S M S = 00 S = 1 M S = 0, ±1 : S M S = 10, 11, ps 142 ns 1: F 4 (2015) Japanese Positron Science Society 15

18 27) 1 F 00 = 8(1 + y 2 ) [ (1 y) 2 (1 P + cos φ)(1 + P ) + (1 + y) 2 (1 + P + cos φ)(1 P ) ] (19) 1 F 10 = 8(1 + y 2 ) [ (1 + y) 2 (1 P + cos φ)(1 + P ) + (1 y) 2 (1 + P + cos φ)(1 P ) ] (20) F 11 = 1 + P + cos φ + P + P + P cos φ 4 F 1 1 = 1 P + cos φ P + P + P cos φ 4 (21) (22) P + (P ) y = x/ ( 1 + x ) x = 4μ B B/ΔE (μ B : B: ΔE: ( ev)) φ λ 00 λ p (= 8ns 1 ) λ 10 = λ 11 = λ 1 1 λ o (= ns 1 ) λ pick-off λ λ 00 = κλ p 1 + y 2 + κy2 λ o 1 + y 2 + λ pick-off (23) λ 10 = κy2 λ p 1 + y 2 + κλ o 1 + y 2 + λ pick-off (24) λ 11 = λ 1 1 = κλ o + λ pick-off (25) κ Ps = Ψ m (0) 2 / Ψ v (0) 2 λ p λ o λ pick-off F 2γ Ps = F ( ) 00 κλp λ y + λ 2 pick-off + F ( 10 κy 2 ) λ p λ y + λ 2 pick-off + ( F 11 + F 1 1 ) λ pick-off λ 11 (= λ 1 1 ) (26) F Ps 3γ = F 00 λ 00 κλ o y y + F 10 2 λ 10 κλ o 1 + y 2 κλ o κλ o +F 11 + F 1 1 (27) λ 11 λ 1 1 (26) 00 (λ 10 ) P = 0 κ = 1 λ pick-off = 0 (27) 2 4 [( ) dn(t) κλ o κλ o = N F 11 + F 1 1 λ o exp( λ o t) dt λ 11 = N 4 + F 10 λ 10 [ 2λ o exp( λ o t) λ 1 1 κλ o 1 + y 2 λ 10 exp( λ 10 t) ( + 1 cos φ 2yP ) ] y 2 λ 10 exp( λ 10 t) (28) N φ φ (28) 29) S S S = (S Ps S SiO2 )I(B) + S SiO2 ( F 00 κλ p = (S Ps S SiO2 ) λ y 2 + F 10 κy 2 ) λ p λ y 2 + S SiO2 (29) S Ps S S SiO2 S I(B) (26) F 2γ Ps λ pick-off κ λ pick-off P = 0 S (29) α = S Ps S SiO2 β = S SiO2 P + ] 16 Japanese Positron Science Society 4 (2015)

19 ( ) ( ) ρ ( ) i (p) = e ipr Ψ + (r)ψ ( ) i (r) 2 γ(n (r))dr (30) 8 (a) 68 Ge/ 68 Ga (b) 22 Na S 10, 25) 8(a) (b) 68 Ge/ 68 Ga 22 Na S 7mm (29) 22 Na 68 Ge/ 68 Ga 38 % 65 % 30 % 47 % ) Ψ + (r) Ψ i (r) γ(n (r)) i i (30) N ( ) i (p z ) = ρ ( ) i (p)dp x dp y (31) (31) i (w ( ) i ) w ( ) i = + N ( ) i (p z )dp z (32) ( ) ( ) i ( ) ( ) S = 0 S = 1 M S = 0 S = 1 M S = 1 3 λ ( ) = 1 occ [ λs w ( ) 2 i + λ T (w ( ) i + 2w ( ) i ) ] (33) i=1 4 (2015) Japanese Positron Science Society 17

20 3 ( ) ( ) λ S = 4πr 2 e c r e: c: λ T = λ S /1115 w ( ) : i i S = 0 S = 1, M S = 0 S = 1, M S = 1 S = 1, M S = 1 ( ) λ S w i /2 λ Tw i /2 λ Tw i 0 ( ) λ S w i /2 λ Tw i /2 0 λ Tw i P + (+) ( ) N ± (p z ) = λ S occ [ (1 ± P+ )N i (p z ) + (1 P +)N ] i (p z ) (34) 4 i=1 λ λ ΔN = N + (p z ) N (p z ) = λ SP + occ [ Ni (p z ) N i ] (p z ) 2 i=1 λ λ (35) P + = 0 (34) (33) P + = 0 (35) [ ] (36) N occ [ Ni (p z ) N i (p z ) ] = λ + λ λ [ΔN λ ] + P + ΣN λ S P + λ + λ i=1 ΔN + P 3γ ΣN (36) N = N + (p z )+N (p z ) P 3γ = (N 3γ + N 3γ )/(N 3γ + +N 3γ ) L ± (t) = λ S 4 + λ S 4 occ w i (1 ± P +)exp( λ t) i=1 occ w i (1 P +)exp( λ t) (37) i=1 λ ± = 1 ± P + 2 λ + 1 P + λ (38) 2 λ ( ) λ S w ( ) /2 λ ( ) = 1 2 4πr e 2 c n + (r)n ( ) (r)γ[n ( ) (r)]dr (39) P + = 0 N+(p) - N-(p) (arb. units) Ni Co Fe Electron momentum, p (10-3 m 0 c) 9 5 Fe Co Ni (±1 T) 22) 18 Japanese Positron Science Society 4 (2015)

21 Hanna Preston 3) Fe Fe Ni Co Gd 30 42) 43) 1986 NiMnSb 44) 9 22) Fe Co Ni 7 mrad 14 mrad 3d Ni Co Fe Intensity (arb. units) Gd Tb TC=90K Temperature (K) 10 TC=222K TC=293K Dy Gd Tb Dy (±1 T) T C T C Weiss 23) 4 Fe Co Ni 45) Fe (BCC) Co (HCP) Ni (FCC) 95.1 ps 94.5 ps ps ps 98.2 ps 96.8 ps 10 4f 23) Weiss M/M 0 = B J [g J μ B J(H + λ mf M)/k B T] M 0 : B J : g J : J: λ mf : 45) 4 Fe Co Ni Fe Co Ni Ni sp 3.2 Φ Ps Φ Φ + E B (= 6.8eV) Φ Ps =Φ + +Φ E B (40) Φ Φ + +2 ev +4 ev 3 ev +1 ev ( 4 ev 2 ev) 4 (2015) Japanese Positron Science Society 19

22 P + P φ (19) (22) (y = 0) (a) Decelera on tube Detector e + beam 12 kev Sample P - -j c DC voltage F 00 = (1 P + P cos φ)/4 (41) P + F 10 = (1 P + P cos φ)/4 (42) F 11 = (1 + P + + P cos φ + P + P cos φ)/4 (43) F 1 1 = (1 P + P cos φ + P + P cos φ)/4 (44) F 2γ Ps = F 00 (45) F 3γ Ps = ε(1) ( F 11 + F 1 1 ) + ε(0)f 10 (46) ε(1) ε(0) 46) (F 2γ Ps : F3γ Ps ) 1:3 1:3 P + +P P A A 3γ = F Ps 3γ (+P ) F 3γ Ps ( P ) F 3γ Ps (+P ) + F 3γ Ps ( P ) 2ε(1) ε(0) = 2ε(1) + ε(0) P +P cos φ (47) A 2γ = F Ps 2γ (+P ) F Ps 2γ ( P ) F Ps 2γ (+P ) + F Ps 2γ ( P ) = P +P cos φ (48) A 125 ps 142 ns (I 142 ns ) (46) (I 142 ns = F 3γ Ps ) (b) Counting rate (arb. units) R R R GND HV 0 12 kv 511 kev (2 ) peak 10-3 E + =50 ev with ortho-ps (3 ) E + =12 kev without Ps Area = R x y z +j c Gamma-ray energy (kev) 11 (a) 47, 48) (b) 12 kev 50 ev 511 kev 12 kev 50 ev 511 kev ΔR (511 kev) R R = (1 F3γ Ps )R 0 + F 3γ Ps R 1P 1 /P 0 1 F 3γ Ps + F3γ Ps P (49) 1/P 0 R 0 R % R P 511 kev R F 3γ Ps 100 % R R 0 ΔR ΔR = R R 0 F 3γ Ps (50) 6) Ni Ni 20 Japanese Positron Science Society 4 (2015)

23 R = R R0 F Ps j c -j c...+j c -j c +j c -j c...+j c -j c Au/Fe/MgO@0.6A Pt/Al 2 O -Ta@0.25A -W@0.1A Cu/MgO@0.6A Pd/Al O -Ta@0.05A -W@0.1A +j c -j c...+j c -j c +j c -j c...+j c -j c Current direction Pt Pd Au Cu α-, β-ta α-, β-w ΔR 48) Pt Pd Ta W (47) 10 5 Acm 2 5 % 15 % Φ Ps 0 E F +Φ Ps E E F E F : 0 E Ps = Φ Ps E F + E Φ Ps E f Ps (E) P (E) F 3γ Ps (E) = f Ps(E) [ ] ε(1)(f 11 + F 1 1 ) + ε(0)f 10 (51) Dead Layer *1 47, 48) 11(a) (b) Pt 12 kev 50 ev 511 kev (50) ΔR 12 Pt Pd Au Cu α-, β-ta α-, β-w ΔR Au Cu ΔR Pt Pd Ta W Pt Pd Ta W *1 A 3γ (E) = 2ε(1) ε(0) 2ε(1) + ε(0) P +P (E)cosφ (52) F 3γ Ps (E) D (E) D (E) P (E) = D (E) D (E) D (E) + D (E) (53) A 3γ (E) 4. β + RI 4 (2015) Japanese Positron Science Society 21

24 RI 1) T. D. Lee, C. N. Yang: Phys. Rev. 104 (1956) ) C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes, R. P. Hudson: Phys. Rev. 105 (1957) ) S. S. Hanna, R. S. Preston: Phys. Rev. 106 (1957) ) P. W. Zitzewitz, J. C. van House, A. Rich, D. W. Gidley: Phys. Rev. Lett. 43 (1979) ) L. M. Liebermann, D. R. Fredkin, H. B. Shore: Phys. Rev. Lett. 22 (1969) 539; L. M. Liebermann, J. Chilton, D. M. Edwards, J. Mathon: Phys. Rev. Lett. 22 (1970) ) D. W. Gidley, A. R. Koymen: Phys. Rev. Lett. 49 (1982) ) T. Kumita, M. Chiba, R. Hamatsu, M. Hirose, T. Hirose, H. Iijima, M. Irako, N. Kawasaki, Y. Kurihara, T. Matsumoto, H. Nakabushi, T. Omori, Y. Takeuchi, M. Washio, J. Yang: Appl. Surf. Sci. 116 (1997) 1. 8) F. Saito, T. Hyodo, Y. Nagashima, T. Kurihara, N. Suzuki, Y. Itoh, A. Goto: New Directions in Antimatter Chemistry and Physics, Eds.C.M.Surko,F.A.Gianturco(KluwerAcademic Publishers, The Netherlands, 2001) p.35. 9) ) M. Maekawa, Y. Fukaya, A. Yabuuchi, I. Mochizuki, A. Kawasuso: Nucl. Instrum. Methods B 308 (2013) 9. 11) S. Valkealahti, R. M. Nieminen: Appl. Phys. A 35 (1984) 51; Appl. Phys. A 32 (1983) ) A. Vehanen, J. Maikinen: Appl. Phys. A 36 (1985) ) I. K. MacKenzie, C. W. Shulte, T. Jackman, L. Campbell: Phys. Rev. A 7 (1973) ) F. Rohrich, B. C. Carlson: Phys. Rev. 93 (1954) ) K. A. Ritley, M. McKeon, K. G. Lynn: Proceedings of 4th International Workshop on Slow-positron Beam Techniques for Solids & Surfaces (American Institute of Physics, 1990) p.3. 16) K. O. Jensen, A. B. Walker: Surf. Sci. 292 (1993) ) K. O. Jensen, A. B. Walker: J. Phys.-Condes. Matter 2 (1990) ) C. K. Iddings, G. L. Shaw, Y. S. Tsai: Phys. Rev. 135 (1964) B ) R. M. Sternheimer: Phys. Rev. B 103 (1956) ) M. E. Rose, H. A. Bethe: Phys. Rev. 55 (1938) ) J. van House, P. W. Zitzewitz: Phys, Rev. A 29 (1984) ) A. Kawasuso, M. Maekawa, Y. Fukaya, A. Yabuuchi, I. Mochizuki: Phys. Rev. B (R) (2011). 23) A. Kawasuso, M. Maekawa, Y. Fukaya, A. Yabuuchi, I. Mochizuki: Phys. Rev. B 85 (2012) ) A. Kawasuso, M. Maekawa: Appl. Surf. Sci. 255 (2008) ) M. Maekawa, Y. Fukaya, H. Zhang, H. Li, A. Kawasuso: J. Phys.-Conf. Ser. 505 (2014) ) L. A. Page: Rev. Mod. Phys. 31 (1959) ) A. Rich, H. R. Crane: Phys. Rev. Lett. 5 (1966) ) G. Gerber, D. Newman, A. Rich, E. Sweetman: Phys. Rev. D 15 (1977) ) Y. Nagai, Y. Nagashima, J. Kim, Y. Itoh, T. Hyodo: Nucl. Instrum. Methods B 171 (2000) ) S. Berko: Positron Annihilation, Ed. A. T. Stewart, L. O. Roellig (Academic Press, New York, 1967) p ) P. E. Mijnarends, L. Hambro: Phys. Lett. 10 (1964) ) P. E. Mijnarends: Physica 63 (1973) ) S. Berko, J. Zuckerman: Phys. Rev. Lett. 13 (1964) ) T. W. Mihalisin, R. D. Parks: Phys. Rev. Lett. 18 (1967) ) T. W. Mihalisin, R. D. Parks, Solid State Commun. 7 (1969) ) N. Shiotani, T.Okada, H. Sekizawa, T. Mizoguchi, T. Karasawa: J. Phys. Soc. Jpn. 35 (1973) ) M. Sǒb, S. Szuszkiewicz, M. Szuszkiewicz: Phys. Status Solidi B-Basic Res. 123 (1984) ) T. Jarborg, A. A. Manuel, Y. Mathys, M. Peter, A. K. Singh, E. Walker: J. Magn. Magn. Mater (1986) ) S. Szuszkiewicz, M. Sǒb, M. Szuszkiewicz: J. Magn. Magn. Mater. 62 (1986) ) P. Genoud, A. K. Singh, A. A. Manuel, T. Jarlborg, E. Walker, M. Peter, M. Welle: J. Phys. F 18 (1988) ) P. Genoud, A. A. Manuel, E. Walker, M. Peter: J. Phys.-Condes. Matter 3 (1991) ) H. Kondo, T. Kubota, H. Nakashima, T. Kawano, S. Tanigawa: J. Phys.-Condes. Matter 4 (1992) ) S. Wakoh: J. Phys. Soc. Jpn. 20 (1965) ) K. E. H. M. Hanssen, P. E. Mijnarends: Phys. Rev. B 34 (1986) ) J. Lin, K. Nishida, M. Saito: Jpn. J. Appl. Phys. 51 (2012) ) R. M. Drisko: Phys. Rev. 102 (1956) ) A. Kawasuso, Y. Fukaya, M. Maekawa, H. Zhang, T. Seki, T.Yoshino, E. Saitoh, K. Takanashi: J. Magn. Magn. Mater. 342 (2013) ) H. J. Zhang, S. Yamamoto, Y. Fukaya, M. Maekawa, H. Li, A. Kawasuso, T. Seki, E. Saitoh, K. Takanashi: Sci. Rep. 4 (2014) ( ) : 7 22 Japanese Positron Science Society 4 (2015)

25 4 (2015) Japanese Positron Science Society Theoretical calculation of positron lifetime Abstract: This article describes the methods used for calculating positron lifetimes. Positron lifetimes can be calculated by integrating the product of the electron and positron charge densities with an enhancement factor that describes the pileup of electrons around a positron. In the case of semiconductors and insulators, the enhancement factor needs to be modified because the effect of the pileup is reduced by the existence of the band-gap. There are two ways of calculating the electron and positron densities. In the two-component scheme, the electron and positron densities are calculated self-consistently and simultaneously. On the other hand, in the conventional scheme, the electron densities are calculated without the effect of the positron. The conventional scheme is often employed because positron lifetimes obtained by the conventional scheme are comparable to those obtained by the two component scheme. Keywords: defect, vacancy, first-principles calculation, metal, alloy, metal oxide, semiconductor, insulator Puska Nieminen 1) Masataka Mizuno (Division of Materials and Manufacturing Science, Osaka University), TEL: , FAX , mizuno@mat.eng.osaka-u.ac.jp Atomic Superposition Method, ATSUP ATSUP 2) ZnO

26 2. V + V + (r) = V c (r) + V corr (n (r)) (1) n V c V corr 1 V corr Broński Nieminen Arponen Pajanne 3) BN 4) V corr (0.56 r s < 8.0) = (r s + 2.5) (2) r s r s r s = (3/4πn ) 1/3 1 r s r s BN (2) ev Broński Nieminen r s 4 Sterne Kaiser Arponen Pajanne 1 5) V corr (r s ) = (arctan r s ) 1/ exp [ (r s 4.092) 2 ] SK Sterne Kaiser (3) 0.1 Broński Nieminen (2) (3) 1 1 BN, Broński Nieminen (2) SK, Sterne Kaiser (3) 2 Cu Cu (a) ; (b)1 ; (c) 0.1 V c Cu (001) [110] 1 4 Å 6.5 ev ev 3.9 ev 3 24 Japanese Positron Science Society 4 (2015)

27 3 MgO Mg O. (a)mg ; (b)o MgO Mg O MgO Mg O Mg O Mg O 10.5 ev Cu O Mg 6.0 ev O ev O 3. 3 ATSUP ATSUP Projector Augmented Wave (PAW) 6) VASP 7 9) PAW 1 (finite-difference) (Two-component Scheme TC Scheme) 1 Broński Nieminen 4) GaAs TC scheme Gilgen Galli Gygi Car 4 10) TC scheme GGGC Puska Seitsonen Nieminen 11) TC scheme PSN 4 (2015) Japanese Positron Science Society 25

28 (Conventional Scheme CONV scheme) CONV scheme TC scheme TC scheme 12, 13) τ λ 1 τ = πr2 0 c drn + (r)n (r)g(n (r), n + (r)) (4) r 0 c g (Enhancement Factor Contact Density) n (r) n + (r) TC scheme Broński Nieminen CONV scheme g 0 r s 4) g 0 (r s ) = r s r 3/2 s 1.26r 2 s r 5/2 s + r 3 s /6 (5) 4 BN (5) (10 3 ) 10 1 (3) 1 Sterne Kaiser Broński Nieminen 5) g 0 (r s ) = r s rs 3/2 2.01rs r5/2 s + rs 3 /6 (6) 4 SK (6) (5) 4 BN, Broński Nieminen (5) SK, Sterne Kaiser (6) 14) Puska 15) g 0 (r s ) = r s rs 3/2 1.26rs r5/2 s + (1 1/ε )rs 3 /6 (7) ε (7) (5) rs 3 ε 5 DV-Xα 16 18) DV-Xα Al Cu 5 43 CONV scheme Al 26 Japanese Positron Science Society 4 (2015)

29 1 Al Al (169 ps) Al (250 ps) [%] [ns 1 ] [%] [ns 1 ] s p d Al Al (a) ; (b)al Al 1 Al (3) 3.8 % 1.0 % 3p 50 % Al 3d 3p Al Cu Cu 3d Al 73 ps 108 ps Cu 3d 4p 6 Cu Cu (a) ATSUP ; (b) Conventional scheme; (c) Two-component scheme Al Cu Cu ATSUP CONV scheme TC scheme (001) [100] CONV scheme ATSUP Cu Cu 2 Cu Cu (108 ps) Cu (181 ps) [%] [ns 1 ] [%] [ns 1 ] d s p (2015) Japanese Positron Science Society 27

30 3 (ps) Method Cu Ag Au Al Fe Nb fcc fcc fcc fcc bcc bcc LMTO-ASA a FP-LMTO a DV-Xα ATSUP a Experiment b a 11) b 19) 162 ps CONV scheme 181 ps 19 ps TC scheme 177 ps CONV scheme Korhonen Puska Al, Cu, Ag, Au, Fe, Nb 12, 13) 3 4 LMTO-ASA FP-LMTO FP-LMTO 3 CONV scheme TC scheme CONV scheme ATSUP ATSUP CONV scheme TC scheme 5ps ATSUP CONV scheme TC scheme 5 MgO ATSUP Mg 2+ O 2 CONV scheme TC scheme MgO Mg 2+ O 2 MgO NaCl TiC CONV scheme TC scheme Ti C 60 ps ATSUP Ti C TiC Ti-C Ti C Ti C Ti C BCC 5 (ps) ATSUP CONV TC MgO Mg MgO O TiC Ti TiC C CoAl Co CoAl Al CoTi Co CoTi Ti (ps) Method Cu Ag Au Al Fe Nb fcc fcc fcc fcc bcc bcc LMTO-ASA, TC a LMTO-ASA, CONV a FP-LMTO, CONV a DV-Xα, CONV ATSUP, CONV a Experiment 179 b 198 c 210 d 251 e 175 f 210 g a 11) b 20) c 21) d 22) e 23) f 24) g 25) 28 Japanese Positron Science Society 4 (2015)

31 B2 CoAl CoTi CoAl ATSUP CONV scheme CoTi Co Ti ATSUP CoAl Al Co 0.13 CoTi Ti Co 1.02 Co Ti ATSUP CONV scheme TC scheme ATSUP CONV scheme TC scheme ) TC scheme (7) 1989 Puska 14) (7) Semiconductor model Puska Semiconductor model Insulator model Insulator model 2 Puska MgO 166 ps 29) Tanaka MgO 140 ps 30) Mg Puska Semiconductor model Insulator model Insulator model 31) Puska 5.2 (GGA) (Local Density Approximation, LDA) LDA (Generalized Gradient Approximation, GGA) Barbiellini 1 32, 33) Arponen Pajanne Broński Nieminen (4) g 0 (r s ) = r s rs 2 + r3 s /6 (8) g GGA g LDA g GGA = 1 + (g LDA 1) exp( αε) (9) ε ε = n 2 n q TF = ln n 2 q 2 TF (10) (q TF ) 1 1 ( VGGA corr = Vcorr LDA exp αε ) 3 (11) 4 (2015) Japanese Positron Science Society 29

32 7 (ps) BN GGA Method Cu Ag Au Al Fe Nb fcc fcc fcc fcc bcc bcc BN a GGA, BPTN a a 34) 7 BN, Broński Nieminen (5) BTPN, Barbiellini (8) KB, Kuriplach Barbiellini (12) 6 (ps) LDA GGA Method Cu Ag Au Al Fe Nb fcc fcc fcc fcc bcc bcc LDA, BPTN a GGA, BPTN a LDA, KB b GGA, KB b a 33) b 37) (9), (11) α α = 0.22 Barbiellini Broński Nieminen 7 BPTN Barbiellini BN Barbiellini BN Barbiellini LDA GGA LDA (8) Broński Nieminen (4) 3 10 ps Al 20 ps GGA 3 Al GGA 10 ps Ag 10 ps BN BN GGA Campillo Robles 34) 7 6 Fe Nb BN Al Ag (8) LDA BN α = 0.22 (8) GGA α GGA Puska Semiconductor model Insulator model ZnO GGA BN Semiconductor model 20 ps 35) ZnO GGA 2014 Kuriplach Barbiellini 36) 37) (8) rs 2 g 0 (r s ) = r s 0.22r 2 s + r 3 s /6 (12) 30 Japanese Positron Science Society 4 (2015)

33 7 KB (8) BPTN BN BN α = 0.22 α = LDA GGA 7 LDA BN ps Al Ag GGA GGA GGA MgO ZnO 5.3 MgO ZnO MgO Puska Insulator model 167 ps 14) Insulator model 2001 Xu Insulator model MgO 155 ps 31) ZnO GaN 38) Si GaAs GaN 39) ZnO ZnO 1989 Fernández ZnO 195 ps 40) 1992 Cruz 169 ps 41) 2003 Uedono Eagle-Picher 155 ps 158 ps 42) Chen Eagle-Picher Scientific Production Company 171 ps 189 ps 43) Chen ATSUP Semiconductor model 158 ps Zn 187 ps Zn Tuomisto ZnO 170 ps 177 ps 44) Brauer 34) Barbiellini GGA 30 ps 8 Al MgO Semiconductor model GGA 20 ps ZnO MgO ZnO 2 MO 3 X MO + 2X MO 2X + V M (13) 3 V M ppm Shirai Tanaka MgO Al Ga 30, 45) 8 Al MgO Al 135 ps Al 180 ps 3 Al Mg Al 130 ps 185 ps Shirai Tanaka ZnO ZnO 1 ppm Eagle-Picher 153 ps 155 ps 46) MgO ZnO 130 ps 153 ps 155 ps 4 (2015) Japanese Positron Science Society 31

34 8 MgO ZnO (ps) SM: Semiconductor model, IM: Insulator model MgO bulk Mg vac. ZnO bulk Zn vac. Puska, SM a 119 Puska, IM a Xu, IM b Chen, SM c Tuomist, GGA d 177 Brauer, SM e Brauer, GGA e Mizuno, BN f Mizuno, SM f Kuriplach, GGA g Kuriplach, GGA2 g a 14) b 31) c 43) d 44) e 35) f 46) g 37) MgO ZnO 8 BN Semiconductor model (7) Semiconductor model Barbiellini GGA MgO ZnO 8 GGA2 Kuriplach Barbiellini GGA 37) Semiconductor model GGA BN BN Semiconductor model GGA 6. TC scheme PSN GaAs Ga 10) TC scheme GGGC GaAs As 11) TC scheme Saito Si GGGC 47) Si 256 ps 279 ps 270 ps Wiktor SiC GGGC PSN 48) SiC Si C 153 ps 32 Japanese Positron Science Society 4 (2015)

35 PSN 195 ps Si 198 ps 227 ps TC scheme GaAs Si SiC 4.2 CONV scheme TC scheme TC scheme Si SiC CONV scheme TC scheme TC scheme 7. IT PHASE/0 WEB 49) PHASE URL 50) Linux UNIX Windows CONV scheme BN Semiconductor model VASP PHASE/0 ABINIT WEB 51) PHASE/0 Windows WEB WEB CONV scheme BN TC scheme PSN Semiconductor model Barbiellini GGA α = 0.22 BN (AIST) QMAS 52, 53) 8. ABINIT 1) M. J. Puska, R. M. Nieminen: J. Phys. F 13 (1983) ) J. Kuriplach, O. Melikhova, C. Domain, C. S. Becquart, D. Kulikov, L. Malerba, M. Hou, A. Almazouzi, C. A. Duque, A. L. 4 (2015) Japanese Positron Science Society 33

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37 4 (2015) Japanese Positron Science Society New precise measurement of the hyperfine splitting of positronium Abstract: A significant divergence of 3.9σ exists between the theoretical prediction and the averaged experimental value for the ground state hyperfine splitting of positronium (Ps), Δ HFS. We have performed a new measurement of Δ HFS taking into account the Ps thermalization effect. As a result Δ HFS = ± (statistical) ± (systematic) GHz was obtained, consistent with theoretical calculations. Our new result differs from the average of previously measured values by 2.6σ, and it was found that the effect of assuming that Ps is instantly thermalized after formation is 10 ± 2 ppm. This result suggests that the previous divergence between the theoretical and experimental values can be explained by a failure to take account of Ps thermalization. Keywords: positronium, quantum electrodynamics, hyperfine splitting, thermalization 1. (Ps) Ps 2 1. QED QED g Ps 2. p-ps o-ps Ps Akira Ishida (Graduate School of Science, The University of Tokyo), TEL: , FAX: , ishida@icepp.s.u-tokyo.ac.jp Ps 2000 Δ HFS Ps Ps 1 1 S 0, p-ps Γ p-ps = (17) ns ps 1) 2 γ 1 3 S 1 o-ps Γ o-ps = (7) μs ns 2) 3 γ o-ps p-ps 0.84 mev (203 GHz) Δ exp HFS = (67) GHz (3.3 ppm) 3 5) QED α QED 1 α α α 1/137 O(α 3 ln α 1 ) Δ th HFS = (41) GHz (2.0 ppm) 6 8)

38 α α Δ 1 (a 4) b 5) QED 6 8) 21) 6) 1 15 ppm (3.9σ [σ: ]) 2014 O(α 3 ) +1 ppm 9, 10) O(α 3 ) Ps QED (QCD) 2 1. Ps Ps Ps Ps Ps Ps 20 o-ps 11 13) 2. ppm Δ HFS ppm 10 cm 3 ppm 100 cm (Δ Zeeman ) Δ HFS Δ HFS 14) 15, 16) B Ps 2 0 o-ps p-ps Δ HFS Ps o-ps m = 0 p-ps + 0 o-ps 0 p-ps 2 m = ±1 + Δ Zeeman Δ HFS Δ Zeeman Breit-Rabi Δ Zeeman 1 ( ) 2 2 Δ g μ B B HFS (1) hδ HFS g = g ( α2) Ps g 17 20) μ B h Δ HFS 203 GHz Δ Zeeman 1T 3 GHz Ps 36 Japanese Positron Science Society 4 (2015)

39 4 3 2 m 0 GHz 1 0, E o Ps 203 E p Ps 204 HFS o-ps m ± m B T 2 Ps 0 o-ps 0 3 γ o-ps kev γ (1) ppm 21) Ps Δ HFS n, t Ps v(t) nv(t) 3/5 Lennard-Jones 22) v(t) Ps Ps 23) v(t) ( ) 3kT 1 + Ae bt v(t). (2) 1 Ae bt b = 16 3 m Ps 2 π σ mps kt mn M, 3 (a) (b) (a) (b) (a) (b) (b) 21) / 3 A = E0 2 kt 3 E0 + 2 kt, σ m Ps m Ps Ps k T M E 0 Ps ( 1 amagat, amagat 0 C, 1 atm ) ns o-ps o-ps ( 0.3 amagat ) Ps 2.2 Ps (2015) Japanese Positron Science Society 37

40 Ps Ps Ps Ps γ 38.1 mm 50.8 mm LaBr 3 (Ce) 6 UVT PMT 511 kev 8 %FWHM, 16 ns 2γ back-to-back γ 2γ 3γ mm, 2m B T 40 mm 100 mm 100 cm ppm RMS Ps 1 1 ppm 1 MBq 22 Na Ps β- 10 mm 0.1 mm PMT 1.2 ns Ps CW GaN 500 W 0.2 % 128 mm 100 mm γ 1.5 mm TM GHz, Q L Pa amagat amagat (> 99.9 %) 2γ Ps Doppler Broadening Spectroscopy, DBS 0.15 ev 1.52 ev E 0 = ev σ m = 146 ± 11 Å 2 24) 24) 0.17 ev Ps 0.17 ev σ m DBS 0.17 ev Ps 2, 11, 12) Ps (Ps + e 2γ + e ) Γ pick (t) Γ pick (t)/γ o-ps = (2γ )/(3γ ) γ Γ pick (t) 25) 26) nv(t) 0.6 Γ pick (t) v(t) 0.17 ev σ m = 47.2 ± 6.7Å khz, 910 Hz PMT NIM CAMAC 11 (0.129, 0.133, 0.167, 0.232, 0.660, 0.881, 0.969, 1.193, 1.353, 1.358, amagat) RF-ON RF-OFF Ps 50 ns 440 ns Ps Japanese Positron Science Society 4 (2015)

41 (/kev/ns/s) RF-ON RF-OFF RF-OFF RF-OFF Ps (ns) 4 (0.881 amagat, T) RF-OFF RF-ON 21) ns ns ns ns ns ns (T) ns ns ns ns ns (/kev/ns/s) RF-ON RF-OFF RF-OFF RF-OFF (kev) (T) amagat ) 5 50 ns 60 ns (0.881 amagat, T) RF-OFF RF-ON RF-ON RF-OFF 21) γ ns 1430 ns 511 kev ± 1σ ( 17 kev) [(RF-ON ) (RF-OFF )]/(RF-OFF ) ) Ps Δ HFS Γ pick n Ps t Δ HFS (n, t) =Δ 0 HFS Cnv(t) 3 5, (3) ( ) 0.6 v(t) Γ pick (n, t) =Γ pick (n, ). (4) v( ) Δ 0 HFS Δ HFS, C 2 ( ) Γ pick (n, ) RF-OFF N(t) Ps 4 (2015) Japanese Positron Science Society 39

42 (GHz) Δ HFS amagat amagat amagat Ps (ns) 7 Δ HFS amagat, amagat, amagat 21) t N(t) = N 0 exp [ Γ o-ps 0 t + N 1 exp [ Γ + 0 ( 1 + Γ pick(t ) Γ o-ps ( 1 + Γ pick(t ) Γ + ) dt ] ) ] dt. (5) N 0 N 1 Γ ps 6 Δ 0 HFS = (16) GHz (6) χ 2 /ndf = 633.3/592, p Ps Δ HFS 50 ns 100 ppm 100 ns 10 ppm Ps Ps Ps (3) (4) v(t) v( ) Δ HFS (16) GHz Ps 10 ± 2 ppm (15 ppm) 0 50 ns (GHz) Δ HFS (amagat) Δ HFS 21) Ps Δ HFS Δ HFS Δ HFS 8 (3) Δ HFS (n, t) ppm 5 1. o-ps Γ pick (n, ) RF-OFF Δ HFS 3.5 ppm 2. (1) Δ HFS ppm 3.0 ppm 3. Ps Ps Δ HFS Γ pick 40 Japanese Positron Science Society 4 (2015)

43 1 21) Δ HFS (ppm) : o-ps Ps : E DBS σ m 0.5 σ m 1.8 : NMR 1.0 : 1.2 Q L <0.1 : <0.2 <0.1 o-ps <0.1 p-ps < ppm Δ HFS = ± (, 8.0 ppm) ± (, 6.4 ppm) GHz. (7) 1 QED 1.2σ 2.6σ 4. Ps Ps o-ps Δ HFS 10 ± 2 ppm Ps Δ HFS = ± (, 8.0 ppm) ± (, 6.4 ppm) GHz O(α 3 ln α 1 ) QED 1.2σ 2.6σ Ps Ps Δ HFS Δ HFS 2.5 ppm Δ HFS 4. Ps Ps E 0,DBS σ m, σ m Δ HFS 1.9 ppm ns 440 ns 40 ns, 60 ns 260 ns, 620 ns Δ HFS KEK KEK JSPS ) A. H. Al-Ramadhan, D. W. Gidley: Phys. Rev. Lett. 72 (1994) ) Y. Kataoka, S. Asai, T. Kobayashi: Phys. Lett. B 671 (2009) ) A. P. Mills, Jr., G. H. Bearman: Phys. Rev. Lett. 34 (1975) ) A. P. Mills, Jr.: Phys. Rev. A 27 (1983) ) M. W. Ritter, P. O. Egan, V. W. Hughes, K. A. Woodle: Phys. Rev. A 30 (1984) ) B. A. Kniehl, A. A. Penin: Phys. Rev. Lett. 85 (2000) ) K. Melnikov, A. Yelkhovsky: Phys. Rev. Lett. 86 (2001) ) R. J. Hill: Phys. Rev. Lett. 86 (2001) (2015) Japanese Positron Science Society 41

44 9) M. Baker, P. Marquard, A. A. Penin, J. Piclum, M. Steinhauser: Phys. Rev. Lett. 112 (2014) ) G. S. Adkins, R. N. Fell: Phys. Rev. A 89 (2014) ) S. Asai, S. Orito, N. Shinohara: Phys. Lett. B 357 (1995) ) O. Jinnouchi, S. Asai, T. Kobayashi: Phys. Lett. B 572 (2003) ) R. S. Vallery, P. W. Zitzewitz, D. W. Gidley: Phys. Rev. Lett. 90 (2003) ) A. Miyazaki, T. Yamazaki, T. Suehara, T. Namba, S. Asai, T. Kobayashi, H. Saito, Y. Tatematsu, I. Ogawa, T. Idehara: arxiv: v3 (2014). 15) Y. Sasaki, A. Miyazaki, A. Ishida, T. Namba, S. Asai, T. Kobayashi, H. Saito, K. Tanaka, A. Yamamoto: Phys. Lett. B 697 (2011) ) D. B. Cassidy, T. H. Hisakado, H. W. K. Tom, A. P. Mills, Jr.: Phys. Rev. Lett. 109 (2012) ) H. Grotch, R. A. Hegstorm: Phys. Rev. A 4 (1971) ) E. R. Carlson, V. W. Hughes, M. L. Lewis, I. Lindgren: Phys. Rev. Lett. 29 (1972) ) H. Grotch, R. Kashuba: Phys. Rev. A 7 (1973) ) M. L. Lewis, V. W. Hughes: Phys. Rev. A 8 (1973) ) A. Ishida, T. Namba, S. Asai, T. Kobayashi, H. Saito, M. Yoshida, K. Tanaka, A. Yamamoto: Phys. Lett. B 734 (2014) ) N. Allard, J. Kielkopf: Rev. Mod. Phys. 54 (1982) ) F. Saito, Y. Nagashima, T. Hyodo: J. Phys. B 36 (2003) ) M. Skalsey, J. J. Engbrecht, C. M. Nakamura, R. S. Vallery, D. W. Gidley: Phys. Rev. A 67 (2003) ) R. S. Vallery, A. E. Leanhardt, M. Skalsey, D. W. Gidley: J. Phys. B 33 (2000) ) B. N. Miller, T. L. Reese, G. A. Worrell: Can. J. Phys. 74 (1996) 548. ( ) : 2014 ALPHA 42 Japanese Positron Science Society 4 (2015)

45 4 (2015) Japanese Positron Science Society Positron annihilation lifetime spectroscopy as a tool for further insights into the transport of water and solutes during reverse osmosis Takahiro Fujioka, Long D. Nghiem School of Civil Mining and Environmental Engineering, The University of Wollongong Abstract: Reverse osmosis (RO) filtration is an important separation process for water treatment and many industrial applications. Despite many decades of research and development efforts, solute transport through an RO membrane is still not fully understood. This article provides an insight into transport of small and uncharged solutes in RO membranes, with a particular focus on free-volume hole-size of the membrane active skin layer determined by positron annihilation lifetime spectroscopy (PALS). Free-volume hole-size is one of the most important membrane properties governing solute rejection. In fact, the rejection of boric acid (which is a small and uncharged solute) by RO membranes decreases with increasing free-volume hole-radius. In addition to free-volume hole-size, other properties of the active skin layer may also influence the rejection of uncharged small solutes. Thus, future development of PALS or other analytical techniques to characterise the free-volume hole-shape, hole-size distribution, and free-volume fraction of the active skin layer can provide an unprecedented level of insight into the separation of small and uncharged solutes by RO membranes. Keywords: boron, free-volume hole, positron annihilation lifetime spectroscopy, reverse osmosis 1. Introduction Reverse osmosis (RO) filtration is a key separation technology in many water treatment applications. Modern seawater desalination plants are primarily based on seawater reverse osmosis (SWRO) membranes which can offer more than 99.5 % rejection of inorganic salts. 1) Low pressure reverse osmosis (LPRO) membranes have been widely employed in potable water recycling applications for the removal of soluble organic substances and partial removal of inorganic salts. 2) RO applications for specific industrial applications in food processing, biotechnology, and hydrometallurgyhave also significantly increased recently. Central to the application of RO membranes for desalination, water recycling, and many other industries is their ability to reject small and dissolved solutes. However, there remains scope for further improvement in rejection properties, particularly with respect to small and uncharged solutes. Boron and N-nitrosodimethylamine (NDMA) are two of the most notable examples of such solutes. Takahiro Fujioka and Long D. Nghiem (Strategic Water Infrastructure Laboratory, School of Civil Mining and Environmental Engineering, The University of Wollongong), NSW 2522, Australia TEL: , FAX: , takahiro@uow.edu.au Most commercial RO membranes can only achieve up to 90 % rejection of boron at lower than ph 8. 3) As a result, most seawater desalination plants have to employ a two pass RO system (seawater is filtered twice by RO membranes) to comply with the boron limit for potable water supply. 3) NDMA has been classified as a probable human carcinogen 4) and its concentration in recycled water for potable reuse has been regulated in Australia and several other countries at 10 ng L 1 or below. 2) NDMA rejection by RO membranes can be as low as 10 %; 5) thus, a subsequent advanced oxidation process or a dilution with other clean water sources is often required to meet the NDMA level. Any improvement on the rejection of these small and uncharged solutes by RO membranes can lead to a reduction in capital and operational costs. In fact, some membrane manufacturers have been developing new RO membranes designed for high boron removal (e.g. ESPAB and SWC4B membranes supplied by Hydranautics/Nitto), however the specific details behind the high boron rejection capacity of these high rejection membranes are proprietary information of the respective manufacturers. To further optimize the rejection of small and neutral solutes by RO membranes, an understanding of the solutemembrane interaction is of paramount importance. Solute transport through an RO membrane can be described by the irreversible thermodynamic model, 6) in which the membrane is considered as a black box and the transport of solute

46 Fujioka et al. PALS as a tool for further insights into the transport of water and solutes during reverse osmosis is driven by the partition of the solute into the membrane followed by diffusive and convective movement across the membrane. Based on the irreversible thermodynamic model, the solution-diffusion model has been developed to describe the transport of solutes through RO membrane. 7) Another approach that has been widely used for nanofiltration membranes is the pore-flow model. The pore-flow model describes the RO membrane as a thin separation layer with cylindrical pores where solutes and water pass through by pressure-driven convective and diffusive flow. 8) It is noteworthy that the pore-flow model was first introduced by Loeb and Sourirajan 9) in the early 1960s to describe the transport of water and solutes in the cellulose acetate membranes that they have invented. In recent years, significant progress in deploying the positron annihilation lifetime spectroscopy (PALS) technique has been made to explore the internal structure of the membrane active skin layer at near atomic-scale. PALS allows for an accurate measurement of free-volume hole-size within the active skin layer of an RO membrane and can potentially offer a new horizon in our understanding of the transport of water 10, 11) and solutes in the RO process. Despite the significant increase in the number of studies using PALS to characterise RO membranes, the significance of free-volume holes on the rejection of small and uncharged solutes has not been fully elucidated. Thus, this article aims to identify the relationship between free-volume hole-size of RO membranes and their rejection capacity for small and uncharged solutes. Directions for further developments to better understand the transport of water and solutes in RO membranes will also be delineated. Feed Ac ve skin layer ( μm) Support layer (50 μm) Permeate Backing layer ( μm) Fig. 1 Layers and thickness of a typical thin composite flat sheet membrane. 2. Thin film composite membranes Most commercial RO membranes are thin-film composites (TFC) and comprise an active polyamide or polyamide derivative skin layer on top of a polysulfone porous support layer and a polyether non-woven fabric backing layer 12) (Fig. 1). The polyamide active skin layer is so densely packed and crosslinked that it contains subnanometer-scale free-volume holes. The active skin layer playsan important role in the permeation of water and solutes through membranes. 11) In contrast, the polysulfone porous support layer and the polyether non-woven backing layer have no significant resistance to water permeation. Their roles are solely to provide mechanical strength to the membrane. Thus, separation performance of RO membranes is governed exclusively by the physicochemical properties of the active skin layer. The separation performance of RO membranes is generally Table 1 Separation properties of commercial membranes. Model Type Manufacturer NaCl rejection a [%] Boron rejection b [%] SWC5 SWRO Hydranautics/Nitto c ESPAB LPRO Hydranautics/Nitto c TFC-HR LPRO KMS d BW30 LPRO Dow/Filmtec d ESPA2 LPRO Hydranautics/Nitto c ESPA1 LPRO Hydranautics/Nitto d a Manufacturer s data. b Determined using a laboratory-scale RO system with overall permeate flux = 20 L m 2 h 1 ; feed solution contains 20 mm NaCl; 1 mm NaHCO 3 ; and 1 mm CaCl 2 ; cross flow velocity 40.2 cm s 1 ; feedtemperature = 20.0 C; feed ph 8. c Ref. 13), d Ref. 14). 44 Japanese Positron Science Society 4 (2015)

47 Fujioka et al. PALS as a tool for further insights into the transport of water and solutes during reverse osmosis Table 2 Properties of boric acid and NDMA. Membrane type Boric Acid NDMA Structure OH Molecular weight [g mol 1 ] HO B OH N N O LogD a Molecular volume b [nm 3 molecule 1 ] pk a /(pk b ) c 8.70 (3.52) a ACD/PhysChem Suite software (Advanced Chemistry Development, Inc., Ontario, Canada). b The molecular volume of each molecule (V m ) was estimated with the equation (V m = Molecular volume [nm 3 mol 1 ]/N A ) where Avogadro constant (N A ) is mol 1.The molecular volume of each molar was obtained from the ACD/PhysChem Suite software. c Chemaxon ( determined based on the rejection of NaCl. In general, high NaCl rejection by RO membranes (> 99 %) can be readily achieved (Table 1). Although sodium and chloride ions are very small in size (molecular mass = 23 g mol 1 and 35.5 g mol 1, respectively), they exist in charged and hydrated form in an aqueous solution. These hydrated ions can be highly rejected due to the size exclusion mechanism in combination with electrostatic interactions. In contrast, small and uncharged solutes often exhibit low rejection by RO membranes. Typical examples include boron and NDMA that are present in natural water in an uncharged form as B(OH 3 ) (M W = 62 g mol 1 )andc 2 H 6 N 2 O(M W = 74 g mol 1 ), respectively (Table 2). These compounds are not hydrated and smaller in size than hydrated sodium ions. 12) The rejection of boron by RO membranes can be very low and highly variable in the range of 12 % 81 % 13, 14) (Table 1). Unlike charged solutes, uncharged solutes including boric acid and NDMA are primarily rejected under the size exclusion mechanism. 15) In fact, the rejection of uncharged solutes by RO membranes generally increases in proportion to their molecular size (e.g. molecular volume) 13) (Fig. 2). Although hydrophobic interactions between these solutes and the membrane could influence the rejection of uncharged solutes by TFC membranes, 16) both boric acid and NDMA are hydrophilic (Table 2). As a result, free-volume hole-size can be one of the most important factors governing the rejection of these solutes. 3. Membrane characterisation by PALS PALS is currently the only available technique that can determine free-volume hole-radius within a polymeric layer including the active skin layer of RO membranes. 17) PALS us- Rejection [%] Boric Acid (0.071) NDMA (0.124) NPYR (0.134) NMOR (0.145) NMEA (0.151) NPIP (0.161) NDEA (0.178) SWC5 ESPAB ESPA2 NDPA (0.232) Fig. 2 Rejection of boric acid and N- nitrosamines (20 mm NaCl, 1 mm NaHCO 3, 1mMCaCl 2, permeate flux 20 L m 2 h 1,cross flow velocity 40.2 cm s 1, feed ph 8.0 ± 0.1, feed temperature = 20.0 ± 0.1 C). 13) The molecular volume (nm 3 molecule 1 )isshownin NDBA (0.268) the parentheses. Values reported here are the average and ranges of duplicate results. ing a variable energy slow positron beam can analyse freevolume hole-radius in a specified depth without the need to isolate the target active skin layer. Mean free-volume holeradius (r [nm]) of an RO membrane can be determined from the pick-off lifetime of ortho-positronium (τ o-ps ) measured by PALS using the Tao-Eldrup model: 18) [ τ o-ps = r r ( 2π sin 2π r )] 1. (1) 4 (2015) Japanese Positron Science Society 45

48 Fujioka et al. PALS as a tool for further insights into the transport of water and solutes during reverse osmosis Table 3 Free-volume hole-radii of commercial polyamide RO membranes analysed by PALS. Membrane type Model Manufacturer Free-volume hole-radius [nm] Reference SWRO SWC5 Hydranautics/Nitto 0.26 Fujioka et al. 13) LPRO LF10 Nitto 0.20 Chen et al. 20) ESPA2 Hydranautics/Nitto 0.29 Fujioka et al. 13) ESPAB Hydranautics/Nitto 0.29 Fujioka et al. 13) AG GE 0.23 Ito et al. 21) AK GE 0.24 Ito et al. 21) Boron Rejeciton [%] Free-volume Hole-radius [nm] Fig. 3 Boron rejection as a function of free-volume hole-radius of SWRO membranes (TDS = mg L 1, feed ph 6.5, flow rate = 3.51 L min 1, temperature = 25 C, boron = 5mgL 1 ). 10) separation, rejection of a given solute could vary in response to changes in free-volume hole-size. In fact, a strong correlation between uncharged solute rejections and free-volume 10, 19, 20) hole-size has been reported in previous studies. For example, Henmi et al., 10) evaluated boron rejections using similar types of SWRO membranes and reported that the rejection of boron decreased with increasing free-volume hole-radius (Fig. 3). Fujioka et al., 13) reported that the free-volume hole-radius of a SWRO membrane (0.26 nm) was smaller than that of LPRO membranes (0.29 nm), and accordingly boron rejection by the SWRO membrane (81 %) was greater than that of the LPRO membranes (36 % 59 %) (Fig. 4). It is noteworthy that free-volume holes are approximated as a spherical shape. The free-volume hole-radius of RO membranes analysed by PALS using a variable slow positron beam is summarised in Table 3. The range of beam intensity (1 kev 2 kev) used in these studies corresponds to a mean positron implantation depth of 40 nm 120 nm, which was determined so that most positrons are implanted into the active skin layer of typical RO membranes. The reported mean free-volume hole-radius for 13, 19, 20) LPRO membranes is in the range of 0.20 nm 0.29 nm (Table 3). Although a notable difference in free-volume holeradius is observed among RO membranes, these data alone do not provide any significance of the difference on solute rejection. 4. Effects of free-volume hole-radius on solute rejection Because the free-volume hole-radius of RO membranes could be a dominant factor governing uncharged solute Boron Rejeciton [%] SWC5 ESPAB ESPA Free-volume Hole-radius [nm] Fig. 4 Boron rejection as a function of freevolume hole-radius of a SWRO membrane (SWC5) and LPRO membranes (ESPAB and ESPA2) (20 mm NaCl, 1 mm NaHCO 3, 1 mm CaCl 2, feed ph 8.0 ± 0.1, permeate flux = 20 L m 2 h 1, feed temperature = 20 C, boron = 5mgL 1 ). 13) 46 Japanese Positron Science Society 4 (2015)

49 Fujioka et al. PALS as a tool for further insights into the transport of water and solutes during reverse osmosis 5. Findings by the authors While the free-volume hole-size of RO membrane is indeed an important factor determining uncharged solute rejection as described above, a variation in free-volume hole-size is not necessarily correlated with a variation in uncharged solute rejection. A recent study performed by Fujioka et al., 13) revealed a remarkable difference in boron rejection by two LPRO membranes (i.e. ESPA2 and ESPAB) with equivalent free-volume hole-radius (i.e nm) (Fig. 4). A similar difference in rejection between the two LPRO membranes was also observed for several other small and uncharged compounds (e.g. NDMA and N-nitrosomethylethylamine (NMEA)). 13) In addition to free-volume hole-size, there are other physicochemical properties of RO membranes that may play an important role in solute rejection. These properties include free-volume hole-shape, free-volume hole-size distribution and free-volume fraction, all of which can vary considerably depending on manufacturing method and polymer materials even if the RO membranes have an identical mean free-volume hole-radius. These properties have not yet been determined by current characterization techniques. Although further development is still needed, PALS has arguably the best potential to characterise these properties. 6. Directions for future development While the contribution of membrane properties described above (i.e. free-volume hole-shape, hole-size distribution and free-volume fraction) toward the rejection of uncharged solutes still remains unclear, the quantification of these properties may lead to a breakthrough in understanding the solutemembrane interaction during RO filtration. Firstly, free-volume holes analysed using PALS are assumed to be spherical and uniform size and their shapes 15, 21) cannot be determined by PALS. Many previous studies have reported that the molecular width of solutes among molecular size parameters shows the best correlation with solute rejections, indicating that shape and size interactions between free-volume holes and solutes are important factors influencing solute rejection. Thus, it is necessary to reconcile the difference between the actual hole-shape and hole-size distribution and the assumption of current PALS techniques (i.e. spherical shape and uniform size). Free-volume fraction of the active skin layer is another property that can influence solute rejection according to the pore-flow model. 22) Solute and water fluxes can vary largely depending on free-volume fraction. The degree of free-volume fraction among several TFC membranes may be compared using o-ps intensity (I 3 ) data obtained through PALS. 23) In fact, Sasaki et al., 24) reported that boron rejection by modified SWRO membranes does not depend on the free-volume hole-radius but is dependent on V I 3, where V = free-volume hole-space (V = 4/3πr 3 ). Nevertheless, the o-ps intensity (I 3 ), which is the ratio of the o-ps component to the total implanted positron intensity, does not necessarily represent free-volume fraction; thus, the evaluation using V I 3 for understanding the role of hole-size and free-volume fraction on solute rejection may not be sufficiently accurate. 7. Conclusions PALS using a slow positron beam has the potential to elucidate the subnanometer-scale inner structure of RO membranes. PALS data previously reported in the literature reveal that commercially available RO membranes have a mean free-volume hole-radius of 0.20 nm 0.29 nm. Free-volume hole-size can be an important parameter in determining the rejection of boron which is uncharged at environmental ph values. Data in the literature also indicate that in addition to the free-volume hole-size, other membrane properties may also play an important role in boron rejection. Major challenges lie in the measurement of free-volume hole-shape, free-volume hole-size distribution and free-volume fraction of the active skin layer, all of which may require further development of PALS or support from other analytical techniques. References 1) K. P. Lee, T. C. Arnot, D. Mattia: J. Membr. Sci. 370 (2011) 1. 2) T. Fujioka, S. J. Khan, Y. Poussade, J. E. Drewes, L. D. Nghiem: Sep. Purif. Technol. 98 (2012) ) K. L. Tu, L. D. Nghiem, A. R. Chivas: Sep. Purif. Technol. 75 (2010) 87. 4) USEPA, (1993). 5) M. J. Farré, K. Döderer, L. Hearn, Y. Poussade, J. Keller, W. Gernjak: J. Hazard. Mater. 185 (2011) ) K. S. Spiegler, O. Kedem: Desalination 1 (1966) ) J. G. Wijmans, R. W. Baker: J. Membr. Sci. 107 (1995) 1. 8) T. Matsuura, S. Sourirajan: Ind. Eng. Chem. Proc. Des. Dev. 20 (1981) ) S. Loeb, S. Sourirajan: Sea Water Demineralization by Means of an Osmotic Membrane, in Saline Water Conversion II (American Chemical Society, 1963), Vol.38, pp ) M. Henmi, Y. Fusaoka, H. Tomioka, M. Kurihara: Water Sci. Technol. 62 (2010) ) S. H. Kim, S.-Y. Kwak, T. Suzuki: Environ. Sci. Technol. 39 (2005) (2015) Japanese Positron Science Society 47

50 Fujioka et al. PALS as a tool for further insights into the transport of water and solutes during reverse osmosis 12) T. Uemura, K. Kotera, M. Henmi, H. Tomioka: Desalin. Water Treat. 33 (2011) ) T. Fujioka, N. Oshima, R. Suzuki, S. J. Khan, A. Roux, Y. Poussade, J. E. Drewes, L. D. Nghiem: Sep. Purif. Technol. 116 (2013) ) K. L. Tu, T. Fujioka, S. J. Khan, Y. Poussade, A. Roux, J. E. Drewes, A. R. Chivas, L. D. Nghiem: Environ. Sci. Technol. 47 (2013) ) C. Bellona, J. E. Drewes, P. Xu, G. Amy: Water Res. 38 (2004) ) T. Fujioka, S. J. Khan, J. A. McDonald, L. D. Nghiem: Sep. Purif. Technol. 136 (2014) ) Y. C. Jean, P. E. Mallon, D. M. Schrader: Principles and Applications of Positron and Positronium Chemistry (World Scientific, Singapore, 2003). 18) M. Eldrup, D. Lightbody, J. N. Sherwood: Chem. Phys. 63 (1981) 51; S. J. Tao, J. Chem. Phys. 56 (1972) ) K. Ito, Z. Chen, W. Zhou, N. Oshima, H. Yanagishita, R. Suzuki, Y. Kobayashi: Jpn. J. Poly. Sci. Technol. 69 (2012) ) Z. Chen, K. Ito, H. Yanagishita, N. Oshima, R. Suzuki, Y. Kobayashi: J. Phys. Chem. C 115 (2011) ) Y. Kiso, K. Muroshige, T. Oguchi, T. Yamada, M. Hhirose, T. Ohara, T. Shintani: J. Membr. Sci. 358 (2010) ) Y. Kiso, K. Muroshige, T. Oguchi, M. Hirose, T. Ohara, T. Shintani: J. Membr. Sci. 369 (2011) ) Y. C. Jean, W.-S. Hung, C.-H. Lo, H. Chen, G. Liu, L. Chakka, M.-L. Cheng, D. Nanda, K.-L. Tung, S.-H. Huang, K.-R. Lee, J.- Y. Lai, Y.-M. Sun, C.-C. Hu, C.-C. Yu: Desalination 234 (2008) ) T. Sasaki, H. Tomioka, K. Nakatsuji: USA Patent No. US B2 (2010). ( ) Biographies Takahiro Fujioka: Dr. Takahiro Fujioka has had 13 years of research and industrial experience in water and wastewater treatment. He has worked for Mitsubishi Electric Co. and Fuji Electric Systems Co. for over 5 years. He received a Doctorate of Philosophy from the University of Wollongong (Australia) in July Takahiro is currently employed by the University of Wollongong as a Research Fellow to develop a range of novel membrane applications for wastewater treatment and water reuse. He is a board member and secretary of the Membrane Society of Australasia. Long D. Nghiem: Dr. Long Nghiem is a Professor at the University of Wollongong, where he leads the Strategic Water Infrastructure Laboratory. In 2010, he received the prestigious Vice-Chancellor Award for Research Excellence for Emerging Researchers. His specialised research expertise covers a range of membrane processes including pressure driven membrane filtration, forward osmosis, membrane distillation, membrane electrolysis, and membrane bioreactor. These processes can be applied to industries such as water treatment, biotechnology, and food processing. His current work focuses on the development of a membrane platform for securing a reliable potable water supply and the recovery of energy and nutrients from wastewater. 48 Japanese Positron Science Society 4 (2015)

51 4 (2015) Japanese Positron Science Society Experimental Investigation of Antihydrogen using a Cusp Trap Abstract: In this review, we describe a planned experiment of the Atomic Spectroscopy And Collisions Using Slow Antiprotons (ASACUSA) collaboration at CERN to test CPT symmetry via atomic beam spectroscopy of the ground-state hyperfine splitting of antihydrogen using a cusp trap. The cusp trap which consists of a superconducting anti-helmholtz coil and a stack of ring electrodes, is expected to produce a spin-polarized antihydrogen beam. Recently, the ASACUSA collaboration succeeded in producing antihydrogen atoms in the cusp trap and extracting an antihydrogen beam. This paves the way towards precision in-flight spectroscopy of the antihydrogen atom. Keywords: ASACUSA, antihydrogen, CPT symmetry, cusp trap, atomic beam, non-neutral plasma 1. 1, 2) CPT Lagrangian CPT C: P: T: Lagrangian CPT (CPT ) 3 6) CPT Yugo Nagata (Atomic physics laboratory, RIKEN), Naofumi Kuroda (Institute of Physics, Graduate School of Arts and Sciences, The University of Tokyo), TEL: , FAX: , nagata@radphys4.c.u-tokyo.ac.jp 7) CPT 8, 9) Indiana Kostelecký (Standard Model Extension: SME) CPT 10) CPT K (K 0 ) (K 0 ) ( ) 11) m CPT (Δ) Δ mn+1 Λ n (1) 12) n n > 0 Λ CPT 13) Λ m pl = c/g = h/(2π), h c G m m H GeV n = 1 Δ GeV 10 khz K 0 K Hz

52 1/10 (Weak equivalence principle: WEP) 14) 1995 CERN Low energy antiproton ring (LEAR) 15) Z e e + p p + γ + γ + Z p + e + + e + Z H + e + Z 1.9 GeV c 1 Xe 2pb Z 2 = cm 2 CERN PS (FNAL) E ) 2002 CERN ATHENA, ATRAP 17, 18) LEAR (Antiproton decelerator: AD) AD 22 Na Penning-Malmberg ev 10 ALPHA ATRAP 1S 2S Ioffe-Pritchard 19, 20) 1K 21, 22) Atomic spectroscopy and collisions using slow antiprotons (ASACUSA) CPT AEgIS GBAR 1K μk 23, 24) 2. ASACUSA ASACUSA (1.4 GHz) B = 0 (F = 0 F = 1) 2 Rabi 25) ASACUSA (Multiple ring electrodes: MRE) 2 B = 0 1 1S 50 Japanese Positron Science Society 4 (2015)

53 LFS HFS MRE 2 ASACUSA Ioffe-Pritchard MRE 26) Ioffe-Pritchard ASACUSA 27) (µ B) µ µ μ B µ B Low field seeking (LFS) High field seeking (HFS) 1 LFS 26) ASACUSA mt 1 π 1 σ 1 LFS HFS HFS B / r (T/m) (a) z (m) B / r (T/m) r (m) (b) 0.1 z (m) (a) B / r (b)(a) 29) r (m) π 1 σ 1 28) ASACUSA Hz 2.2 B 4 (2015) Japanese Positron Science Society 51

54 4 (a) (b) LFS (c) HFS 29) B r 2 + 4z 2. (2) z r B = 0 B μ B r r r2 + 4z 2 (3) z = 0 B / r z > r B / r r B B / r 3(a) 3(b) (a) z = 0 B / r r B 4 (a) (b) (c) LFS HFS 10 K 1.5 m (φ100 mm) LFS HFS ASACUSA l K μ B 29) K [K] ± 1.1B [T] l [m] = ±0.085 B [T] (4) 5 (a) (b) LFS 29) LFS HFS 0.05 m K Boltzmann 5 LFS (a) B z (b) f LFS (4) 4 (B = 0) 5 K 10 K 29) (4) 52 Japanese Positron Science Society 4 (2015)

55 3. p + e + H + hν (5) p + e + + e + H + e + (6) p + (e + e ) H + e (7) (5) ρ T ρt 1/2 (6) ρ 2 T 9/2 30) CERN (7) 31) 6 ASACUSA AD Monoenergetic Ultra Slow Antiproton Source for Highprecision Investigations (MUSASHI) 22 Na () 2.7 m ASACUSA 39) 4 (2015) Japanese Positron Science Society 53

56 3.1 8 (MUSASHI) 7 CERN PS Complex 7 CERN proton synchrotron (PS) complex (Linac 2) (PSB) (PS) 25 GeV AD p + p p + p + p + p (8) GeV ev AD 2.8 GeV Kicker 5.3 MeV ns ASACUSA (Radio frequency quadrupole: RFQ) RFQ (Radio frequency quadrupole decelerator: RFQD) 100 kev 8 MUSASHI Penning-Malmberg 2.5 T (MRE) 32) ev MRE 50 V 9(a) 2.5 T 10 8 cm 3 9 MUSASHI (a) (b) (c) (MRE) 54 Japanese Positron Science Society 4 (2015)

57 RFQD MRE 8 kev MRE 13 kv 9(b) 13 kv 9(b) 180 μ gcm 2 PET RFQD 4K Torr ASACUSA RFQD MUSASHI 33) 1eV 2.5 T r m d2 r dt = q2 ρr + qv 2 θ B + mv2 θ 2ɛ 0 r. (9) m, q, v θ ρ ω ± r = ω c 2 1 ± 1 2ω2 p ω 2 c (10) ω c = qb/m, ω p = q 2 ρ/(ɛ 0 m) ɛ 0 34) MUSASHI 35) 150 ev Ne 36) Surko 37) 22 Na (MRE) Na β kev 220 kev ev Ne 0.3 T N 2 /CF 4 55 ev 10 4 (2015) Japanese Positron Science Society 55

58 11 12 (a) MRE (b) (c) MRE 38) φ 1 φ 2 (nested trap) φ φ 4 φ 3 nested trap nested trap 12(c) (FI) FI (FIT) φ 5 FIT FIT MUSASHI 38) 11 MRE 6K 12 (a) MRE (b) (c) MRE 12(c) 13 39) RF 56 Japanese Positron Science Society 4 (2015)

59 13 nested trap 25 nested trap 38) nested trap RF ) BGO (Bi 4 Ge 3 O 12 ) BGO 100 mm 5mm 5inch BGO BGO 49 % BGO 300 MeV c 1 BGO BGO BGO BGO BGO BGO ) 4 (2015) Japanese Positron Science Society 57

60 BGO 15 39) GEANT4 40) 40 MeV 1 (scheme 1, scheme 2) N t BGO N >40 40 MeV scheme 1 94 V cm 1 n 43 BGO scheme 2 (452 V cm 1 ) n 29 4 scheme 1 scheme , 42) ) n ) scheme 1 scheme 2 [s] N t N > Profile likelihood ratio (σ) Z-value (σ) H 25 ± 3 16 ± 2 5. ASACUSA CPT MUSASHI ASACUSA 43 45) ASACUSA 1) J. R. Sapirstein, D. R. Yennie: Quantum Electrodynamics, edited by T. Kinoshita (World Scientific, Singapore, 1990) pp ) C. G. Parthey et al.:phys.rev.lett.107 (2011) ) G. Lüders: Ann. Phys. 2 (1957) 1. 4) W. Pauli: Niels Bohr and the Development of Physics (McGraw- Hill, New York, 1955) p.30. 5) R. Jost: Helv. Phys. Acta 39 (1957) ) J. Schwinger: Proc. Natl. Acad. Sci. 44 (1958) ) A. Kostelecký, R. Potting: Nucl. Phys. B 359 (1991) ) A. D. Dolgov, V. A. Novikov: JETP Lett. 95 (2012) ) M. Chaichian, K. Fujikawa, A. Tureanu: Phys. Lett. B 718 (2013) ) R. Bluhm, A. V. Kostelecký, N. Russel: Phys. Rev. Lett. 82 (1999) ) J. Beringer et al. (Particle Data Group): Phys. Rev. D 86 (2012) and 2013 partial update for the 2014 edition. 12) M. Kobayashi, A. I. Sanda: Phys. Rev. Lett. 69 (1992) ) M. C. Fujiwara et al.: AIP Conf. Proc (2008) ) D. B. Cassidy, S. D. Hogen: Int. J. Mod. Phys. Conf. Ser (2014) 15) G. Baur et al.: Phys. Lett. B 368 (1996) ) G. Blanford et al.: Phys. Rev. Lett. 80 (1998) ) M. Amoretti et al.: Nature, 419 (2002) ) G. Gabrielse et al.: Phys. Rev. Lett. 89 (2002) ) W. Bertsche et al.: Nucl. Instrum. Methods A 566 (2006) ) G. Gabrielse et al.: Phys. Lett. 98 (2007) ) G. B. Andresen et al.: Nature 468 (2010) ) G. Gabrielse et al.: Phys. Rev. Lett. 108 (2012) ) M. Doser et al. (AEGIS Collaboration): Class. Quantum Grav. 29 (2012) Japanese Positron Science Society 4 (2015)

61 24) P. Perez, Y. Sacquin: Class. Quantum Gravity 29 (2012) ) I. I. Rabi, J. M. Kellogg, J. R. Zacharias: Phys. Rev. 46 (1934) ) A. Mohri, Y. Yamazaki: Europhys. Lett. 63 (2003) ) ASACUSA proposal addendum, CERN-SPSC SPSC P-307 Add.1., ) B. Juhász, E. Widmann: Hyperfine Interact. 193 (2009) ) Y. Nagata, Y. Yamazaki: New J. Phys. 16 (2014) ) F. Robicheaux: Phys. Rev. A 73 (2006) ) C. H. Storry et al.: Phys. Rev. Lett. 93 (2004) ) N. Kuroda et al.: Phys. Rev. Spec. Top.-Accel. Beams 15 (2012) ) N. Kuroda et al.: Phys. Rev. Lett. 94 (2005) ) X.-P. Huang, F. Anderegg, E. Hollmann, C. Driscoll, T. O Neil: Phys. Rev. Lett. 78 (1997) ) N. Kuroda et al.: Phys. Rev. Lett. 100 (2008) ) R. Khatri et al.: Appl. Phys. Lett. 57 (1990) ) T. J. Murphy, C. M. Surko: Phys. Rev. A 46 (1992) ) Y. Enomoto et al.: Phys. Rev. Lett. 105 (2010) ) N. Kuroda et al.: Nat. Commun. 5 (2014) ) S. Agostinelli et al.: Nucl. Instrum. Methods A 506 (2003) ) G. Cowan et al.: Eur. Phys. J. C 71 (2011) ) R. Cousins et al.: Nucl. Instrum. Methods A 595 (2008) ) A. Müller, A. Wolf: Hyperfine Interact. 109 (1997) ) M. Amoretti et al.: Phys. Rev. Lett. 97 (2006) ) P. K. Mandel, A. Speck: Phys. Rev. A 81 (2010) ( ) : : 4 (2015) Japanese Positron Science Society 59

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63 Visiting research at Positron Probe Group in AIST Peng Kuang Institute of High Energy Physics, Chinese Academy of Sciences Preamble. In 2014 I was most happy to get the opportunity of being a visiting researcher to Positron Probe Group (PPG), Research Institute of Instrumentation Frontier (RIIF) at AIST from 1 October to 21 October. The opportunity was supported by the Japan Science and Technology Agency (JST) program Japan-Asia Youth Exchange Program in Science (SAKURA Exchange Program in Science). During my stay at AIST, Dr. Nagayasu OSHIMA, Senior Research Scientist of PPG/RIIF/AIST, was my host researcher. In the 21 days, I had the opportunity to visit several research institutes and universities in Japan. Among these were Prof. Uedono s Lab at the University of Tsukuba, the Spin-Polarized Positron Beam Research Group at the Japan Atomic Energy Agency (JAEA), ASRC as well as laboratories at AIST and KEK in Tsukuba. of semiconductor materials, insulating film (low-k high-k), and thin metal films. Afterwards, he guided us around visit their beautiful campus with his three students and we had a group picture before the graceful lake located in the center of campus. : Group picture at Tsukuba University. Back (L-R) Peng Kuang, N. Oshima (AIST), S. Sellaiyan (Tsukuba Uni.), T. Kakizaki (Tsukuba Uni.), T. Murayama (Tsukuba Uni.). Front (L-R) Jiang LiXian (AIST), T. Semba (Tsukuba Uni.), Brian O Rourke (AIST). : Tsukuba Central 2 4A AIST. At these institutes, the directors of the labs introduced the equipment to me and introduced their main research fields and recent research results. Thanks to patient and clear explanations from all the respective researchers, I had the chance to learn about various positron techniques and to see at first hand the current status of positron research in Japan. University of Tsukuba. On October 3, 2014, Dr. Oshima organized a visit to the Positron Annihilation Laboratory at Tsukuba University, along with fellow AIST researchers by Dr. Lixian Jiang and Dr. Brian O Rourke. In Tsukuba University, assistant Professor Selvakumar Sellaiyan introduced the laboratory to us. We had saw a Slow Positron Beam line and three Positron Annihilation Lifetime Spectroscopy equipment in Uedono Lab. During the lab visit, Prof. Sellaiyan explained how they use PALS as a method for defect characterization : Conference in JAEA. JAEA. On October 6, I had a precious opportunity to visit JAEA during an academic meeting between the AIST and JAEA positron groups. I introduced myself to all members at the meeting, and three Chinese postdoctoral researchers based in the JAEA positron group showed us their recent research results. The three post-docs at JAEA all graduated from Wuhan University and have worked in Dr. Kawasuso s group for more 4 (2015) Japanese Positron Science Society 61

64 than one year. We talked in depth about the current situation of working and living in Japan and I found that they were satisfied with their research and life in Japan. After the meeting, Dr. Kawasuso showed us around his laboratory in where they have a wide variety of equipment, including spin-polarized positron beam based in both Ge-68 and Na-22 sources, a lowtemperature STM and a slow Positron Beam. They are developing advanced positron beams and promoting materials research using those positron beams. From 2010 to 2014, they developed a highly spin-polarized positron beam and are now exploring its applications to magnetic substances and spinrelated phenomena. They are also pursuing positron diffraction studies of metal-insulated transitions and magnetic effects associated with surface low-dimensional materials. Furthermore, they are investigating the SCC degradation mechanism of nuclear stainless steels. : Dr. Oshima s lecture. AIST. During my stay at AIST, Dr. Oshima gave several lectures about the techniques of bunching and focusing slow positron beams, and patiently answered my questions every day. He also guided us around his lab, where he introduced the PPMA (positron probe microanalyzer) and high-frequency microwave cavity to us. The spatial resolution of PALS using the PPMA is two and half orders of magnitude smaller than that using conventional methods so that by scanning the sample the PPMA can obtain two or three dimensional positron annihilation spectroscopy images. He also invited other researchers in his lab to show me their research results such as development of a dedicated superconducting accelerator for positron production introduced by Dr. B. O Rourke, the development of portable X-ray sources using carbon nanostructures introduced by Dr. H. Kato, a C-band RF gun for compact radiation sources introduced by Dr. Y. Taira, a positron reemission microscopy apparatus introduced by Dr. H. Ogawa, and a slow positron beam system for in-situ lifetime measurements during ion beam irradiation introduced by Dr. A. Kinomura. Those researches described above are innovative and creative, for example, portable X-ray sources can be used to image object internal structure everywhere as more than 300 high-definition X-ray transmission images can be taken using two AA batteries as a power source. : The commercial PALS system introduced by Dr. Masato Yamawaki (AIST). On October 10, Dr. Kenji Ito warmly invited Dr. Lixian Jiang, Kuzuya-san (a research student from the Kyoto University reactor who was also staying at AIST during my stay) and I to visit his laboratory located the central AIST campus in Tsukuba. During the visit, Dr. Masato Yamawaki showed us around the lab and introduced the experimental facilities in detail including a slow positron beam system, a commercial PALS device and several RI based measurement systems. Additionally, we were shown an on-site positron lifetime inspection device, a very small and exquisite portable positron detector assembly using a sealed Kapton source, which can measure samples directly in situ. : Annual Positron Conference at AIST. On October 17, I was invited to attend the annual positron conference held by the AIST Positron Probe Group. During the conference, Dr. Oshima gave a presentation about the PPMA, and researcher Dr. H. Hagihara talked about the application of PALS. It is a good chance for me to know the de- 62 Japanese Positron Science Society 4 (2015)

65 velopment of the newest research fields in Japan, like positron technology, carbon dioxide separation membrane, etc. After the meeting we had a small celebration party, and enjoyed delicious Japanese food. are a great variety of advanced positron techniques and experimental installations in Japanese research groups. In addition, the daily management and safety facilities of all laboratories are of a very high level. Certainly, I learned much about positron equipment technology thanks to the experience of visiting to the different positron laboratories in Japan. Besides the research activities I had the chance to visit other places in Japan such as Ginza and Sensoji Temple. Additionally, a highlight of my stay was a tour to Mt. Tsukuba (together with Dr. Ito and Kuzuya-san) and the park near to AIST. In our free Dr. Oshima and Dr. Ito kindly invited Kuzuya-san and I for dinner. : Group picture in KEK. (L-R) N. Oshima (AIST), K. Wada (KEK), Y. Kuzuya (KUR), Peng Kuang, I. Mochizuki (KEK). KEK. On October 20, Dr. Oshima took Kuzuya-san and I to visit the high energy accelerator research institute, KEK. Dr. Wada, a researcher at the Slow Positron Facility in KEK, gave us a great overview of ongoing studies in KEK including particle and nuclear studies, materials structure science, accelerator laboratory and applied research laboratory. Then, we had a tour of the Belle II factory which is searching for violations of the symmetry between particles and anti-particles and new physics laws conducted using large numbers of particles, such as B mesons, produced by the KEKB accelerator. We also visited the photon factory which has played a large role in the development of the synchrotron radiation science for more than 30 years since After that, we visited the Slow Positron Facility. In the lab, we were shown the slow positron beam line and associated experimental stations which presently consists of Ps-TOF (positronium time-of-flight) measurement station, a reflection high-energy positron diffraction station, and positronium negative ion station. The positronium negative ion produces pulses of Ps- ions. The Ps-TOF measurement, where the width and the frequency of the incident positron pulse are 1 ns 10 ns (variable) and 50 Hz, is used to measure the energy of positronium emitted from a solid surface. The reflection high-energy positron diffraction is for the analysis of the atomic configuration of a crystal surface by using reflection high-energy positron diffraction (RHEPD). Dr. Wada led me through the different experimental halls and explained working principle of those equipment in detail. Summary. During my stay, I had the impression that there : Group picture at the top of the Mt. Tsukuba. (L-R) Y. Kuzuya (KUR), Dr. Ito (AIST), Peng Kuang. As everyone knows, Japanese people are extremely friendly and helpful. In general, I could feel the enthusiasm of every one I met here as a smile was always appearing on their faces. I deeply appreciate the help I received from everyone I met during my stay. Acknowledgements. I would like to extend my sincere gratitude to my teachers, Dr. Wang and Dr. Cao, who recommended and introduced me to Dr. Oshima at AIST. I would like to express my heartfelt gratitude to JST and AIST for giving such a precious opportunity and much support to me with the help from Dr. Oshima. I would also like to thank all members of the Positron Probe Group in AIST who gave me their help and time in listening to me and helping me work out my problems during my studying in AIST. I am also deeply indebted to all the other tutors and researchers I meet at Tsukuba University, JAEA and KEK for their direct and indirect help to me. Special thanks should go to Dr. Oshima, Kuzuya-san and Dr. Jiang who have put considerable time and effort into minimizing the difficulties I encountered in those days when I was studying and living in Japan. 4 (2015) Japanese Positron Science Society 63

66 5 (RHEPD) j.html : ( ) 64 Japanese Positron Science Society 4 (2015)

67 52 30 : : : th International Conference on Positron Annihilation (ICPA17) : : : () : Dr.Z.Q.Chen chenzq@whu.edu.cn : : WEB HP 14th International Workshop on Slow Positron Beam Techniques and Applications (SLOPOS14) SLOPOS Excursion Banquet Social program WEB WEB : : : : TEL/FAX: : : ( ) ( ) : 4 (2015) Japanese Positron Science Society 65

68 Positron Studies of Defects 2017 (PSD17) : : : E mail reinhard.krause-rehberg@physik.unihalle.de 12th International Workshop on Positron and Positronium Chemistry (PPC12) : 2017 : 3 MLF MLF PF : : : J-PARC CROSS PF-UA MLF : : WEB : E mail: imss-festa@pfiqst.kek.jp WEB : 66 Japanese Positron Science Society 4 (2015)

69 KEK (10 3 ) G615 Si(110) 2 16 (RHEPD) G630 X Ag G /3 2013G694 Ge(001) S /3 2014S G / KEK (4 7 ) (10 3 ) 11 KEK ( (ken.wada@kek.jp).. SPF-A3 SPF-B1 ( Ps ) SPF-B2 (Ps TOF) ( ) ps 300 ps 1 kev 30 kev 0.1 mm 10 mm 100 cps 2000 cps (IBEC) / B) 1 C) sayuri.yamauchi@aist.go.jp A) ( ) 4 (2015) Japanese Positron Science Society 67

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71 BBQ Brian O Rourke 8 Brian O Rourke 8 BBQ Dirac Anderson ( 2 ) : 4 (2015) Japanese Positron Science Society 69

72 Ps Ps Ps e Ps 2 Ps AMOC Ps Ps Ps Ps Ps : Ps Ps 7 AMOC Ps Ps AMOC S-paraemter W-parameter p-ps Ps Ps AMOC AMOC Ps 70 Japanese Positron Science Society 4 (2015)

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74 The 11th International Workshop on Positron and Positronium Chemistry (PPC11) The 11th International Workshop on Positron and Positronium Chemistry (PPC-11) 2012 : 9 Cidade de Goa Maurer Maurer Rätzke Alam 11 Hugenschmidt Alam Van Horn Japanese Positron Science Society 4 (2015)

75 PPC12 ( ) : The 11th International Workshop on Positron and Positronium Chemistry PPC-11 PPC SLOPOS ICPA Stepanov Mohamed He 3 10 Maurer Maurer 2 Cultural program 11 4 (2015) Japanese Positron Science Society 73

76 DJ DJ PPC Polish seminar 1 ( ) The International Workshop on Positron Studies of Defects 2014 (PSD-14) The International Workshop on Positron Studies of Defects 2014 (PSD 14) PSD 14 PSD : 9 17 THE SODOH HIGASHIYAMA KYOTO 74 Japanese Positron Science Society 4 (2015)

77 Journal of Physics: Conference Series (JPCS) 11 1 Martin-Luther University Halle R. Krause- Rehberg 2017 ( ) PSD-14 3 : ( 2 ) 4 (2015) Japanese Positron Science Society 75