Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jagdish K. TuliNNDC
Brookhaven National LaboratoryUpton, NY 11973, USA
Decay Scheme Normalization
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
1.Relative intensity is what is generally
measured
2. Multipolarity and mixing ratio ().
3. Internal Conversion Coefficients
• Theoretical Values:
• From BRICC
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
• Experimental values:
For very precise values ( 3% uncertainty).
E = 661 keV ; 137Cs (K=0.0902 + 0.0008, M4)
Nuclear penetration effects.
233Pa - decay to 233U.
E = 312 keV almost pure M1 from electron
sub-shell ratios.
However K(exp) = 0.64 + 0.02.
(K th(M1)=0.78, K
th(E2)=0.07)
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
For mixed E0 transitions (e.g., M1+E0).
227Fr - 227Ra
E = 379.1 keV (M1+E0); (exp) = 2.4 + 0.8
th(M1) = 0.40; th(E2) = 0.08
675.8
296.6
379.5
½-
½-
<10 ps
227Ra
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Decay Scheme NormalizationRel. Int. Norm. Factor Abs. Int.
I NR BR %IIt NT Br %It
I NB BR %II NB BR %II NB BR %I
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 I to I 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 and Intensities to Intensities Per 100 Decays of This Decay Branch.
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Absolute intensities
“Intensities per 100 disintegrations of the parent nucleus”
• Measured (Photons from -, ++, and decay)
Simultaneous singles measurements
Coincidence measurements
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Normalization Procedures
1. Absolute intensity of one gamma ray is known (%I)
Relative intensity I + I
Absolute intensity %I + I
Normalization factor N = %I / IUncertainty N =[ (I%I)2+(IIx N
Then %Il = N x Il
Il = [(N/N)2 + (IIx Il
I1 I2
%I
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
2. From Decay Scheme
IRelative -ray intensity; : total conversion coefficient
N x I x (1 + ) = 100%
Normalization factor N = 100/ I x (1 + )
Absolute -ray intensity % I = N x I00(1 +
)
Uncertainty % I= 100 x /(1 + )2
100%
I
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Total intensity from transition-intensity balance
200
150
100
95
0
-
TI(7) = TI(5) + TI(3)
If (7) is known, then
I7 = TI(7) / [1 +
(7)]
I6I5 I4
I2 I3
I1
I7
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Equilibrium Decay Chain
T0 > T1, T2 are the radionuclide half-lives,
For t = 0 only radionuclide A0 exists,
% I3, I3, and I1 are known.
Then, at equilibrium
% I1 = (% I3/I3) × I1× (T0/(T0 – T1) × (T0/(T0 – T2)
Normalization factor N = %I1/ I1
A0
A1
A2
A3
I1
I3
T0
T1
T2
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Normalization factor N = 100 / I1(1 + 1) + I3(1 + 3)
% I1 = N x I1 = 100 x I1 / I1(1 + 1) + I3(1 + 3)
% I3 = N x I3 = 100 x I3 / I1(1 + 1) + I3(1 + 3)
% I2 = N x I2 = 100 x I2 / I1(1 + 1) + I3(1 + 3)
Calculate uncertainties in %I1, % I2, and % I3. Use
3% fractional uncertainty in 1 and 3.
See Nucl. Instr. and Meth. A249, 461 (1986).
To save time use computer program GABS
- 100%
I3
I2
I1
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
4. Annihilation radiation intensity is known
I(+) = Relative annihilation radiation intensity
Xi = Intensity imbalance at the ith level = (+ce) (out) – (+ce)
(in)
ri = i / +i theoretical ratio to ith level
Xi = i + +i = +
i (1 + ri), therefore +i = Xi / 1 + ri
2 [X0 / (1 + r0) + Σ Xi / (1 + ri)] = I(+) ……… (1)
[X0 + Σ Ii ( + ce) to gs ] N = 100 ………. (2)
Solve equation (1) for X0 (rel. gs feeding).
Solve equation (2) for N (normalization factor).
+ce) (in)
(+ce)(out)
(++)2
(++)1
(++)0
++
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
5. X-ray intensity is known
IK = Relative Kx-ray intensity
Xi = Intensity imbalance at the ith level = (+ce) (out) – (+ce) (in)
ri = i / +i theoretical ratio to ith level
Xi = i + +i, so i = Xi ri / 1 + ri (atomic vacancies); K=K-fluorsc.yield
PKi = Fraction of the electron-capture decay from the K shell
IK= K [0×PK0 + Σ i× PKi]
IK = K [PK0× X0 r0 / (1 + r0) + Σ PKi× Xi ri / 1 + ri]…(1)
[X0 + Σ Ii( + ce) to gs] N = 100 …. (2)
Solve equation (1) for X0, equation (2) for N.
+ce) (in)
(+ce)(out)
(++)2
(++)1
(++)0
++