228Ra disequilibrium to determine the residence half-lives of radium in vegetation compartments

Journal of Environmental Radioactivity 43 (1999) 291—304

Using Ra/Ra disequilibrium to determine the residence half-lives of radium in vegetation compartments A. Baeza *, J. Barandica
, J.M. Paniagua , M. Rufo , A. Sterling Departamento de Fı´ sica, Facultad de Veterinaria y Escuela Polite&cnica, Avda. de la Universidad s/n UEx- 10071 Ca&ceres, Spain
Departamento de Ecologı& a U.C.M, Avda. Complutense s/n.- 28040 Madrid, Spain Consejo de Seguridad Nuclear, Justo Dorado, no 11 - 28040 Madrid, Spain Received 1 May 1997; accepted 8 February 1998

Abstract The concentrations of Ra and Ra were studied in different vegetation compartments and in available and non-available soil fractions in a Mediterranean scrubland ecosystem. A high percentage of the plant samples showed an apparent discrimination in favour of Ra over Ra. A linear compartmental model was applied to the soil—plant system. It allowed us to explain why these discrimination coefficients differed from unity, to obtain the residence half-lives of radium in the different compartments, to estimate the age of the plants, and to simulate the temporal evolution of the radioactive concentrations in each compartment.  1999 Elsevier Science Ltd. All rights reserved.

1. Introduction There have been many studies of the different links in the food chain by which radioactive contamination can pass from its source to man. A large part of these studies has focused on the dynamics of man-made radioisotopes from the atomic test fallout of the 1960s (UNSCEAR, 1982), from accidents such as that of the nuclear power plant at Chernobyl (UNSCEAR, 1988), or from operating nuclear facilities (Baeza et al., 1991; Pattenden & Mckay, 1994; Tokuyama et al., 1997).

*Corresponding author. Tel.: #34-2725-7153; fax: #34-2725-7153. 0265-931X/99/$ — see front matter  1999 Elsevier Science Ltd. All rights reserved PII: S 02 6 5-9 3 1X (9 8) 0 0 04 7 - 2

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Another group of studies focuses on the release of high concentrations of radionuclides belonging to the natural radioactive series from uranium mines into the environment (Berry et al., 1991; Carnahan, 1988; Burns et al., 1991; Wang et al., 1993; Paige et al., 1992; Meier et al., 1987). The most radiotoxic of the natural radionuclides is Ra, since it is an alpha emitter with a relatively long half-life and with dynamics similar to calcium, an element essential to living beings and with which it competes. This is the reason that studies aimed at quantifying soil radium levels and transfer to different types of plant usually take Ra as reference. Examples may be seen in work on transfer to crops (Vasconcellos & Mishra, 1987; Sam & Eriksson, 1995; Cooper et al., 1995), to foodstuffs (Ramachandran & Mishra, 1989), to cabbage (Bettencourt et al, 1988), edible and wild plants (Markose et al., 1993), spinach, chinese cabbage, and polished rice (Yunoki et al., 1993), grasses and sagebrush (Shawki & Whicker, 1988; Ibrahim & Whicker, 1992). Despite the above, the half-life of Ra, 5.76 years, is long enough for it to persist for some years in living beings after assimilation. Work based on this isotope has focused, for example, on dating vegetation samples (Kobashi & Tominaga, 1985) or on the assimilation, distribution and deposition of radium in tree rings (Haas et al., 1995). It has been observed a number of times that the Ra/Ra ratio in long-lived plants is not the same as in the soil in which they are growing, finding that, with the usual definitions for the transfer coefficient, the plant has a greater transfer coefficient for Ra than for Ra (Haas et al., 1995; Paniagua, 1991). If this were really so, the plant would be discriminating positively in favour of Ra over Ra, which would contradict the common chemistry that two isotopes of the same chemical element should have. In attempting to explain this apparent discrimination in favour of Ra, we have made use of compartmental models. These offer an analytical perspective which is more elaborate than the simple calculation of the transfer coefficients, and provides a fuller description of radionuclide dynamics in the systems analyzed. Particularly noteworthy in this sense are the models developed by Schimmack and Bunzl (1992) and by Schell and Myttenaere (1996) to obtain radioisotope residence half-lives in different plant and soil compartments, and that of Acosta et al. (1995) to detect key processes in radionuclide transfer, amongst others. We here present the results of the analysis of Ra and Ra activities in scrub vegetation in two studies. In the extensive study we studied plants belonging to the species ¸avandula stoechas, Cistus ladanifer and Cytisus multiflorus, analyzing the aerial parts together with the total soil fraction. In the intensive study, we took one of the aforementioned species, Cistus ladanifer, and subdivided it for analysis into different compartments, as well as considering separately the total, available, and non-available soil fractions at different depths. Applying a compartmental model to this last study allowed us to (i) explain the apparent discrimination the plant makes in favour of Ra over Ra, (ii) obtain the radium residence half-lives in the different fractions considered so as to better characterize the absorption and translocation of radium in this type of plant, (iii) estimate the age of the plants, and (iv) predict by simulation the temporal evolution of the radioactive concentrations in the compartments under consideration.

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2. Experimental The extensive study was performed in the province of Ca´ceres (Spain) which is 20 000 km in area. We sampled simultaneously soil and scrubland vegetation at the same sampling points distributed as evenly as possible over the entire study area. The plant species whose aerial parts were sampled for analysis were: ¸avandula stoechas, Cistus ladanifer and Cytisus multiflorus, all characteristic of the Mediterranean scrubland ecosystem. The soil samples were taken from the surface layer (0—3 cm) and in some cases at different depths (0—3, 3—6, 6—9, 9—14, and 14—19 cm layers). The intensive study was centred around the vicinity of the Almaraz nuclear power plant (39° 50 N, 5° 41 W), in the province of Ca´ceres (Spain), and on the species Cistus ladanifer, with five three-monthly sample collections between May 1994 and 1995, inclusive. For each collection, a 4 m area was selected, and we took samples as follows: (a) Plants: fruits, young leaves, old leaves, root#shoot, and litterfall. (b) Soils, from layers corresponding to the depths 0—3, 3—6, 6—9, 9—14, and 14—19 cm. After collection, the biological samples were reduced in volume first by drying at 100°C and followed by calcining at 400°C for 24 h. For the total fraction soil samples, foreign bodies were eliminated, and then the samples were dried at 90°C for 24 h and sifted through a 2 mm mesh sieve. The available fraction soil samples underwent the same process except for the drying stage. Then the available fraction was determined by leaching with ammonium acetate aq. 1 N at pH 7 (Jackson, 1982), followed by filtration and evaporation to adapt the residue to the measurement geometries. The treated samples were put into Petri dishes (dia. "9 cm, h"2.5 cm) and Marinelli beakers (V"1 l) and sealed hermetically. They were then left for 25 days to assure secular equilibrium between Ra, Ra and their gamma emitting descendents, in order to determine the activity of the former from Pb and Bi, and of the latter from Ac. Activities were measured with a germanium detector (25.6% efficiency and 1.85 keV FWHM at 1332 keV) coupled to a multichannel analyzer. Specific activities systematically determined at a 95% level of confidence and detection limits were calculated using an updated PC version of the ESPEC code (Baeza et al., 1992).

3. Results and discussion 3.1. Transfer and discrimination factors We analyzed a total of 18 scrub samples in the first phase of the study, belonging to the species ¸avandula stoechas, Cytisus multiflorus and Cistus ladanifer. Table 1 lists statistical data concerning the specific activities and the soil—plant transfer factors (Bq kg\ d.w. plant)/(Bq kg\ d.w. soil) for the radionuclides Ra and Ra in the three species. The results show ¸avandula stoechas to possess Ra activities an order of magnitude greater than the other two. The values of Ra were also higher, but less so than for Ra. The specific activities alone do not indicate that ¸avandula stoechas necessarily takes up more radium than plants of the other two species. The radioactive

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Table 1 Activity (Bq kg\ d.w.), transfer factor TF (Bq kg\ d.w. plant)/(Bq kg\ d.w. soil), and Ra/Ra discrimination factor DF for three scrub species Activity

TF (;10\)

DF

Ra

Ra

Ra

Ra

3.7 5.6 15.9 31.9 97.0 26.8 118

2.4 4.3 6.6 10.5 18.3 7.6 59.6

11.8 18.5 23.3 44.0 80.3 31.5 69.0

7.2 10.0 13.9 17.4 42.3 16.1 60.8

0.85 1.1 1.9 2.5 5.2 2.2 64.1

Cytisus multiflorus Size"5 Min M Max A CV(%)

0.2 2.1 4.3 2.0 78.9

0.4 1.1 2.3 1.2 59.1

0.78 3.2 7.4 3.6 67.3

1.1 3.8 5.7 3.4 60.3

0.69 0.83 2.1 1.1 53.3

Cistus ladanifer Size"4 Min M Max A CV(%)

1.8 2.0 2.6 2.1 16.5

2.2 2.5 2.8 2.5 11.1

4.9 7.9 12.1 8.2 38.7

4.7 7.8 10.8 7.8 32.5

0.85 0.95 1.5 1.1 28.3

¸avandula stoechas Size"11 Min LQ M UQ Max A CV(%)

Min"minimum; LQ"Lower quartile; M"median; UQ"upper quartile; Max"maximum; A"average; CV"coefficient of variation.

levels in a plant are determined by, amongst other factors, those existing in the soil. Hence, a first estimate of the different uptake rates is given by the soil-plant transfer factor obtained as the ratio between the radionuclide’s activity in the plant and in the soil, both expressed in Bq kg\ d.w. An observation of the values obtained for ¸avandula stoechas shows that the range of variation of the Ra factors is from 11.8;10\ to 80.3;10\, with the median being 23.3;10\. For Cytisus multiflorus, the values vary between 0.78;10\ and 7.4;10\, median 3.2;10\, and for Cistus ladanifer the range was 4.9;10\ to 12.1;10\, median 7.9;10\. The soil—plant transfer factor for ¸avandula stoechas is, again, an order of magnitude greater than that corresponding to Cytisus multiflorus, and three times greater than for Cistus ladanifer. The Ra transfer factor is also greater for ¸avandula stoechas than for the other two species, but the differences are smaller.

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Considering all the samples together, Ra presents soil—plant transfer factors in the range 0.78;10\ to 80.3;10\, which is in agreement in order of magnitude with the results of other workers analyzing similar vegetation. Specifically, Ibrahim and Whicker (1992) and Markose et al. (1993), obtain transfer coefficients for bushes in the range 0.1;10\ to 43;10\, and for edible vegetables Vasconcellos et al. (1987) and Bettencourt et al. (1988) obtain values in the range 0.02;10\ to 50;10\. The Ra soil—plant transfer factor, considering all the samples together, ranges from 1.14;10\ to 42.3;10\, which is greater than, for instance, the value of around 0.4;10\ found in tree rings of spruce (Haas et al., 1995). A feature that stands out in the results is that a great many of the samples presented a Ra soil—plant transfer factor greater than for Ra. These cases could be wrongly interpreted initially on the basis of preferential uptake of Ra as against Ra. One might well draw this conclusion on the basis of an observation of the values listed in the last column of Table 1. These are some of the statistical data of the Ra/Ra discrimination factors for the three plant species considered, which were calculated dividing the Ra transfer factor TF (Ra) by the corresponding Ra value TF (Ra). For ¸avandula stoechas, the discrimination factors vary between 0.85 and 5.2, with median 1.9. Consequently, most of the values are above unity, specifically 50% are above 1.9, so that one may deduce that there seems to be a greater uptake of Ra than of Ra in these plants. In the case of Cytisus multiflorus, the values of the discrimination factor vary between 0.69 and 2.1, median 0.83, and for the case of Cistus ladanifer between 0.85 and 1.5, median 0.95. In these last two cases, the values of the discrimination coefficients are distributed more closely around unity, although some of them lie significantly above this value. Fig. 1 shows a frequency histogram of the Ra/Ra discrimination factors considering all the samples together. One observes that aproximately a third of the values are above the value 2.0. The fact that there are values which are significantly greater than unity in the discrimination factors seems to reaffirm that the plant may be

Fig. 1. Relative frequency histogram of the Ra/Ra discrimination factors considering all the scrub samples analyzed in the extensive study together.

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assimilating Ra preferentially over Ra, which is not very logical as they are isotopes of the same chemical element. A possible cause of this apparent contradiction could be that we are comparing the activity existing in the plant with the activity of the radionuclides considered in the total soil fraction. This form of calculating the soil—plant transfer may be in part unsuitable, since not all of a chemical element present in the soil is available for uptake by the plant. It would therefore be more correct to refer the activities of the radionuclides in the plants to the fraction of the same which are available in the soil. To test whether this aspect is the cause of the existence of discrimination factors greater than unity, we chose two soils for which the corresponding plants possessed discrimination factors above unity, and extracted the available fraction from them as described in the experimental section. The values of the Ra and Ra concentrations in the total and available fractions of the two soil samples are listed in Table 2, together with the discrimination factors in the corresponding plant samples. In soil sample I, the percentages of Ra and Ra in the available fraction are 0.6 and 1.4, and in soil sample II, 2.3 and 13.7, respectively. In both cases there is a greater relative availability of Ra. We also used the t-test to compare the mean values for these two types of soil, obtaing significant differences (p(0.001) between the discrimination factors calculated first with respect to the available fraction and then with respect to the total fraction. One can therefore state that in the two plants sampled in these soils, despite the major relative errors in the quantification of the discrimination factors, these are even farther from unity when the activity present in only the available fraction is considered rather than in its totality. 3.2. Compartmental model: residence half-lives Applying a compartmental model to a system consists in dividing the system into N interconnected compartments. In a linear model, the rate of variation of the parameter of interest in each compartment is a linear function of the value of the parameter of that compartment and of those with which it is related. In setting up

Table 2 Ra/Ra discrimination factors taking the total and available soil fractions as reference, DF (T) and DF(A), respectively Soil I

Total soil (Bq kg\ d.w.) Available soil (%) Plant ¸avandula stoechas

Soil II

Ra

Ra

Ra

Ra

88 $6

104$4

30 $4

0.6$0.4

1.4 $0.3

2.3$0.4

13.7$1.2

DF(T) 2.5$0.4

DF(A) 6 $5

DF(T) 1.0$0.4

DF(A) 6 $4

35 $2

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a compartmental model it is essential to define the compartments of which it consists and the relationships between them. We show in Fig. 2 a conceptual representation of the model used, with the compartments corresponding to the fractions sampled, and the main interrelationships taken into account for the case of radium. An experimental study to obtain the data required for the implementation of the model was carried out in the vicinity of the Almaraz Nuclear Power Plant in Ca´ceres (Spain), on the most abundant woody plant species in the zone, the Cistus ladanifer, of which we possessed the information concerning its radium absorbing behaviour that was reflected in the previous section. The analysis of the three-monthly samples showed that the radioactive concentrations in the different plant compartments and in

Fig. 2. Conceptual model with the compartments and processes taken into account for the study of the dynamics of radium in the soil-plant system. The compartments for which information is presented in Table 3 are drawn with fine lines. The compartments considered in the model are drawn with bold lines.

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Table 3 Mean annual activity levels (A) of Ra and of Ra (in BqmU) and Ra/Ra discrimination factor (DF) for the following three-monthly sampled compartments: NAS" non-available soil; AS" available soil; RS" root # shoot; YL" young leaf; OL " old leaf; F " fruit; FF " leaf and fruit litter (SE: standard error) Ra

NAS AS RS YL OL F FF

Ra

DF (Ra/Ra)

A

SE

A

SE

DF

SE

8000 290 2.5 0.25 0.34 0.036 2.1

500 25 0.8 0.10 0.11 0.015 0.7

16600 950 3.7 0.32 0.35 0.058 3.3

500 40 1.0 0.09 0.10 0.016 1.5

2.2 2.6 3.2 3.7 2.1

0.9 1.3 1.4 2.4 1.2

the soil presented seasonal oscillations at least partly associated with the characteristics of the Mediterranean climate (Baeza et al., 1996). Table 3 lists, for each of the compartments sampled, the mean values of the measured activity levels (expressed in Bq m\ on multiplying the mass collected in each fraction per m by its specific activity), together with the corresponding value of the standard deviation. For the soil, we sampled the layer formed by the first 19 cm of depth, since we have found that this is a good estimate of the depth to which the roots of these plants are normally developed. As Ra and Ra belong to radioactive decay series, they are continually being produced from their precursors in the series as well as continually disappearing by radioactive decay. The secular equilibrium that exists in the total soil fraction in each series is broken in the available soil fractions and in the different plant fractions (Baeza et al., 1996). Specifically, it can be seen in Table 3 that the percentage of Ra concentration in the available soil fraction was 3.6%, while for Ra it was 5.4%. Although in this fraction the Ra activity is less than that of Ra (about one-third), in the different fractions of the plant these activities are very similar. This fact leads to the discrimination factors, obtained from transfer coefficients referred to the available soil fraction, being greater than unity in all the plant fractions. In this particular case, the factors were 2.2 for the root#shoot, 2.8 for the aerial part (which includes fruit, young leaves, and old leaves), and 2.1 for the litterfall. Since both radium isotopes come from the decay of a thorium isotope (Th in the case of Ra and Th in the case of Ra) and the presence of thorium isotopes is very small both in the plant and in the available soil fraction (Baeza et al., 1996), we consider that the production of radium isotopes from thorium isotopes is negligible in all the plant fractions studied, as well as in the available soil fraction (Kobashi & Tominaga, 1985). This process will not therefore be included in the model. We will, however, take into account the radioactive decay in the plant compartments, and assume also that the adsorption and desorption mechanisms between the available and non-available soil fractions

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together with the processes of production and decay maintain the concentrations of these two radium isotopes constant in time in both soil fractions. We did not take into account the deposition of radium from the atmosphere (where it exists due to resuspension) which will affect the aerial part of the plant and the available soil fraction, but in any case its concentration is very small compared to that in the soil. We grouped the compartments fruit, young leaves, and old leaves into a single compartment denominated aerial part, since not all of them exist simultaneously in each of the samples collected. The system of first-order differential equations that describes the dynamics of intercompartmental radionuclide transfer represented in Fig. 2 is dA G"! j A # j A !j A , (1) GH GH HG H  G dt H H where A is the total radionuclide activity accumulated in the compartment i distribG uted over an area of 1 m; j is the rate constant for the transfer from the jth to the ith HG compartment (time\); j is the rate constant for the transfer from the ith compartGH ment to the jth compartment (time\) and j the radionuclide decay rate (time\).  The main problem in resolving the equations that govern the model lies in the precise estimation of the transfer rates j . The only relevant information that we have GH is in the values of the radioactive concentrations in the different compartments involved in the model, at two particular times. Firstly, there is the year during which the three-monthy sampling frequency yielded the mean activity levels given in Table 3, for which we shall assume that, given the longevity of this plant species (Cistus ladanifer), the mean annual levels of activity in each of the compartments that we finally considered were in a quasi-stationary state, and therefore practically did not vary with time. And secondly, there is the initial moment of the plant’s growth, for which we assume that the total radium isotope activity is zero or practically negligible relative to that incorporated in the previously mentioned sampling time. With the simplifications that we took to facilitate the solution of a model to explain the dynamics of the radium isotopes, in the following this model consists exclusively of the compartments drawn in bold lines in Fig. 2. With these considerations, the system of Eq. (1) is converted into: dA  " ! j A # j A !j A ,       dt

(2a)

dA "!j A #j A !j A ,       dt

(2b)

dA "!j A #j A !j A ,       dt

(2c)

dA "!j A #j A !j A , (2d)       dt where A , A , A , and A are the activities in the compartments: available soil fraction,     root#shoot, aerial part, and litterfall, respectively.

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Converting the system of Eqs. (2) into the incremental form and using the data of Table 3 for Ra, we obtain a set of values of j which characterizes the radioactive GH concentrations in the plant on the sampling date. This set of values, however, is not unique, since if we multiply or divide them all by the same factor, we likewise arrive at the situation described in Table 3, although varying the speed of convergence to those values. The optimum set of values was determined by performing simulations with the system of differential equations (2) (using a fourth-order Runge—Kutta method) using the activity levels corresponding to Ra and the coefficients k obtained for Ra GH (since we assume that the behaviour of the two isotopes is the same within the plant). The set of values which best reproduces the Ra/Ra disequilibrium is presented in Table 4, together with the residence half-lives of radium in each compartment obtained from the equation ¹ "ln(2)/j . The associated standard errors were GH GH obtained from the standard errors of the activities of the compartments involved in the determination of each parameter. One observes in Table 4 that the residence half-life of radium in the available soil fraction with relation to uptake by the roots of these plants is 800 years, that of the trunk-root before passing to the aerial part is 6.8 years, that of the aerial part before passing to the litterfall 1.7 years, and that of the litterfall in decomposing is 5.8 years. Given the scarcity of data of this type in the literature, it is difficult to find values of radium residence half-lives for this type of system. Nevertheless, we consider it interesting to compare the orders of magnitude obtained with those corresponding to other radionuclides. Thus, in a work on the distribution of radionuclides in forests, Schell et al. (1996) review the values of residence half-lives of various radionuclides in different ecosystems. By way of example, Sr, a chemical analogue of radium, has half-lives of 0.69 and 1.03 years in trees of deciduous and coniferous ecosystem, respectively (Alekskhin et al., 1976). The half-life obtained in an agricultural ecosystem type is 17.7 years (Thorne et al., 1983). With respect to the organic fraction, in lichen and moss Tuominen and Jaakkola (1973) obtained values of Sr half-lives in the range of 2.1—11 years, while the data for this radionuclide in the litter fraction lie between 2.5 and 53 years in deciduous forest and between 8.0 and 61.5 years in coniferous forest (Alekskhin et al., 1976). The decomposition of the litter fraction varies with climate. Thus, for example, in tropical forests it disappears completely in six months, while in temperate woodlands the time is 3.5 years (Schell et al., 1989), and

Table 4 Lambda coefficients and residence half-lives of radium in the different plant compartments analyzed: AS, Available soil; RS, Root#shoot; AP, aerial part; FF, fallen fruits and leaves (litter) (SE, standard error) Compartment

k(years)\

SE(years)\

T(years)

SE(years)

AS -' RS RS -' AP AP -' FF FF -' AS

8.9 1.0 4.1 1.2

2.4 0.4 2.2 1.2

800 6.8 1.7 5.8

200 2.6 0.9 2.6

10\ 10\ 10\ 10\

10\ 10\ 10\ 10\

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in cool temperate and boreal sites the breakdown can take more than ten years (Pachman & Hasding, 1982). Knowing values for the j coefficients, we now have a set of differential equations, GH and hence the behaviour of the system under study, which is completely determined. Hence, we can perform simulations in which we obtain the temporal evolution of the activities in the different compartments of the system. We show in Fig. 3 simulations of the evolution of the activity of Ra (Fig. 3a), of Ra (Fig. 3b), and of the Ra/Ra discrimination factor (Fig. 3c) in the plant compartments during 50 years of the life of Cistus ladanifer. In these figures we have assumed that the initial concentration of the available soil fraction is that given in Table 3, and that in the plant compartments the initial activity is zero. In the figures corresponding to the temporal evolution of the Ra and Ra activities, one observes a similar behaviour, with an increase of the concentration with time in the different fractions, until the activities reach their stationary values asymptotically. For Ra, however, the difference in activity between the trunk-root fraction and those of the aerial part and the litterfall (especially the latter) is greater than for Ra. This difference is due to these compartments being the last reached by the radium isotopes, and therefore a greater proportion of Ra would have disappeared by decay than in the trunk-root compartment. With relation to the discrimination factor (Fig. 3c), one observes an increase with time in the three compartments, although this increase is greater in the litter fraction for the reason mentioned above. The discrimination factors rise with time, approaching the values of Table 3 for the trunk-root and aerial part fraction for a value of the time of approximately 25 years, which gives us an estimate of the age of the plants sampled. The litter fraction possesses, for this value of t, a discrimination factor of 4.3, which is greater than that given in Table 3. The origin of this difference between the experimental data and those predicted by the simulation is, in all probability, the permanent contact of this fraction with the soil. The surface contamination by particles of the soil, which have a Ra/Ra ratio of the order of 0.5, would lead to the experimental ratio being smaller.

4. Conclusions We have analyzed the Ra and Ra concentrations in scrub-type vegetation and in the soil substrate. The total soil fraction transfer factors (Bq kg\ d.w. plant)/(Bq kg\ d.w. soil) took values between 0.78 10\ and 80.3 10\ for Ra, and between 4.7;10\ and 42.3;10\ for Ra. The Ra/Ra discrimination factors, with all the samples taken together, were between 0.69 and 5.2, with more than 60% being significantly greater than unity. This was not due to considering in the calculations the activity present in the total or available soil fractions. The application of a linear compartmental model to the soil—plant system allowed us to: explain the above-unity discrimination coefficients on the basis of the decay of Ra in the compartments of the plant; to obtain the residence half-lives of radium in the different compartments (800 years in the available soil fraction, 6.8 years in the

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Fig. 3. Temporal evolution of the activities of the fractions: root#shoot (RS), aerial part (AP), and litterfall (FF), expressed as Bq m\, for (a) Ra and (b) Ra. The temporal evolution of the Ra/Ra discrimination factor is shown in (c).

root-shoot, 1.7 years in the aerial part, and 5.8 years in the litterfall); to estimate the age of the plants sampled as around 25 years; and to simulate the temporal evolution of the radioactive concentrations in the different compartments for any time in the growth of this type of plant.

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Acknowledgements This work has been partially financed by the Consejo de Seguridad Nuclear and the Secretarı´ a de Estado para las Polı´ ticas del Agua y del Medio Ambiente under the Specific Agreement: Transferencia de Radionuclidos en Ecosistemas Mediterraneos.

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