Mott Parity P2 Mott
target Mott Parity
Parity Γ = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 t P P ),,, ( 3 2 1 0 1 γ γ γ γ γ γ ν ν µ µ = = Γ 1 : : : Γ P P P P x x P ν ν µ µ vector axial vector ν ν µ µ γ γ Γ ν γ 5 ν µ µ γ γ γ 5 Γ vector axialvector Parity Lagrangian Parity ( V V, A A ) ( V A )
Mott setting x-y target y y = 65 16 =14 =22.5n (0 n 14) =0, 0 =90 PMT B spin Mott count @(, ) > count @(,0) 0 PMT C z e Beam PMT A x y
z = 65 ) 0.25 1.028 0.5 1.056 1 1.116 2 1.245
Rutherford dσ 0( θ ) dω = ( Zαm) r 4 4 4 p sin 2 θ 2 α = 2 e 4πε 0hc Dirac µ ( µ ν ν µ µν ( γ ( i qa ) m) ψ = 0 γ γ + γ γ = 2g ) µ µ spin
Mott [ ] [ ] { } [ ] [ ] 2 1 2 2 0 1 2 2 2 2 0 1 2 2 0 0 0 0 4 2 2 2 2 ) ( ) ( ) ( ) ( ) ( ) (cos 1) ( 1) ( 2 ln sin exp ) (1 ) (1 cot 2 ) ( ) (cos 1) ( 1) ( 2 ln sin exp ) (1 ) (1 2 ) ( ) ( ) ( ) ( ) ( sin ) ( ) )sin( ( 1 ) ( : ) )sin( ( 1 2 sin 4 ), ( 2 2 2 ) ( 0 α ρ ρ ρ ρ θ θ θ θ β α θ θ θ θ θ βγ α θ φ φ θ β θ σ φ φ φ θ θ α φ θ σ πρ π θ θ θ θ σ = + Γ Γ + + Γ Γ + = + + + Γ Γ = + + + + Γ Γ = + = + Ω = = Ω = + = + Ω k iq iq iq e iq k iq k iq k e D P D k D k i iq iq iq q G P D k kd i iq iq iq i F Z q G F G F Z S S d d P PS p m Z d d k k k k i k i k k k k k k k k k k k k d d D
Mott
S
- u d p u n p + e + ν e u n d d e 0 helicity = +1/2 W ν e momentum spin e np -e momentum spin Source Electron emissions from the Hg-203 to Tl-203 decay, measured by A. H. Wapstra, et al., Physica 20, 169 (1954).
P N( N( ) ) + N( N( ) ) Lagrangian ( ) L int = G F 2 µ µ µ 5 µ 5 jµ j ( j = e γ (1 + αγ ) ν + p γ (1 + αγ ) ) n P = * α + α 1+ α 2 β V A current ( ) P = β
spin E r B r spin velocity spin velocity + + = E g B g B g mc es dt s d r r r r r r r r β γ γ β β γ γ γ 1 2 ) ( 1 1 2 1 1 2 spin Thomas
spin r ds dt = e 1 r s mc γ + 1 E 90 r r ( β ) θ s π γ 1 = 2 γ spin spin velocity E r P = β β cosθ s
energy
1st: 2nd: 3rd:
poisson
d=15 d=30 d=10 d=10
kv V
Source 137 Cs Photo Multiplier C 20 25 30 35kV electrode Source
137 Cs
energy (kev) Mean (ch) Sigma (ch) 629 922.3 77.9 77.9 1.1 0 20.5 10.3 10.3 0.0) 0.697 0.061 kev/ch 0keV 14.3 7.4 ch
0kV
20kV 25kV
30kV 35kV
Voltage (kv) Mean (kev) Sigma (kev) (kev) 20 151( 2) 30.2( 1.4) 129 25 163( 2) 39.8( 1.4) 165 30 201( 1) 48.7( 1.0) 194 35 234( 1) 57.3( 0.8) 242 0.24
PMT C PMT A 16 22.5 Back Scattering
58mm PMT B PMT C PMT A PMT A,B 65 Scintillator 0.25mm 0.210 1.67% PMT PMT C Scintillator 5mm
70mm 15mm Null Asymmetry 0.01mm Background Asymmetry 0.0025mm
OR PMT A PMT B AMP AMP DISC A D C Computer PMT C AMP DISC ADC AMP 10 Discriminator Threshold 80mV(A) 500mV(B) Gate Signal ADC Gate Signal AMP Computer Channel
137 Cs 30.2y - 0.514 MeV 94% 1.176 Mev 6% 0.662 Mev 85%
1. 0 2. 0.5Pa 3. 30kV 4. AMP, Discriminator, ADC PMT 1kV 5.,, Count Rate 2 (Computer PMT A PMT B Count Rate ) 6. 7. 90,180,270 2 6
*** CORPORATION Source PMT A B energy peak C B A Source(137Cs)
*** CORPORATION Photo multiplier A Source 137 Cs
*** CORPORATION Photo multiplier B Source 137 Cs
*** CORPORATION
*** CORPORATION Photo multiplier A Source 137 Cs
*** CORPORATION Photo multiplier A - threshold 60mV
*** CORPORATION Photo multiplier B Source 137 Cs
*** CORPORATION Photo multiplier B - threshold 500mV
*** CORPORATION 0 : PM A : PM B : PM C
*** CORPORATION 90 : PM A : PM B : PM C
*** CORPORATION 180 : PM A : PM B : PM C
*** CORPORATION 270 : PM A : PM B : PM C
*** CORPORATION
*** CORPORATION PM A = 0 Au Al
*** CORPORATION PM A = 0
*** CORPORATION PM A = 0 Au Al
*** CORPORATION PM B = 0 Au Al
*** CORPORATION PM B = 0
*** CORPORATION PM B = 0 Au Al
*** CORPORATION
*** CORPORATION
*** CORPORATION
*** CORPORATION
*** CORPORATION PM A
*** CORPORATION PM B
*** CORPORATION
*** CORPORATION