 -Ray Emission Probabilities Edgardo Browne Decay Data Evaluation Project Workshop May 12 – 14, 2008 Bucharest, Romania.

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 -Ray Emission Probabilities Edgardo Browne Decay Data Evaluation Project Workshop May 12 – 14, 2008 Bucharest, Romania

Photon energy and intensity Transition energy and intensity Relative and absolute intensities

Photon energy and intensity Guidelines When possible use evaluated values: Recommended standards for  -ray energy calibration (1999), R.G. Helmer, C. van der Leun, Nucl. Instrum. and Methods in Phys. Res. A450, 35 (2000) Update of X-ray and gamma-ray decay data standards for detector calibration and other applications. IAEA - Report, Vienna 2007.

Guidelines Weighted averages of values from the same type of measurements (e.g. with Ge detectors). The uncertainty on the average (recommended) value should not be smaller than the smallest input uncertainty. For discrepant data use the “Limitation of Relative Statistical Weight” method (Program LWEIGHT).

Transition Energy E T = E  + E R, where E R = E  2 /2 M R c 2 is the nuclear recoil energy E   is the photon energy (in MeV) M R ~ A is the mass of the daughter nucleus M R c 2 ~ x A

Transition Intensity I T = I  (1 +  ), where I  is the photon intensity,  is the total conversion coefficient (theoretical interpolated value)

Relative and Absolute Intensities Relative intensities (relative to the intensity of the strongest  ray, usually taken as 100). Also called relative emission probabilities. Absolute intensities (per 100 disintegrations of the emitting radionuclide, usually given in %). Also called absolute emission probabilities, usually given “per decay.”)

1993Al15, 1994En022000He14Fitted E   (keV) UnevaluatedEvaluated (18) (15) (9) (6) (11) (9) (24) (24) (13) (13) (11) (11) (10) (7) (9) (7) (18) (18) (7) (7) (3) (3) (5) (5) (13) (13) (9) (9) (5) (5) (5) (5) (6) (5) (18) (16) (3) (5) (16) (16) 66 Ga  -ray energies

Combining evaluated and unevaluated energies

66 Ga Relative  -Ray Intensities

Absolute  -Ray Emission Probabilities Ice(1039  )/I  + (gs) = 2.08 (10)x10 -4 (experimental, 1960Sc06) I  + (gs)/  I  i + = (experimental, 1960Sc06) Ice(1039 ,E2)/I  (1039  ) = 2.69 (8)x10 -4 (Theory, 1978Ro22) Therefore I  (1039  )/  I  i + = 2.08 (10)x10 -4 x / 2.69 (8)x10 -4 =0.67(4) Also  I  i + /  I  i = (from decay scheme and theoretical I  i+/I  i). Since  I  i + +  I  i = 100%, then  I  i + = 55.8 (24)%, and I  (1039  ) = 0.67 (4) x 55.8 (24) = 37 (3)%

233 Pa  - decay I  (312) = 38.6 (5) % (experimental value, Gehrke et al.)  I(  +ce) (gs) = 102 (2) %  %

What went wrong? E  (keV)  T (exp.)  T (theo. M1) (2) (2) (2)0.75 Answer: Nuclear penetration effects

Using X rays to normalize a decay scheme 231 U  -ray spectrum

I  (25)=100 (6) I  (84)=50 (3) I KX =390 (14) EC(K)/EC(Total) = 0.59  K = B K =115.6 keV, thus most K-x rays originate from vacancies produced by the electron-capture process. Total vacancies = I KX EC(Total) /  K EC(K) = 680 (33) Normalization factor N = 100 / 680 (33) = (7) I  (25)=100 (6) x (7) = 15 (1)% I  (84)=50 (3) x (7) = 7.5 (6)%

192 Ir   and electron capture decay E  (keV)I   I   (6)0.305 (9) 5.23 (8) (9) (7) (9)  = 5.77 (8) (5)0.085 (3) (6) (20) (9) (20) (25) (5) (25)  = (6)

The normalization factor is: N = 100 / [I  (489) (1+  489 ) + I  (206) (1+  206 ) + I  (316) (1+  316 ) + I  (612) (1+  612 )] = 100 / (7) = (5) N = (5) The electron capture  and   decay branchings are:    = 100 [I  (489) (1+  489 ) + I  (206) (1+  206 )] /120.7 (7) = 100 / [1 + (I  (316) (1+  316 ) + I  (612) (1+  612 )/(I  (489) (1+  489 ) + I  (206) (1+  206 )) = 100 / [ (6)/5.77 (8)] = 100 / 20.9 (3) = 4.78 (7)%   = 100 – EC = 100 – 4.78 (7) = (7)%   = (7)%  = 4.78 (7)%

125 Sb Decay Scheme It takes about a year for the intensity of the 109-keV  ray to be in equilibrium (within 1%) with the other  rays. The intensity of the 35-keV  ray is also affected by the 58-year half-life of the 144-keV 125m Tc isomer.

Decay Scheme Normalization [  I  (1 +  i ) (gs and 144-keV level)]  N =100% N = (24) The equilibrium correction for I  (109) is [T 1/2 ( 125 Sb) – T 1/2 ( 125m Te)/ T 1/2 ( 125 Sb) ]=  - feeding to the 144-keV 125m Te isomer I  - =[I  (109)(1+  109 ) x – I  (176) (1+  176 ) – I  (380)(1+  380 ) – I  (497)(1+  497 )]  N I  - = 13.4%

Absolute  -Ray Intensities Deduced from Decay Scheme

Decay Branching Ratios Assuming EC(gs) =  - (gs) = 0%

 -ray transition intensity balance The corresponding normalization factor is N = 100 /  [ I i (out) + I i (gs) – I i (in)] = 100 /  [ I i (out) – I i (in)] +  I i (gs), but  [ I i (out) – I i (in)] = 0, therefore N = 100 /  I i (gs) I i (out) I i (in) I i (gs) 0 IiIi

Uncertainties of Absolute  -Ray Emission Probabilities Deduced from Decay Scheme I 1 + dI 1 I 2 + dI 2  (I 1 + I 2 ) N = 100% N = 100 / (I 1 + I 2 )

The absolute emission probabilities are I 1 (%) = 100 x I 1 /(I 1 + I 2 ) I 2 (%) = 100 x I 2 /(I 1 + I 2 ), Their uncertainties have the same value, irrespective of their values in the relative emission probabilities!! dI 1 (%) 2 =dI 2 (%) 2 = 10 4 x (I 1 2 dI 2 2 +I 1 dI 2 2 )/(I 1 +I 2 ) 2

If I 1 = I 2 = I, and dI 1 = dI 2 = dI, then dI 1 (%)/I 1 (%) = dI 2 (%)/I 2 (%) = [(2) 1/2 /2] dI/I The fractional uncertainties are smaller than those in the corresponding relative spectral emission probabilities!! See Nucl. Instr. and Meth. In Phys. Res. A249, 461 (1986) for general mathematical formulae.

240 Am EC Decay to 240 Pu E2E2 (<1% M1) – E2 43 – E Pu 240 Am     h y  

240 Am Gamma Rays 1972Ah LeZO 1972PoZS Recommended Values E  (keV)I  (rel)E  (keV)I  (rel)  keV)I  (rel) E  (keV)I  (rel)I  (abs) 42.9 (1)0.09 (1)42.87 (4)*0.09 (1)^0.110 (3) 98.9 (1)1.5 (2)98.9 (1)#1.5 (2)^1.49 (3) (10)0.012 (3)152.4 (10)†0.012 (3)‡0.012 (3) (10)0.020 (3)249.7 (10)†0.020 (3)‡0.020 (3) (10)0.005 (2)251.8 (10)†0.005 (2) (20) (10)0.009 (2)305.3 (10) (10)&0.009 (2)‡0.009 (2) (10)0.049 (5)343.7 (10) (10)&0.049 (5)‡0.048 (5) (10)0.053 (5)382.3 (10) (10)&0.053 (5)‡0.052 (5) (10)0.013 (4)447.8 (10)†0.013 (4)‡0.013 (4) (10)0.072 (6)508.2 (10) (10)&0.072 (6)‡0.071 (6) (10)0.010 (5)555.4 (10)†0.010 (5)‡0.010 (5) (10)0.014 (6)600.7 (10)†0.014 (6)‡0.014 (6) (10)0.070 (8)606.9 (10) (10)&0.070 (8)‡0.069 (8) (8)697.8†0.035 (8)‡0.035 (8) (1)25.1 (9) (5)25.1 (4) (5) (4)24.7 (5) (3)0.10 (1)916.1 (2)0.087 (6)917.1 (2) (6)0.089 (6) (5)0.025 (3)935.7 (5) (6)&0.025 (3)‡0.025 (3) (6)0.007 (3)938.2 (10) (5)&0.007 (3)‡0.007 (3) (3)0.005 (1)959.1 (5)0.037 (4)960.2 (2) (4)0.038 (5) (1)73.3 (25) (6)73.2 (10) (6) (10)72.2 (6) (5)0.011 (2) (3)0.010 (1)1034 (1) (1) (10) (4)0.017 (3) (3)0.015 (2)1037 (1) (2) (20) (10) (6) (10) (8)& (6)‡ (6)

Normalization Procedures 1.Assumes  (43) < 1%,  (142) < 1%, and  T  (GS, 43, 142) > 98% (= %)  I  (988) = % 2.Assumes just  (43) < 1%, and  T  (GS, 43) > 99% (= %)  I  (988) = %  Recommended value  I  (988) = %

Program GABS

INPUT: ENSDF Data Set

OUTPUT: Absolute  -Ray Intensities REPORT FILE Current date: 03/09/ AM EC DECAY NR= BR= 1.00 FOR INTENSITY UNCERTAINTIES OF GAMMA RAYS NOT USED IN CALCULATING NR, COMBINE THE UNCERTAINTY IN THE RELATIVE INTENSITY IN QUADRATURE WITH THE UNCERTAINTY IN THE NORMALIZING FACTOR (NR x BR). FOR THE FOLLOWING GAMMA RAYS: E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS.(Compare with ) E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS.(Compare with ) E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS.(Compare with ) E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS.(Compare with ) E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS.(Compare with ) E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS. E= %IG= PER 100 DECAYS.(Compare with ) E= %IG= PER 100 DECAYS.