Radioactive Equilibrium: 99Mo/99mTc

Valery Chechev

V.G. Khlopin Radium Institute, 194021 Saint Petersburg, Russia

Second Workshop for Radioactive Decay Data Evaluators: Training Sessions of the Decay Data Evaluation Project

(DDEP-2008)

12 – 14 May 2008, IFIN-HH, Bucharest

Radioactive equilibrium of two (or more) radionuclides composing a radioactive series is achieved when the half-life of the daughter (T2) is shorter than that of the parent (T1): T2 T1 .A ratio of the daughter and parent activities is described by the formula A2/A1 = [T1/(T1T2)] {1exp[0.693(1/T2 1/T1)t]} where the time t=0 corresponds to a pure parent radionuclide. In equilibrium a ratio of number of daughter atoms to that of parent atoms as well as a ratio of their activities is approximately constant: A2/A1 [T1/(T1T2)].

Generally, equilibrium is considered to be established after 10T2.

   

For an equilibrium mixture of radionuclides all absolute intensity values are given usually per 100 disintegrations of the parent nuclide. This rule is applied also if the daughter is an isomer (e.g. 95Zr/95mNb, 99Mo/99mTc, 125Sb/125mTe).

GENERAL REMARKS

Here only the equilibrium 99Mo/99mTc decay data is considered. I do not concern the evaluation of proper 99mTc decay data done on usual DDEP procedures for separate radionuclide in 2000 (Fig. 1). (The half-life of 99mTc was updated in 2004).

RADIOACTIVE EQUILIBRIUM WITH ISOMER

For the equilibrium mixture of the parent radionuclide and daughter isomer (t10T2), the emission probabilities for isomer transitions are P(i) + P(cei) = [T1/(T1T2)] Pi , where Pi is the isomeric transition probability.

In this report, as example of radioactive equilibrium with isomer, the evaluation of 99Mo/99mTc decay data done jointly by researchers of LNHB and KRI in 2000 is examined.

For users it is of interest of decay data both for the equilibrium mixture of 99Mo/99mTc and pure 99mTc. Therefore, both evaluations are presented on the DDEP web site.

55 9944Ru

5/2+

3/2+

(5/2+)

0

89.8

322.4

140.511

142.681

56 99m

43Tc

56 9943Tc

9/2+

7/2+

1/2–

stable

β–

β–

Fig. 1

0.004%

99Tc

99Mo66 h

6.0 h

Other Levels

920.6

509.1

181.1

142.7

140.5140.52.17142.7

40.6181.1

366.4

739.5777.9

823.0960.8

411.5

Fig. 2

1/2+

3/2¯

5/2+

1/2¯

9/2+

7/2+

0

For 99Mo/99mTc equilibrium the factor T1/(T1T2) is equal 1.1005(8). It should be taken into account in the equilibrium intensities of the isomeric 142.7 keV -ray and a “slow” component of the 140.5 keV -ray which are concerned with the 99mTc decay (Fig.2). The contribution of a “prompt” component (5%) is conditioned mainly by the intensity of the -transition 40.6 keV.

99Mo with a half-life of 66 hours disintegrates to the 99Tc excited levels by transitions. About 88% decays of 99Mo occur to the 142.7 keV level (99Tc isomer) which has a half-life of 6 hours. The basic lines of the 99Mo decay were determined as long ago as in the middle of the last century and later on they were confirmed and worked out in details. The latest experimental work devoted to a detailed analysis of the 99Mo decay scheme was published by Goswamy et al. (1992Go22). Subsequent NDS evaluations by Peker (1994Pe15) and by Tuli et al. (2001Tu04) as well as the DDEP one (2000) are based mainly on the decay scheme from Goswamy et al.

In the last columns of Table 1 the evaluated values are displayed. References are given using the NSR keynumbers and can be found on the DDEP web site.

RELATIVE EMISSION PROBABILITIES OF GAMMA RAYS

The results of measurements of relative -ray emission probabilities along with ICC are key experimental data for obtaining a set of evaluated 99Mo/99mTc decay characteristics.

In the DDEP evaluation (Morillon et al., 2000) the 739.5 keV -ray has been taken as the reference one because it is not a part of the isomer 99mTc decay scheme (in contrast to the 140.5 keV -ray), and also, because most of measurements was done relatively to the 739.5 keV -ray.

In Table 1 the available experimental values for the -ray relative emission probabilities are given. Where necessary, these data (including uncertainties) have been corrected by the evaluators to the values in units of 100 to the 739.5 keV -ray relative emission probability.

99Tc

99Mo66 h

6.0 h

Other Levels

920.6

509.1

181.1

142.7

140.5140.52.17142.7

40.6181.1

366.4

739.5777.9

823.0960.8

411.5

Fig. 2

1/2+

3/2¯

5/2+

1/2¯

9/2+

7/2+

0

Energy,keV

1968Va14

1969Co18

1974HeYW

1978Morel

1980Di16

1982Si16

1990Me15

1992Go22

Evaluated(old

values)

2003La27

Evaluated(new

values)

40.58 6.9(8) R 4.6(18) R 5.9(15) R 8.68(27) 7.7(6) 8.6(5) 8.49(25) 8.43(20) 8.51(25)

140.5 649(25) R 704(45) 730(49) 743(19) 747(12) 686(49) 755(26) 739(11) 739(11) 744(11)

142.7 0.195(40) 0.149(25) 0.189(11) 0.174(14) 0.183(11)

158.8 0.10(3) 0.095(30) 0.112(15) 0.11(4) 0.139(8) 0.156(6) 0.12(4) 0.146(7) 0.144(6)

162.4 0.073(22) 0.067(15) 0.078(13) 0.097(5) 0.098(5) 0.094(5) 0.110(6) 0.098(5)

181.1 48.7(23) 49.9(34) 49.6(42) 49.1(16) 50.1(7) 49.8(33) 50.3(17) 49.4(8) 49.6(7) 49.5(21) 49.6(7)

366.4 10.6(8) 10.7(6) 10.0(9) 9.8(3) 9.52(32) 9.8(8) 9. 92(25) 9.82(15) 9.85(15) 9.8(4) 9.84(15)

380.1 0.071(20) 0.07(2) 0.058(15) 0.045(15) 0.07(2) 0.075(3) 0.086(7) 0.075(4) 0.069(6) 0.074(3)

411.5 0.18(2) R 0.13(2) 0.134(23) 0.14(2) 0.120(6) 0.133(10) 0.118(30) 0.123(6)

457.6 0.039(20) 0.08(2) 0.04(2) 0.056(5) 0.067(5) 0.061(5) 0.057(5) 0.060(5)

528.8 0.39(5) 0.49(5) 0.36(4) 0.43(6) 0.44(4) 0.447(15) 0.47(2) 0.446(15) 0.411(16) 0.436(15)

620.0621.7

0.21(3) 0.217(22) 0.19(6) 0.30(4) R 0.26(2) 0.232(11) 0.24(4) 0.236(11) 0.222(12) 0.229(11)

739.5 100 100 100 100 100 100 100 100 100 100 100

777.9 35.1(24) 34.9(20) 35.8(30) 35.5(10) 35.8(9) 34.8(19) 35.3(12) 35.1(5) 35.3(5) 35.3(12) 35.3(5)

823.0 1.04(8) 1.11(8) 1.09(10) 1.09(5) 1.09(5) 1.10(7) 1.06(4) 1.10(2) 1.09(2) 1.12(5) 1.10(2)

960.8 0.78(7) 0.78(6) 0.80(8) 0.76(4) 0.84(4) 0.79(6) 0.76(4) 0.78(2) 0.78(2) 0.768(26) 0.78(2)

Table 1. Experimental and evaluated relative emission probabilities of most intense -rays from the 99Mo/99mTc equilibrium mixture decay

R indicates that the value has been omitted as outlier

Here in Table 1* the results are shown for 16 most intense -rays of 32. The evaluated values-2000 are given in the third column from the right edge of the table.

I have revised these results taking into account the new measurements of Lashko (2003La27) for -rays with energy more than 150 keV. Besides, new statistical processing was done with the LWEIGHT computer program (instead of the EV1NEW program used previously). The uncertainty assigned in this evaluation to the recommended value is always greater than or equal to the smallest uncertainty in any of the experimental values used in the statistical processing.

The new evaluated values are given in the last column. They differ slightly from the evaluation results-2000.* Additionally for convenience in Table1 it is not shown the single measurement result of Yang et al. (1980) and two ones of Chen Da et al.

(1980) which were taken into account in statistical processing.

Below the evaluation results are given for ICC (T and K) of the basic low energy gamma transitions in comparison with the BRICC values obtained currently. BRICC values vary from those of Rösel et al. (1978) in limits of the adopted ICC uncertainty of 2%.

INTERNAL CONVERSION COEFFICIENTS (ICC)

In the DDEP evaluation-2000 most of ICC was adopted from tables of Rösel et al. (1978) in the issue of analysis and averaging available results of measurements of ICC and multipolarity mixing ratios. For pure multipolarities the relative uncertainties of ICC were adopted to be 2%. In case of mixed multipolarities the uncertainties of ICC were evaluated taking into account the uncertainties on the respective multipolarity admixture coefficients.

Not changing the results of analysis-2000 of the available experimental data I have obtained BRICC values for the same gamma transitions and their multipolarities.

Transition 40.6 keV

First author and year Multipolarity T (Rösel et al.)

-0.008 (8) GARDULSKI (1974) M1 + 0.0064%E2 3.76

0.03 (3) SINGH (1982) M1 + 0.09%E2 3.87

-0.119 (8) ALFTER (1993) M1 + 1.4%E2 4.19

Adopted:* MCDONALD (1971) M1 + 1.4(2)%E2 4.19(10)

BRICC: M1 + 1.4(2)%E2 4.10(8)

K Multipolarity First author and year

3.2 (2) M1 Ranakumar (1969)

3.7 (5) M1 Bashandy (1969)

3.27 (19) Weighted average LWEIGHT (2= 0.86 )

Adopted: 3.50(8) M1 + 1.4(2)%E2 Rösel et al.

BRICC: 3.44(7) M1 + 1.4(2)%E2

* Hereinafter “Adopted” concerns to the DDEP evaluation-2000

T First author and year0.118 (8) AMTEY et al. (1968)0.113 (6) DICKENS and LOVE (1980)0.122 (5) VUORINEN (1969)0.118 (3) LEGRAND et al. (1973)

0.1181(23) LWEIGHT (reduced 2= 0.44, weighted average and internal uncertainty)

Adopted: 0.119(3)BRICC: 0.118(2)

Rösel et al. (1978) for M1+3.2(3)%E2For M1+3.5(3)%E2

Transition 140.5 keV

K First author and year0.096 (6) VOINOVA et al. (1971)0.093 (6) VOINOVA et al. (1971)0.102 (7) VAN EIJK et al. (1968)0.094 (8) VUORINEN (1969)0.102 (5) DICKENS and LOVE (1980)0.096 (3) LWEIGHT (2=0.35; weighted average and internal uncertainty)0.104 (3)0.103(3)

Rösel et al. (1978) for M1 + 3.2(3)%E2 multipolarity (adopted)BRICC for M1 + 3.5(3)%E2

Transition 142.7 keVInternal Conversion Coefficient T For M4 the theoretical value from Rösel is  40.9(8) [BRICC: 40.2(8)].Internal Conversion Coefficient K The theoretical K conversion coefficient, for M4, is 29.3(6) (Rosel et al.) [BRICC: 29.1(6)].

Transition 181.1 keV

K Multipolarity

First author and year

0.13(3) RAVIER et al. (1961)0.127(11) E2, 12%M1 VAN EIJK et al. (1968) 0.133(20) E2 BASHANDY (1969)

0.12(1) VOINOVA et al. (1972)0.125(7) LWEIGHT (reduced 2 of 0.16, weighted

average and the internal uncertainty)0.125(3) E2 Rösel et al. 0.125(3) E2 BRICC

Internal Conversion Coefficients T

0.140(5) DICKENS and LOVE (1980) GARDULSKI and WIENBECK (1974) measured a low mixing ratio of 0.002(7) for M3/E2 multipolarity.For E2, the theoretical value is  0.149(3) (Rosel et al.) [BRICC: 0.148(3)]

As above said already, in this calculation we should take into account the factor [T1/(T1T2)] = 1.10 in the equilibrium intensities of the 142.7 keV -ray and a “slow” component of the 140.5 keV -ray which are concerned with the 99mTc decay. The “prompt” component of the 140.5 keV -ray is conditioned mainly by the intensity of the -transition 40.6 keV and can be deduced accurately from the sum intensity of -transitions populated the level 140.5 keV with the exception of the 2.17 keV -transition in 99mTc:

It (“prompt” 140.5 keV) = It (40.6 keV) + It (621.8 keV) + It (1001 keV) = 43.6(15) in relative units of Table 1. From here I (“prompt” 140.5 keV) = 39.3(12). Using the evaluated equilibrium intensity of 744(11), we obtain 705(11) for the “slow” component of the140.5 keV -ray intensity. [Here It I (+ce) = I (1+T)].

Thus we have for the intensity balance to the ground state of 99Tc:100% disintegrations of 99Mo = It (“prompt” 140.5 keV) + [It (“slow” 140.5

keV) / 1.10] + [It (142.7 keV) / 1.10] + It (181.1 keV) + It (761.8 keV) + It (1072 keV) = 824(13).

From here N = 0.1214(19)% and P( 739.5 keV) = 12.14(19)%.

NORMALIZATION FACTOR

A normalization factor (N) for obtaining absolute -ray emission probabilities P() per disintegration of 99Mo can be deduced by three ways:1). From the (+ce)-intensity balance to the ground state of 99Tc using the decay scheme (Fig. 2, 3) and evaluated total ICC.

0

140.511

142.683

181.094

509.11

534.4

671.49

761.7

920.59

1004.07

1072.2

1129.12

1141.87

1198.9(3/2¯)

3/2+

(3/2)¯

(7/2+)

3/2(¯)

1/2+

5/2+

3/2¯

3/2¯

5/2+

1/2¯

7/2+

9/2+

57 9942Mo

1/2+

(3/2+)

1172.03/2+

Fig. 3

2). From the sum of probabilities of all the beta transitions leaving 99Mo that must be equal to 100 %. The probabilities of --transitions have been obtained from the P(+ce) balance at each level in the same relative units of Table 1.

Balance at the level 142.7 keV:I( 1214 keV) = {[It (2.17 keV) + It(142.7 keV)] / 1.10} It ( input) =

677(11). Here, for evaluation of the total intensity of the low energy transition 2.17 keV, the intensity balance for the level 140.5 keV was used. The -transition to this level is negligible due to a great forbiddenness.

Balance at the level 140.5 keV: It (2.17 keV) = It (140.5 keV) It (40.6 keV) It (621.8 keV) It (1001 keV) =

788(13).Balance at the level 181.1 keV leads to the negligible intensity of the

-transition to this level, 1.7(17), in relative units of Table 1.Similar evaluations for higher levels have led to the -transition

intensities as follows:I ( 848 keV) = 9.69(15), I ( 823 keV) = 0.008(5), I ( 686 keV) =

0.423(17), I ( 437 keV) = 135.8(5), I ( 353 keV) = 1.12(2), I ( 285 keV) = 0.015(4), I ( 228 keV) = 0.090(5), I ( 215 keV) = 0.91(2), I ( 185 keV) = 0.013(3), I ( 158 keV) = 0.016(3).

Thus 100% disintegrations of 99Mo = 825(12). From here N = 0.1212(17)% and P ( 739.5 keV) = 12.12(17)%.

Using the relative intensities from Table 1 and the normalization factor N = 0.1212(15), the absolute emission probabilities (number of photons per 100 disintegrations of 99Mo ) of all -rays from the 99Mo/99mTc equilibrium mixture decay have been deduced.

3). From the measured directly absolute emission probability of the 739.5 keV -ray.

Absolute measurements : number of photons per 100 decays12.3 (3) A. Simonits - 1981 (Ge(Li))11.9 (3) Chen Da - 1985 (Ge(Li))12.00 (33) R.A. Meyer - 1990 (HPGe, Ge(Li))

The LWEIGHT computer program has used a weighted average and an internal uncertainty. Reduced 2 = 0.45.Evaluated absolute 739.5 keV emission probability: 12,12(15)% and N = 0.1212(15)%.This value obtained from the above experimental data was adopted in the DDEP evaluation (2000) as recommended.

As seen it agrees very well with the values deduced currently from intensity balances based on the adopted 99Mo decay scheme and new evaluated equilibrium -ray intensities from Table 1: 0.1214(19) and 0.1212(17).

GAMMA RAY TRANSITION PROBABILITIES AND ABSOLUTE X-RAY AND ELECTRON EMISSION PROBABILITIES

Using the evaluated absolute -ray emission probabilities and total ICC, the probabilities of all gamma ray transitions (except 2.17 keV transition) have been deduced for the 99Mo/99mTc equilibrium mixture. The probability of the 2.17 keV transition has been deduced from the intensity balance at the level 140.5 keV (see above).

Using the evaluated ICC for K-, L- shells, the conversion electron emission probabilities have been deduced and with adopted atomic data the Tc KX-, LX- ray emission probabilities have been obtained. It should be noted that the emission probabilities of conversion electrons from the 142.7 keV isomeric transition and “slow” component of the 140.5 keV transition are increased for equilibrium mixture by factor of 1.10.

1980Di16 1992Go22 Calculated (adopted)

11.3(5) 11.5(4) 11.3(2)

Below the measured values of the total absolute emission probability of Tc KX-rays (100) are compared to the adopted value calculated using the EMISSION computer program:

Using the P(+ce) balance at each level (see above) and the normalization factor N = 0.1212(15), the probabilities of all -transitions in the 99Mo decay have been obtained. The -transitions to the ground state and level 140 keV have a high degree of forbiddenness and they are unobserved.

Measured(1971Na01, 1982KhZW)

Evaluated (deduced from balance correlations of

decay scheme)

Energy, keV Probability 100 Energy, keV Probability 100

-0,12 245 0.2 228.1(10) 0.0109 (6)

-0,9 450(10) 14 436.6(10) 16.46 (21)

-0,4 840(5) 2 848.1(10) 1.174 (23)

-0,2 1214(1) 80(2) 1214.5(10) 82.1 (17)

Below the measured energies and probabilities of some - transitions are given for comparison with the evaluated ones:

66.0(1) Seiler (1947Se25) 235U(n,f) ic66.00(15) Gunn et al. (1957Gu62) 235U(n,f),Mo(n,) pc66.96(9) Wright et al. (1957Wr37) 98Mo(n,)67.2(2) Protopopov et al. (1958Pr71) 235U(n,f) GM65.6(2) Newman (1961Ne15) 235U(n,f) pc66.7(1) Crowther and Eldridge (1965Cr03) 98Mo(n,) well scin65.98(10) Baldwin (1967Ba37) Mo(n,) from 2 meas. pc +

scin66.69(6) Reynolds et al. (1968Re04) 235U(n,f) ic66.5(2) Baba et al. (1971Ba28) 238U(p,f) 66.02(1) Emery et al. (1972Em01) 235U(n,f)66.16(30) Dickens (1979Di07)65.945(3) Houtermans et al. (1980Ho17) ic65.924(6) Hoppes et al. (1982HoZJ)

Unterweger et al. (1992Un01)ic

65.942(12) Walz et al. (1983Wa26) Superseded by 2003Sc4966.02(9) Butsev et al. (1998) 98Mo(n,)65.85(10) Butsev et al. (1998) 235U(n,f)64.92(25) Butsev et al. (1998) 181Ta(12C,x) 99Mo65.974(14) Schrader et al. (2003Sc49) ic

The measured half-life values are given, in hours, below:

HALF-LIFE Of 99MO (Updated In 2004)

When processing the 17 remained values, the LWEIGHT computer program has detected 1957Wr37, 1958Pr71, 1961Ne15, 1965Cr03, 1968Re04, 1971Ba28, 1979Di07 and 2 values of Butsev et al. (65.85(10) and 64.92(25)) to be outliers, based on Chauvenet’s criterion. The Limited Relative Statistical Weight method increases the uncertainty for the 1980Ho17 value from 0.003 to 0.00481 and the LWEIGHT program chooses the unweighted mean of 65.983(38) with the large uncertainty that does not correspond to the most accurate measured values (1980Ho17, 1982HoZJ or 1992Un01 and 2003Sc49).

With the set of the 5 most recent values (1972Em01, 1980Ho17, 1982HoZJ or 1992Un01, 1998Bu01 and 2003Sc49), the Limited Relative Statistical Weight method increases the uncertainty for the 1980Ho17 value from 0.003 to 0.00482 and the LWEIGHT program has used the weighted mean of 65.949(14), 0.014 is the external uncertainty, the reduced-2 is 10.4.

The adopted value is 65.949(14) h or 2.7479(6) d.

Looking at the graphical representation given above, it appears that 5 high values are 66.5 hours, 10 values are in the range about 66.0 h and 2 low values are 65.6 h. The value of 1983Wa26 given by Walz et al. was superseded in 2003 by Schrader.

All things considered, I show the table of revised (updated) evaluated data for basic gamma ray emissions and transitions in comparison with the evaluations-2000.

CONCLUSION

Energy Photons per100 disint.

Photons per100 disint.

T T P(tr.) 100

P(tr.) 100

*2.1726 1.410 10 1.410 10 86.8(19) 86.8(19)

40.583 1.022(27) 1.031(33) 4.19(10) 4.10(10) 5.30(19) 5.26(19)

*140.51 89.6(17) 90.2(17) 0.119(3) 0.118(3) 92.1(19) 92.1(18)

*142.68 0.0211(17) 0.0222(14) 40.9(8) 40.2(8) 0.88(6) 0.83(6)

181.09 6.01(11) 6.01(11) 0.149(3) 0.148(3) 6.91(13) 6.91(13)

366.42 1.194(23) 1.193(23) 0.0092 0.0090 1.21(3) 1.203(23)

739.50 12.12(15) 12.12(15) 0.00173 0.00171 12.14(15) 12.14(15)

777.92 4.28(8) 4.28(8) 0.00059 0.00059 4.28(8) 4.28(8)

Table 2. Evaluated data for basic gamma ray emissions and transitions from the 99Mo/99mTc equilibrium mixture decay

Evaluation-2000 – by red, revised (updated) evaluation-2008 – by blue. The revision leads to small changes in the evaluated values improving their consistency in the network of intensity balance correlations of 99Mo decay scheme. *Note: P(tr.) is not equal P() (1+T) for these equilibrium -rays.