Decay Scheme Normalization Jagdish K Tuli NNDC Brookhaven
Decay Scheme Normalization Jagdish K. Tuli NNDC Brookhaven National Laboratory Upton, NY 11973, USA Jag Tuli DDP-Workshop
1. Relative intensity is what is generally measured 2. Multipolarity and mixing ratio (d). 3. Internal Conversion Coefficients • • Theoretical Values: From BRICC Jag Tuli DDP-Workshop
• Experimental values: For very precise values ( 3% uncertainty). Eg = 661 ke. V ; 137 Cs (a. K=0. 0902 + 0. 0008, M 4) Nuclear penetration effects. 233 Pa b- decay to 233 U. Eg = 312 ke. V almost pure M 1 from electron sub-shell ratios. However a. K(exp) = 0. 64 + 0. 02. (a. K th(M 1)=0. 78, a. K th(E 2)=0. 07) Jag Tuli DDP-Workshop
For mixed E 0 transitions (e. g. , M 1+E 0). 227 Fr b- 227 Ra Eg = 379. 1 ke. V (M 1+E 0); a(exp) = 2. 4 + 0. 8 ath(M 1) = 0. 40; ath(E 2) = 0. 08 ½- <10 ps 675. 8 379. 5 296. 6 ½ 227 Ra Jag Tuli DDP-Workshop
Jag Tuli DDP-Workshop
Jag Tuli DDP-Workshop
Decay Scheme Normalization Rel. Int. Ig It Ib Ie Ia Norm. Factor NR BR NT Br NB BR Abs. Int. %Ig %It %Ib %Ie %Ia BR: Factor for Converting Intensity Per 100 Decays Through This Decay Branch, to Intensity Per 100 Decays of the Parent Nucleus NR: Factor for Converting Relative Ig to Ig Per 100 Decays Through This Decay Branch. NT: Factor for Converting Relative TI to TI Per 100 Decays Through This Decay Branch. NB: Factor for Converting Relative B- and E Intensities to Intensities Per 100 Decays of This Decay Branch. DDP-Workshop Jag Tuli
Jag Tuli DDP-Workshop
Absolute intensities “Intensities per 100 disintegrations of the parent nucleus” • Measured (Photons from b-, e+b+, and a decay) Simultaneous singles measurements Coincidence measurements Jag Tuli DDP-Workshop
Jag Tuli DDP-Workshop
Normalization Procedures 1. Absolute intensity of one gamma ray is known (%Ig) b- Ig 1 Ig 2 %Ig 2. 3. 4. 5. 6. 7. Relative intensity Ig + DIg Absolute intensity %Ig + D%Ig Normalization factor N = %Ig / Ig Uncertainty DN =[ (D%Ig/ %Ig)2+(DIg/ Ig)2]1/2 x N Then %Igl = N x Igl D%Igl = [(DN/N)2 + (DIg 1/ Ig 1)2]1/2 x Igl Jag Tuli DDP-Workshop
2. From Decay Scheme b- 100% Ig Ig: Relative g-ray intensity; a: total conversion coefficient N x Ig x (1 + a) = 100% Normalization factor N = 100/ Ig x (1 + a) Absolute g-ray intensity % Ig = N x Ig = 100/ (1 + a) Uncertainty D% Ig = 100 x Da/(1 + a)2 Jag Tuli DDP-Workshop
Total intensity from transition-intensity balance b- 200 Ig 6 Ig 5 Ig 4 150 Ig 2 Ig 3 100 Ig 7 95 Ig 1 0 TI(g 7) = TI(g 5) + TI(g 3) If a(g 7) is known, then Ig 7 = TI(g 7) / [1 + a(g 7)] Jag Tuli DDP-Workshop
Jag Tuli DDP-Workshop
Jag Tuli DDP-Workshop
Equilibrium Decay Chain T 0 A 0 Ig 1 T 1 A 1 T 2 A 2 Ig 3 A 3 T 0 > T 1, T 2 are the radionuclide half-lives, For t = 0 only radionuclide A 0 exists, % Ig 3, and Ig 1 are known. Then, at equilibrium % Ig 1 = (% Ig 3/Ig 3) × Ig 1× (T 0/(T 0 – T 1) × (T 0/(T 0 – T 2) Normalization factor N = %Ig 1/ Ig 1 Jag Tuli DDP-Workshop
Jag Tuli DDP-Workshop
Jag Tuli DDP-Workshop
Jag Tuli DDP-Workshop
Jag Tuli DDP-Workshop
Jag Tuli DDP-Workshop
Jag Tuli DDP-Workshop
Jag Tuli DDP-Workshop
Jag Tuli DDP-Workshop
Jag Tuli DDP-Workshop
b- 100% Ig 2 Ig 3 Ig 1 Normalization factor N = 100 / Ig 1(1 + a 1) + Ig 3(1 + a 3) % Ig 1 = N x Ig 1 = 100 x Ig 1 / Ig 1(1 + a 1) + Ig 3(1 + a 3) % Ig 3 = N x Ig 3 = 100 x Ig 3 / Ig 1(1 + a 1) + Ig 3(1 + a 3) % Ig 2 = N x Ig 2 = 100 x Ig 2 / Ig 1(1 + a 1) + Ig 3(1 + a 3) Calculate uncertainties in %Ig 1, % Ig 2, and % Ig 3. Use 3% fractional uncertainty in a 1 and a 3. See Nucl. Instr. and Meth. A 249, 461 (1986). To save time use computer program GABS Jag Tuli DDP-Workshop
4. Annihilation radiation intensity is known e+b+ (g+ce) (in) (g+ce)(out) (e+b+)2 (e+b+)1 (e+b+)0 I(g+) = Relative annihilation radiation intensity Xi = Intensity imbalance at the ith level = (g+ce) (out) – (g+ce) (in) ri = ei / b+i theoretical ratio to ith level Xi = ei + b+i = b+i (1 + ri), therefore b+i = Xi / 1 + ri 2 [X 0 / (1 + r 0) + Σ Xi / (1 + ri)] = I(g+) ……… (1) [X 0 + Σ Igi (g + ce) to gs ] N = 100 ………. (2) Solve equation (1) for X 0 (rel. gs feeding). Solve equation (2) for N (normalization factor). Jag Tuli DDP-Workshop
5. X-ray intensity is known e+b+ (g+ce) (in) (g+ce)(out) (e+b+)2 (e+b+)1 (e+b+)0 IK = Relative Kx-ray intensity Xi = Intensity imbalance at the ith level = (g+ce) (out) – (g+ce) (in) ri = ei / b+i theoretical ratio to ith level Xi = ei + b+i, so ei = Xi ri / 1 + ri (atomic vacancies); w. K=Kfluorsc. yield PKi = Fraction of the electron-capture decay from the K shell IK= w. K [e 0×PK 0 + Σ ei× PKi] IK = w. K [PK 0× X 0 r 0 / (1 + r 0) + Σ PKi× Xi ri / 1 + ri]…(1) [X 0 + Σ Ii(g + ce) to gs] N = 100 …. (2) DDP-Workshop Jag Tuli Solve equation (1) for X , equation (2) for N.
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