Variation among chlorine concentration ratios for native and agronomic plants

Variation among plant/soil concentration ratios (CRs) for important radionuclides requires attention because it is a major source of uncertainty in nuclear environmental safety assessments. For agronomic plants, variation among plant species is easy to deal with because there are relatively few species. In natural settings, there are vastly more species and the question becomes how to develop representative statistical distributions of CRs. Chlorine (Cl) is a good element with which to address this problem, because ³⁶Cl is a key radionuclide in nuclear waste disposal and yet stable Cl is easily measured in the environment. We measured CRs (dry weight basis) for Cl among edible parts of agronomic plants at one site, and found a geometric mean (GM) of 10, a geometric standard deviation (GSD) of 1.9 and a range of 5–66. When the GM was weighted by the relative contributions of the various plants to the human diet, it rose to 16. Among native plants at five sites, each site representative of a specific environment, the GMs were 4.0–13 and the GSDs were 2.9–6.2. The CRs for individual species ranged from 0.8 to 170. However, when weighted by relative contributions of the plants to selected animal diets, the GMs were as high as 50. The conclusions are that: the variation in CR for agronomic plants is a subset of the variation among native or all plants, variation among species (the GSD) can be sixfold, and variation among species is large enough that typical diets of specific animals could expose them to several-fold higher amounts of Cl (or ³⁶Cl) than expected from generic CR values.     

Assessment of Po and Pb in marine biota of the Mallipattinam ecosystem of Tamil Nadu, India

To provide baseline data on background radiation levels for the future assessment of the impact of nuclear and thermal power stations, a systematic study was carried out in the Mallipattinam ecosystem of Tamil Nadu, India. Mallipattinam is located between the Kudankulam and Kalpakkam nuclear power plants and near to Tuticorin thermal power plant. Water, sediments, seaweeds, crustaceans, molluscs, and fish were collected to measure the concentrations of ²¹⁰Po and ²¹⁰Pb. The concentrations of ²¹⁰Po and ²¹⁰Pb in most samples are comparable to values reported worldwide. In fish, the concentrations of ²¹⁰Po and ²¹⁰Pb are in the range 16-190 Bq kg⁻¹ and 8-153 Bq kg⁻¹, respectively. The concentration factors of ²¹⁰Po and ²¹⁰Pb for the biotic components ranges from 10³ to 10⁶.     

Uptake of 226Ra and 210Pb by food crops cultivated in a region of high natural radioactivity in Brazil

The Poços de Caldas Plateau is a deeply weathered alkaline igneous intrusion of about 35 km diameter, in which several radioactive anomalies exist. The first Brazilian uranium mine and mill are located in this region. A study is in progress to assess the edible vegetable uptake of the most abundant natural radionuclides in the local environment and this paper reports the results for ²²⁶Ra and ²¹⁰Pb. In farm soils, both nuclides have similar concentrations. The minimum values are comparable to those found in areas of normal radioactivity but the maximum concentrations are ten-fold higher. ‘Exchangeable’ radium in soils ranges from 2·3% to 34·5% of the total. No statistical correlation was found between the ‘exchangeable’ ²²⁶Ra and several physico-chemical soil parameters. In the vegetables analyzed, ²²⁶Ra concentrations are slightly higher than those of ²¹⁰Pb and the maximum values are also one order of magnitude greater than in normal regions. For both radionuclides, the average soil-to-plant concentration factors are of the order of 10⁻³ and 10⁻², when related to total and to ‘exchangeable’ contents in soils, respectively. For each vegetable, no statistical correlation was observed between the ²²⁶Ra or ²¹⁰Pb concentrations in the plant (fresh weight) and concentrations in the soil, either total or ‘exchangeable’. The ‘exchangeable’ Ca in soils does not seem to influence radium uptake by plants in a defined way.     

Cs uptake by four plant species and Cs-K relations in the soil-plant system as affected by Ca(OH)2 application to an acid soil

Three rates of Ca(OH)₂ were applied to an acid soil and the ¹³⁴Cs uptake by radish, cucumber, soybean and sunflower plants was studied. The ¹³⁴Cs concentration in all plant species was reduced from 1.6-fold in the sunflower seeds to 6-fold in the soybean vegetative parts at the higher Ca(OH)₂ rate. Potassium (K) concentration in plants was also reduced, but less effectively. The significantly decreased ¹³⁴Cs-K soil to plant distribution factors (D.F.) clearly suggest a stronger effect of soil liming on ¹³⁴Cs than on K plant uptake. This observation was discussed in terms of ionic interactions in the soil matrix and within the plants. The results also indicated that the increased Ca²⁺ concentration in the exchange phase and in the soil solution along with the improved root activity, due to the soil liming, enhanced the immobilization of ¹³⁴Cs in the soil matrix and consequently lowered the ¹³⁴Cs availability for plant uptake.     

Diffusive gradient in thin FILMS (DGT) compared with soil solution and labile uranium fraction for predicting uranium bioavailability to ryegrass

The usefulness of uranium concentration in soil solution or recovered by selective extraction as unequivocal bioavailability indices for uranium uptake by plants is still unclear. The aim of the present study was to test if the uranium concentration measured by the diffusive gradient in thin films (DGT) technique is a relevant substitute for plant uranium availability in comparison to uranium concentration in the soil solution or uranium recovered by ammonium acetate. Ryegrass (Lolium perenne L. var. Melvina) is grown in greenhouse on a range of uranium spiked soils. The DGT-recovered uranium concentration (C_DGT) was correlated with uranium concentration in the soil solution or with uranium recovered by ammonium acetate extraction. Plant uptake was better predicted by the summed soil solution concentrations of UO₂²⁺, uranyl carbonate complexes and UO₂PO₄⁻. The DGT technique did not provide significant advantages over conventional methods to predict uranium uptake by plants.     

Simulation of biological uptake of uranium and radium in an industrially polluted area

Distribution of ²³⁸U and ²²⁶Ra in soils and plants of an industrially polluted area are considered. The dependence between the biological uptake coefficients (BUCs) for the plant species studied and the radionuclide concentrations in soil can be approximated by a decreasing power function. Species differences in radionuclide uptake are demonstrated.     

The Kinetics of Caesium absorption by roots of winter wheat and the possible consequences for the derivation of soil-to-plant transfer factors for radiocaesium

Caesium (Cs) uptake in roots of winter wheat was found to follow a dual pattern similar to that established for potassium uptake in barley roots. This suggests the operation of two discrete uptake systems for Cs, as for potassium. The ‘System 1’ (low concentration) uptake mechanism for caesium, however, can be resolved into two hyperbolic components which both obey Michaelis-Menten kinetics. The Michaelis-Menten equation was used to derive a function which describes the variation in solution-to-root transfer factor for any element for which the appropriate root uptake constants (K_m andV_max) can be determined. This function successfully described available data for root uptake of caesium and potassium, predicting that the solution-to-root transfer factor decreases in relation to an increase in the substrate concentration of each respective element. At substrate concentrations equivalent to carrier-free radiocaesium concentrations, however, the solution-to-root transfer factor predicted by the function and by empirical data suggests that the relationship between root uptake and solution concentration of caesium is linear. These findings are discussed in relation to the comparative physiology of caesium and potassium uptake by plant roots and with respect to the application of the soil-to-plant transfer factor concept to radioecological studies.     

Plant/soil concentration ratios for paired field and garden crops, with emphasis on iodine and the role of soil adhesion

In the effort to predict the risks associated with contaminated soils, considerable reliance is placed on plant/soil concentration ratio (CR) values measured at sites other than the contaminated site. This inevitably results in the need to extrapolate among the many soil and plant types. There are few studies that compare CR among plant types that encompass both field and garden crops. Here, CRs for 40 elements were measured for 25 crops from farm and garden sites chosen so the grain crops were in close proximity to the gardens. Special emphasis was placed on iodine (I) because data for this element are sparse. For many elements, there were consistent trends among CRs for the various crop types, with leafy crops > root crops ≥ fruit crops ≈ seed crops. Exceptions included CR values for As, K, Se and Zn which were highest in the seed crops. The correlation of CRs from one plant type to another was evident only when there was a wide range in soil concentrations. In comparing CRs between crop types, it became apparent that the relationships differed for the rare earth elements (REE), which also had very low CR values. The CRs for root and leafy crops of REE converged to a minimum value. This was attributed to soil adhesion, despite the samples being washed, and the average soil adhesion for root crops was 500 mg soil kg⁻¹ dry plant and for leafy crops was 5 g kg⁻¹. Across elements, the log CR was negatively correlated with log Kd (the soil solid/liquid partition coefficient), as expected. Although, this correlation is expected, measures of correlation coefficients suitable for stochastic risk assessment are not frequently reported. The results suggest that r ≈ −0.7 would be appropriate for risk assessment.     

Transfer factors of Polonium from soil to parsley and mint

Transfer factors of ²¹⁰Po from soil to parsley and mint have been determined. Artificial polonium isotope (²⁰⁸Po) was used as a tracer to determine transfer factor of Po from soil to plant in pot experiments. Two plant growing systems were used for this study namely, an outdoor system and a sheltered system by a polyethylene tent. ²⁰⁸Po and ²¹⁰Po were determined in soil and different parts of the studied plants (stem and leaf), using alpha spectroscopy. The results have shown that there was a clear uptake of ²⁰⁸Po by roots to leaves and stems of both plants. Higher values of transfer factors using the ²¹⁰Po activity concentrations than the ²⁰⁸Po activity concentration were observed. Transfer factors of ²¹⁰Po from soil to parsley varied between 20 × 10⁻² and 50 × 10⁻² and 22 × 10⁻³ and 67 × 10⁻³ in mint, while ²⁰⁸Po transfer factors varied between 4 × 10⁻² and 12 × 10⁻² for parsley and 10 × 10⁻² and 22 × 10⁻² in mint. Transfer factors of Po were higher in those plants grown in the sheltered system than in the open system; about 75% of Po was transferred from atmosphere to parsley parts using the two systems. Ratios of transferred Po from soil to mint stem and leaf in the sheltered system were higher by 2 times from those in the open system.     

Polonium-210 and lead-210 in the terrestrial environment: a historical review

The radionuclides ²¹⁰Po and ²¹⁰Pb widely present in the terrestrial environment are the final long-lived radionuclides in the decay of ²³⁸U in the earth’s crust. Their presence in the atmosphere is due to the decay of ²²²Rn diffusing from the ground. The range of activity concentrations in ground level air for ²¹⁰Po is 0.03-0.3 Bq m⁻³ and for ²¹⁰Pb 0.2-1.5 Bq m⁻³.In drinking water from private wells the activity concentration of ²¹⁰Po is in the order of 7-48 mBq l⁻¹ and for ²¹⁰Pb around 11-40 mBq l⁻¹. From water works, however, the activity concentration for both ²¹⁰Po and ²¹⁰Pb is only in the order of 3 mBq l⁻¹.Mosses, lichens and peat have a high efficiency in capturing ²¹⁰Po and ²¹⁰Pb from atmospheric fallout and exhibit an inventory of both ²¹⁰Po and ²¹⁰Pb in the order of 0.5-5 kBq m⁻² in mosses and in lichens around 0.6 kBq m⁻². The activity concentrations in lichens lies around 250 Bq kg⁻¹, dry mass.Reindeer and caribou graze lichen which results in an activity concentration of ²¹⁰Po and ²¹⁰Pb of about 1-15 Bq kg⁻¹ in meat from these animals. The food chain lichen-reindeer or caribou, and Man constitutes a unique model for studying the uptake and retention of ²¹⁰Po and ²¹⁰Pb in humans. The effective annual dose due to ²¹⁰Po and ²¹⁰Pb in people with high consumption of reindeer/caribou meat is estimated to be around 260 and 132 μSv a⁻¹ respectively.In soils, ²¹⁰Po is adsorbed to clay and organic colloids and the activity concentration varies with soil type and also correlates with the amount of atmospheric precipitation. The average activity concentration levels of ²¹⁰Po in various soils are in the range of 20-240 Bq kg⁻¹.Plants become contaminated with radioactive nuclides both by absorption from the soil (supported Po) and by deposition of radioactive fallout on the plants directly (unsupported Po). In fresh leafy plants the level of ²¹⁰Po is particularly high as the result of the direct deposition of ²²²Rn daughters from atmospheric deposition. Tobacco is a terrestrial product with high activity concentrations of ²¹⁰Po and ²¹⁰Pb. The overall average activity concentration of ²¹⁰Po is 13 ± 2 Bq kg⁻¹. It is rather constant over time and by geographical origin.The average median daily dietary intakes of ²¹⁰Po and ²¹⁰Pb for the adult world population was estimated to 160 mBq day⁻¹ and 110 mBq day⁻¹, corresponding to annual effective doses of 70 μSv a⁻¹ and 28 μSv a⁻¹, respectively. The dietary intakes of ²¹⁰Po and ²¹⁰Pb from vegetarian food was estimated to only 70 mBq day⁻¹ and 40 mBq day⁻¹ corresponding to annual effective doses of 30.6 μSv a⁻¹ and 10 μSv a⁻¹, respectively. Since the activity concentration of ²¹⁰Po and ²¹⁰Pb in seafood is significantly higher than in vegetarian food the effective dose to populations consuming a lot of seafood might be 5-15 fold higher.     

Study of soil-plant transfer of 226Ra under greenhouse conditions

A soil-plant transfer study was performed using soil from a former uranium ore processing factory in South Bohemia. We present the results from greenhouse experiments which include estimates of the time required for phytoremediation. The accumulation of ²²⁶Ra by different plant species from a mixture of garden soil and contaminated substrate was extremely variable, ranging from 0.03 to 2.20 Bq ²²⁶Ra/g DW. We found differences in accumulation of ²²⁶Ra between plants from the same genus and between cultivars of the same plant species. The results of ²²⁶Ra accumulation showed a linear relation between concentration of ²²⁶Ra in plants and concentration of ²²⁶Ra in soil mixtures. On the basis of these results we estimated the time required for phytoremediation, but this appears to be too long for practical purposes.     

Dynamic model for radionuclide uptake in lichen

Samples of atmospheric particulate material and terrestrial plants, including lichens, were collected in New Brunswick, Canada between 1980 and 1983 and analyzed for a wide range of artificial and naturally-occuring radionuclides, including fission products (¹⁴¹Ce, ¹⁴⁴Ce, ¹⁰³Ru, ¹⁰⁶Ru, ⁹⁵Zr and ¹³⁷Cs) derived from the 16 October 1980 Chinese nuclear test. Activity ratios of some of the short-lived fission products in air particulates and lichens are in reasonable agreement with those predicted from fission product yields for nuclear weapons tests, indicating that only minor fractionation occurred for these radionuclides during their transport through air particulate and lichen environmental phases. The ⁷Be inventories measured in a suite of lichen (Cladonia rangiferina) samples were used to calibrate each lichen plant for its collection efficiency for atmospheric particulates and fallout radioactivity.A lichen model has been developed to predict lichen inventories of radioactivity for different lichen growth functions and bio-elimination rates. Assuming that lichen growth results in a linear increase in surface area with time, the experimental results yield biological residence times of 1–2 years for ²¹⁰Pb and Pu and 5–8 years for ¹³⁷Cs. The more efficient retention of ¹³⁷Cs is probably due to its physiological uptake in lichen plants as a proxy for potassium, as evidenced by an observed, inverse relationship between ¹³⁷Cs and ⁴⁰K activities in lichen.     

Trace element and radionuclide mass balances at a coal-fired electric generating station

Coal, bottom ash, and fly ash from Milliken Station, a coal-fired 270 MW power plant, were analyzed for 20 elements (Ag, Al, As, Be, Cd, Co, Cr, Cu, Ga, Hg, Mn, Ni, Pb, Sb, Se, Sn, Te, Tl, V, and Zn) and the major natural radionuclides (²³⁸U series, ²³²Th series, and ⁴⁰K). Mass balance calculations showed that most of the Hg, and some of the Sb and Se, were unaccounted for by ash collection, suggesting their possible discharge into the atmosphere. Silver, As, Hg, Pb, Cd, and Zn were more concentrated in the fly ash than in the bottom ash while all of the other elements were equally distributed, by concentration, between the ash fractions. The radionuclides showed a 46% higher concentration in fly ash than in bottom ash, and ²¹⁰Pb was enriched in the fly ash relative to the other radionuclides by a factor of 2.4. Mass balance calculations indicated a balance within statistical error for the radionuclides, except for ²¹⁰Pb.     

The distribution of Cs, K, Rb and Cs in plants in a Sphagnum-dominated peatland in eastern central Sweden

We record the distribution of ¹³⁷Cs, K, Rb and Cs within individual Sphagnum plants (down to 20 cm depth) as well as ¹³⁷Cs in vascular plants growing on a peatland in eastern central Sweden. In Calluna vulgaris¹³⁷Cs was mainly located within the green parts, whereas Andromeda polifolia, Eriophorum vaginatum and Vaccinium oxycoccos showed higher ¹³⁷Cs activity in roots. Carex rostrata and Menyanthes trifoliata showed variable distribution of ¹³⁷Cs within the plants. The patterns of ¹³⁷Cs activity concentration distribution as well as K, Rb and Cs concentrations within individual Sphagnum plants were rather similar and were usually highest in the capitula and/or in the subapical segments and lowest in the lower dead segments, which suggests continuous relocation of those elements to the actively growing apical part. The ¹³⁷Cs and K showed relatively weak correlations, especially in capitula and living green segments (0-10 cm) of the plant (r = 0.50). The strongest correlations were revealed between ¹³⁷Cs and Rb (r = 0.89), and between ¹³⁷Cs and stable Cs (r = 0.84). This suggests similarities between ¹³⁷Cs and Rb in uptake and relocation within the Sphagnum, but that ¹³⁷Cs differs from K.     

Bioaccumulation of Ra by plants growing in fresh water ecosystem around the uranium industry at Jaduguda, India

A field study has been conducted to evaluate the ²²⁶Ra bioaccumulation among aquatic plants growing in the stream/river adjoining the uranium mining and ore-processing complex at Jaduguda, India. Two types of plant group have been investigated namely free floating algal species submerged into water and plants rooted in stream & riverbed. The highest ²²⁶Ra activity concentration (9850 Bq kg⁻¹) was found in filamentous algae growing in the residual water of tailings pond. The concentration ratios of ²²⁶Ra in filamentous algae (activity concentration of ²²⁶Ra in plant Bq kg⁻¹ fresh weight/activity concentration of ²²⁶Ra in water Bq l⁻¹) widely varied i.e. from 1.1 × 10³ to 8.6 × 10⁴. Other aquatic plants were also showing wide variability in the ²²⁶Ra activity concentration. The ln-transformed filamentous algae ²²⁶Ra activity concentration was significantly correlated with that of ln-transformed water concentration (r = 0.89, p < 0.001). There was no correlation between the activity concentrations of ²²⁶Ra in stream/riverbed rooted plants and the substrate. For this group, correlation between ²²⁶Ra activity concentration and Mn, Fe, Cu concentration in plants were statistically significant.     

Verification of radionuclide transfer factors to domestic-animal food products, using indigenous elements and with emphasis on iodine

Recent reviews have established benchmark values for transfer factors that describe radionuclide transfer from plants to animal food product such as milk, eggs and meat. They also illustrate the paucity of data for some elements and some food products. The present study quantified transfer data using indigenous elements measured in dairy, poultry and other livestock farms in Canada. Up to 62 elements are reported, with particular emphasis on iodine (I) because of the need to accurately assess the behaviour of ¹²⁹I from disposal of nuclear fuel waste. There was remarkable agreement with the literature values, and for many elements the present study involved many more observations than were previously available. Perhaps the most important observation was that product/substrate concentration ratios (CR) were quite consistent across species, whereas the traditional fractional transfer factors (TF, units of d kg⁻¹ or d L⁻¹) necessarily vary with body mass (feed intake). This suggests that for long-term assessments, it may be advisable to change the models to use CR rather than TF.     

Global radioxenon emission inventory based on nuclear power reactor reports

Atmospheric radioactivity is monitored for the verification of the Comprehensive Nuclear-Test-Ban Treaty, with xenon isotopes ^131mXe, ¹³³Xe, ^133mXe and ¹³⁵Xe serving as important indicators of nuclear explosions. The treaty-relevant interpretation of atmospheric concentrations of radioxenon is enhanced by quantifying radioxenon emissions released from civilian facilities. This paper presents the first global radioxenon emission inventory for nuclear power plants, based on North American and European emission reports for the years 1995–2005. Estimations were made for all power plant sites for which emission data were unavailable. According to this inventory, a total of 1.3 PBq of radioxenon isotopes are released by nuclear power plants as continuous or pulsed emissions in a generic year.     

Plutonium isotopes concentration in seawater and bottom sediment off the Pacific coast of Aomori sea area during 1991-2005

A radioactivity survey was launched in 1991 to determine the background levels of ^239+240Pu in the marine environment off a commercial spent nuclear fuel reprocessing plant before full operation of the facility. Particular attention was focused on the ²⁴⁰Pu/²³⁹Pu atom ratio in seawater and bottom sediment to identify the origins of Pu isotopes. The concentration of ^239+240Pu was almost uniform in surface water, decreasing slowly over time. Conversely, the ^239+240Pu concentration varied markedly in the bottom water and was dependent upon the sampling point, with higher concentrations of ^239+240Pu observed in the bottom water sample at sampling points having greater depth. The ²⁴⁰Pu/²³⁹Pu atom ratio in the seawater and sediment samples was higher than that of global fallout Pu, and comparable with the data in the other sea area around Japan which has likely been affected by close-in fallout Pu originating from the Pacific Proving Grounds. The ²⁴⁰Pu/²³⁹Pu atom ratio in bottom sediment samples decreased with sea depth. The land-originated Pu is not considered as the reason of the increasing ^239+240Pu concentration and also decreasing the ²⁴⁰Pu/²³⁹Pu atom ratio with sea depth, and further study is required to clarify it.     

Assessing the fate of radioactive nickel in cultivated soil cores

Parameters regarding fate of ⁶³Ni in the soil–plant system (soil: solution distribution coefficient, K_d and soil plant concentration ratio, CR) are mostly determined in controlled pot experiments or from simple models involving a limited set of soil parameters. However, as migration of pollutants in soil is strongly linked to the water migration, variation of soil structure in the field and seasonal variation of evapotranspiration will affect these two parameters. The aim of this work was to explore to what extent the downward transfer of ⁶³Ni and its uptake by plants from surface-contaminated undisturbed soil cores under cultivation can be explained by isotopic dilution of this radionuclide in the pool of stable Ni of soils. Undisturbed soil cores (50 cm × 50 cm) were sampled from a brown rendzina (Rendzic Leptosol), a colluvial brown soil (Fluvic Cambisol) and an acidic brown soil (Dystric Cambisol) using PVC lysimeter tubes (three lysimeters sampled per soil type). Each core was equipped with a leachate collector. Cores were placed in a greenhouse and maize (DEA, Pioneer^®) was sown. After 44 days, an irrigation was simulated at the core surfaces to supply 10 000 Bq ⁶³NiCl₂. Maize was harvested 135 days after ⁶³Ni input and radioactivity determined in both vegetal and water samples. Effective uptake of ⁶³Ni by maize was calculated for leaves and kernels. Water drainage and leaching of ⁶³Ni were monitored over the course of the experiment. Values of K_d in surface soil samples were calculated from measured parameters of isotopic exchange kinetics. Results confirmed that ⁶³Ni was strongly retained at the soil surface. Prediction of the ⁶³Ni downward transfer could not be reliably assessed using the K_d values, since the soil structure, which controls local water fluxes, also affected both water and Ni transport. In terms of ⁶³Ni plant uptake, the effective uptake in undisturbed soil cores is controlled by isotope dilution as previously shown at the pot experiment scale.     

The assumption of linearity in soil and plant concentration ratios: An experimental evaluation

We have evaluated one of the main assumptions in the use of concentration ratios to describe the transfer of elements in the environment. The ratios examined in detail were the ‘concentration ratio’ (CR) of leaf to soil and the ‘partition coefficient’ of (K_d) of solid- to liquid-phase concentrations in soil. The ‘translocation ratio’ of berry to leaf was also computed when possible. Use of these ratios implies a linear relationship between the concentrations. Soil was experimentally contaminated to evaluate this linearity over more than a 1000-fold range in concentration. A secondary objective was to determine CR and K_d values in a long-term (2 y) outdoor study using a peat soil and a slow-growing native plant species, specifically blueberries (Vaccinium angustifolium). The elements I, Se, CS, Pb and U wer chosen as environmentally important elements expected to provide a broad range in CR and K_d values. the reuslts indicated that relationships of leaf and leachate concentrations were not consistently linearly related to the total soil concentrations for each of the elements. The modelling difficulties implied by these concentration dependencies can be partially offset by including in the models the strong negative correlation between CR and K_d. The error introduced by using a mean value of the ratios for Se or U resulted in up to a ten-fold increase in variability for CR and a three-fold increase for K_d.