positron 1930 Dirac 1933 Anderson m 22Na(hl=2.6years), 58Co(hl=71days), 64Cu(hl=12hour) 68Ge(hl=288days) MeV : thermalization m psec 100

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1 positron 1930 Dirac 1933 Anderson m 22Na(hl=2.6years), 58Co(hl=71days), 64Cu(hl=12hour) 68Ge(hl=288days) MeV : thermalization m psec 100psec nsec E total = 2mc 2 + E e + + E e Ee+ Ee-c mc mc 0.511MeV - (0 ) 1

2 Positron annihilation lifetime measurement Doppler broadning - - Anguler correlation of annihilation radiation 2 e γ γ

3 Hartree-Fock-Slater ψ- [ 2 + V( r) ]ψ ( r) = E ψ ( r) (1) ψ+ [ 2 + V( r) ]ψ + ( r) = E + ψ + ( r) (2) ( p 1,p 2 ) ψ p1 ( r) = exp ir p 1 ψ p2 ( r) = exp ir p 2 (3) (h ) { } Γ( p)d 3 p d 3 rψ ( r)ψ + ( r)exp ir p 1 + p 2 M.J.Puska (LDA) LDA (Vc : Coulomb part) (Vcorr : correlation part) = V c ( r) + V corr n ( r) V r 2 d 3 p (4) [ ] (5) d

V c ( r) = i 2Z 2 r i ρ( t)dt 2 r i r 0 i r i ρ( t) dt t Z ri i t t

n) ψ + ( r k ) ( ε ( n) ) (8) λ = σ drn + [ ( ) + n c ( r)γ c + n d

4 V c ( r) = i 2Z 2 r i ρ( t)dt 2 r i r 0 i r i ρ( t) dt t Z ri i t t t dt r(t) (2) Schrödinger Kimball and Shortley method (6)(5) n ε ( n) = i 1 n ψ h 2 + ( n) ψ + r i k i r k 6ψ + n 2 ( n) ψ + r i r i + V r n ( i)ψ + n+1 ( n +1) ψ + r i = k 6 + h 2 V r i 2 r i (6) (7) ( n) ψ + ( r k ) ( ε ( n) ) (8) λ = σ drn + [ ( ) + n c ( r)γ c + n d ( r)γ d ] (9) ( r) n v ( r)γ v n v r c r 0 σ = πr o 2 c R F (10)

5 nv nc d nd Γ(enhancement factor)(8) n + ( r) = ψ + ( r) 2 (11) σ ( 2) > σ ( 3) > σ ( 1) σ ( 3) σ ( 2) = 4( π 2 9) α 3π =1/372 α = e 2 /h 2 c =1/137

6 σ ( 2) = πr 2 Bc v φ = vn e λ = σ ( 2) φ λ = πr B 2 cn e τ = 1 λ 500 Positron lifetime (ps) Fe Mo Al Ni Number of vacancies Two State Trapping Model v f

7 n f ( t) = n 0 exp( λt) (19) nf t n n sec dn f dt = λ f n f κ v n f +κ v n v (20) dn v dt = λ vn v +κ v n f κ v n v (21) nf nv f v v v (20) (21)i Nf i Ni (20) (21) dn f dt dn i dt N = λ f N f κ i N f + κ i N i N i =1 N i=1 = λ i N i + κ i N f κ i N i i =1 N i =1 Ni(0)=0 Nf(0)=N0 Nf, Ni N f = N 0 exp λ 0 t κ i N i = N 0 λ 0 λ i λ 0 = λ f + κ i [ exp( λ i t) exp( λ 0 t) ] (22) (23) (24) T(t) (25)

8 T = λ 0 N f + N i = 2 λ i N i = N 0 λ 0 exp λ 0 t + N i =2 λ i κ i { exp( λ λ 0 λ i t) exp( λ 0 t )} i (26) τ 1 =1 λ f + I i = ( κ i ) τ n =1 λ n (27) κ i λ 0 λ i I 1 = 1 N i= 2 κ i λ 0 λ i τ = n i =1 τ i I i (28) (29) 1 1 (28) κ v I 2 = 1 τ 1 1 τ 2 (30) (24) τ 1 cal (31) =1 λ = 1 λ f +κ v = τ f 1 +τ f κ v (30), (31) v τ 1 cal = 1 I 2 1 τ f I 2 τ 2 (32) Fe f=110psec (4.12) κ v = I 2 ( 1 τ f 1 τ 2 ) I 1 = µ v c v (33)

9 C (26) (26) i=3 CONTIN-PALS-II Gregory (4.8) n n T( t) = I i λ i exp λ i t i=1 I (34) T( t) = I( λ)λ exp( λt) dλ 0 (35) I( ) (35) F(t) S(t)=F(t)*T(t) Sr(t), S(t) N F(t) T(t) ( t) = N r F( t) *T r ( t) S( t) = N F( t)* T( t) S r (4.18) S( t)* T r t = NN r 1 T t * S r t (36) (37)

10 Tr(t) S( s)t r ( s) = NN 1 r T( s)s r s T r ( t) = I( λ)exp( st) exp( λ r t )dt 0 (37) = λ r λ r + s (38) Intensity (%) S(t)(37) (38) S( t) = NN 1 r λ 1 1 r I r λ I( λ) { 1+ ( λ λ)s t 0 r r * exp ( λt )}dλ (39) = P( λ) s t 0 N L K( λ,t)dλ + β i L i t i =1 P λ (40) = λi( λ) (41) (41) RI (x10) Neutron Irradiation(KUR) Fe0.22%Cu Alloy at 100K -ray Ge-detector scintilator start signal -ray 1.275MeV 22 Ne 22 Na Positron Annihilation rate λ(/nsec) scintilator -ray 0.511MeV stop signal sample

11 (19) START SIGNAL Constant Fraction Discriminator High Voltaged Photomultiplier Preamplifier Amplifier Timing SCA BaF2 Identified Specimens High Voltaged BaF2 γ (1.28MeV) γ (0.511MeV) Photomultiplier 22Na (positron source) Preamplifier Amplifier FAST COINCIDENCE Timing SCA BIASED TIME TO PULSE HIGHT CONVERTER Multi Channel Analyzer STOP SIGNAL Constant Fraction Discriminator DELAY MeV 1/KT 0.025eV p L (i) γ 1, γ 2 E 1, E 2, m e +, m e m e + = m e c E 1, E 2 = 2mc 2 (42) 2E γ = E 1 + E 2 E 1 = E 2 (43)

12 E 1 = mc 2 = 0.511MeV (44) E 2 = mc 2 = 0.511MeV (45) (ii) p L p 1, p 2 2mc 2 = cp 1 + cp 2 (46) p 1 p 2 = p L (47) (46),(47) E 1 = cp 1 = mc 2 + cp L 2 = 0.511MeV + cp L 2 (48) E 2 = cp 2 = mc 2 cp L 2 = 0.511MeV cp L 2 (49) p L 0.511MeV cp L /2 511keV 180 py

13 I(θ)=π(p 2 F -(mc* θ) 2 ) θ p T /m 0 c (50) mrad m Positron Affinity A+ (ev) Positron Affinity Li Na Al K Sc V Mn Co Cu Ge Sr Zr Mo Ru Pd Cd Cs Lu Ta Re Ir Au Elements 2 (A,B) AB Δ AB = µ A µ B µ A µ B

14 µ A + µ B + Δ + AB = µ A B + µ + ΔE A,B + ΔE A,B + = Δ + AB Δ AB µ B B ( + µ + ) = µ A + µ + A A + A + = µ + + µ ΔE A,B + = A A B + A + ΔE A,B + ΔE A,B + 1 2

positron2018

positron2018 陽電子陽電子 (positron) は 1930 年 Dirac によって理論的予言され 1933 年に Anderson によって発見された電子の反粒子であるその性質としては電子の静止質量と同質量 m 同じスピン反対符号の正電荷を持つため電子と極性を反対にみることでほぼ同じ扱いをとることができる陽電子を放出する白色陽電子線源としては主に 22 Na(T 1/2 =2.6years), 58