Jagdish K. Tuli NNDC Brookhaven National Laboratory Upton, NY 11973, USA

Jag Tuli DDP-Workshop

Bucharest, Romania, May 08

Jagdish K. TuliNNDC

Brookhaven National LaboratoryUpton, NY 11973, USA

Decay Scheme Normalization



1.Relative intensity is what is generally

measured

2. Multipolarity and mixing ratio ().

3. Internal Conversion Coefficients

• Theoretical Values:

• From BRICC



• 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)



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



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.



Absolute intensities

“Intensities per 100 disintegrations of the parent nucleus”

• Measured (Photons from -, ++, and decay)

Simultaneous singles measurements

Coincidence measurements



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



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



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



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



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



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

++



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

++

Jagdish K. Tuli NNDC Brookhaven National Laboratory Upton, NY 11973, USA

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