Continuous on-line chromatography of short lived isotopes of tungsten as homolog of seaborgium (element 106)

Radiochim. Acta 88, 273 278 (2000) by Oldenbourg issenschaftsverlag, München Continuous on-line chromatography of short lived isotopes of tungsten as homolog of seaborgium (element 106) By G. Pfrepper 1, R. Pfrepper 1, A. Kronenberg 2, J. V. Kratz 2, *, A. Nähler 2,. Brüchle 3 and M. Schädel 3 1 Universität Leipzig, Karl-Sudhoff-Institut, D-04109 Leipzig, Germany 2 Universität Mainz, Institut für Kernchemie, D-55099 Mainz, Germany 3 Gesellschaft für Schwerionenforschung, D-64220 Darmstadt, Germany (Received January 31, 2000; accepted March 3, 2000) Anion-exchange separations / Tungsten / Tantalum / Continuous chromatography / Multi-column technique Summary. e have studied the sorption of on anion-exchange resins from HNO 3 /HF solutions under on-line conditions using continuous chromatography with the multi-column technique. K d values and the charge of the species were determined. In order to achieve an effective separation of mother () and daughter (Ta), also the sorption of Ta from HNO 3 /HF solutions on various anion exchange resins with different functional groups was studied. This investigation serves the purpose to select a suitable anion exchange resin for planned experiments with Sg. 1. Introduction The synthesis [1] of the new isotopes 265 Sg and 266 Sg produced in the 248 Cm( 22 Ne, 4 5 n) reactions has opened the possibility to study the chemical properties of seaborgium in detail [2 4]. These experiments have also allowed for a better characterization of their nuclear properties, i.e. the half lives were determined as t 1/2 ( 265 Sg) 7.4 3.3 2.7 s and t 1/2 ( 266 Sg) 21 20 12 s [5]. Due to the short half lives and the low production cross sections (about 240 pb and 25 pb at 121 MeV [5] for 265 Sg and 266 Sg, respectively), the chemical investigations of seaborgium require a fast separation technique with high yields, an efficient counting technique, and a careful conceptual preparation. First experiments on the chromatographic behavior of seaborgium in aqueous solution, in which the Automated Rapid Chemistry Apparatus ARCA performed 5000 identical separations, had shown that seaborgium can be eluted from cation-exchange columns within 10 s in 0.1 M HNO 3 /5 10 4 M HF [3]. This shows that Sg, like its homologs Mo and resumes the hexavalent state under these conditions and forms neutral or anionic oxo- and oxofluoro complexes, and that the chemical properties of Sg are not similar to those of U(VI). In contrast to, Sg is not eluted from cation-exchange columns in 0.1 M HNO 3 indicating that Sg, in the absence * Author for correspondence (E-mail: JVKratz@mail.kernchemie.uni-mainz.de). of fluoride ions, is sorbed on the cation exchanger [4]. This was explained as an indication for a weaker tendency of Sg to hydrolyse. In the case of, the stepwise hydrolysis reactions lead to the neutral species O 2 (OH) 2 [6], while for Sg cationic species such as Sg(OH) 5 (H 2 O) may be formed [4]. This result allows for the additional conclusion that Sg in 0.1 M HNO 3 /5 10 4 M HF forms neutral or anionic oxofluoro complexes such as SgO 2 F 2 or SgO 2 F 3. Distribution coefficients (K d ) of Sg that would allow a direct and quantitative comparison with the homologs Mo and are not yet available. ith ARCA, this would require an exceedingly high number of identical separations that is beyond its technological limits. Therefore, in order to measure K d values of Sg, the use of the continuous online chromatography with the multi-column technique [7 9] is envisaged. In the present work, the sorption of on anion-exchange resins from HNO 3 /HF solutions is studied under online conditions with the multi-column technique. K d values and the charge of the species are determined. First related results can be found in [10, 11]. In order to achieve an effective separation of mother () and daughter (Ta), also the sorption of Ta from HNO 3 /HF solutions on various anion-exchange resins of different functionality was studied. These investigations serve the purpose to select a suitable anion exchanger for planned experiments with Sg. It should be pointed out that in these planned experiments, the daughter Rf and its descendants form cations and will be retained on cation-exchange resins. 2. Methods 2.1 The continuous on-line chromatography The principle of this method was outlined in [8, 9] where it was used for the determination of K d values and the charge of the fluoride complexes of Hf and Rf in HNO 3 / HF solutions. ith this technique, the retention time t R of the radioelement of interest is determined through the measurement of the decrease of its activity during passage through the chromatographic column by using the nuclear half life of the radioisotope as an internal clock. Assume that in a chro-

274 Designation Functional group Capacity K K K [meq./g] (/NO 3 ) (Ta/NO 3 ) (Ta/) Quarternary N-group Kr 146/11 N(CH 2 ) 3 N (CH 3 ) 3 3.9 7.28 73 10 Dowex 1x8 N (CH 3 ) 3 3.53 3.4 189 55.6 SNL 36 N (C 2 H 5 ) 3 3.0 1.0 317 317 Kr 146/4 N (C 2 H 5 ) 3 3.25 1.046 341 326 HS 36 I/92 N (C 2 H 5 ) 3 0.82 0.99 2248 2270 Kr 146/13 N (i-c 3 H 7 )(CH 3 ) 2 2.62 0.817 208 Kr 146/12 N (n-c 4 H 9 ) 2 (CH 3 ) 2.37 0.609 1271 2087 Tertiary N-group Kr 146/5 NH(CH 2 ) 3 N(CH 3 ) 2 4.4 7.20 47.8 6.64 Kr 146/14 N(C 2 H 5 ) 2 3.8 1.55 99 63.9 Kr 146/16 N(i-C 3 H 7 ) 2 3.13 1.086 212 194 Kr 146/7 N(n-C 4 H 9 ) 2 2.97 0.196 69.2 353 HB 36 I/92 N(n-C 4 H 9 ) 2 3.01 1.48 1018 687 Kr 146/17 N(i-C 4 H 9 ) 2 2.81 0.14 57 407 Secondary N-group Kr 146/15 NH(n-C 3 H 7 ) 3.55 1.55 45 29 Kr 146/8 NH(i-C 3 H 7 ) 2.64 0.95 36 37.9 Kr 146/6 NH(n-C 4 H 9 ) 3.23 0.424 13.8 32.5 Matrix Polyacrylamide-DVB Y 17 NH(CH 2 ) 3 N(CH 3 ) 2 4.22 4.34 7.8 1.8 KBA 245 NH(CH 2 ) 2 N(CH 3 ) 2 2.16 1.42 3.8 2.7 IDE I NH(CH 2 ) 2 N(CH 2 COOH) 2 3.81 0.997 2.3 2.3 G. Pfrepper, R. Pfrepper, J. V. Kratz et al. Table 1. Influence of the matrix and the functional group of various anion exchange resins on the selectivity of the sorption of and Ta from 0.27 M HF/HNO 3. matographic process N m (t o ) atoms of the mother nuclide are fed onto the column and N m (t R ) atoms leave the column. Then, N 1 atoms of the daughter nuclide are formed during the retention time t R. The N m (t R ) atoms of the mother nuclide that pass the column result, after their radioactive decay, in N 2 atoms of the daughter nuclide. The retention time t R and the K d value can then be calculated according to Eqs. (1) and (2) t R 1 λ ln N m(t o ) N m (t R ) 1 λ ln N 1 N 2 N 2 (1) K d (t R t f ) V (2) with V being the volume flow of the mobile phase in ml/ min, the weight of the ion exchanger in the chromatographic column in g, and t f the column hold-up time due to the free column volume in min. This principle can be applied to any chromatographic process with continuous transport of the mobile phase to the column provided that the retention time is on the order of the nuclear half life. The simplest application of this technique is the direct measurement of the activities N m (t o ) and N m (t R ) which, however, is only possible in the case of γ-ray activities. For the investigation of the transactinide elements, the direct measurement is not possible because of the A-decay mode of the mother nuclide. Therefore, one must revert to the measurement of the activity of a long-lived decay product whose half life is long enough for the preparation of counting samples. For the exact determination of the daughter activities N 1 and N 2, a quantitative mother/daughter separation is required before the mother nuclide enters into the chromatographic column. Also, immediately after elution from the column, such a mother/daughter separation is required. In this case, the continuous on-line chromatography is a multicolumn technique as these mother/daughter separations must be realized continuously by a column or a filter, too. Generally, the experimental arrangement consists of 3 to 4 columns connected in line. In a filter column (F), the daughter nuclides that are present before the mobile phase is fed onto the chromatographic column (C) are completely retained while the mother nuclides pass column F. The daughter nuclides that are formed during passage of the mother nuclides through column C are retained on a third column (D) positioned directly behind C (activity N 1 ). The effluent from columns C and D containing that part of the mother nuclides that survived the retention time on the chromatographic column C is collected, and, after the complete decay of the mother nuclide, the activity N 2 is measured off-line. Likewise, the activity N 1 is eluted from column D and is measured. 2.2 The separation of and Ta in HNO 3 /HF For the present investigation of the sorption of from mixed HNO 3 /HF solutions under on-line conditions, the short-lived isotopes 145-s, 6.7-min, and 29-min were produced on-line at an accelerator. Their radioactive daughter nuclides are 6.76-min Ta, 37-min Ta, and 1.04-h Ta, respectively. For the multi-column technique, a quantitative /Ta separation is required. From the literature [12, 13] it is known that both and Ta form anionic complexes in HF solutions. This makes the separation scheme used for the investigation of Hf and Rf [8, 9] unsuitable. Instead, an anion exchange separation scheme must be elaborated for the /Ta separation. For the choice of an effective separation scheme, the sorption of

Continuous on-line chromatography of short lived isotopes of tungsten 275 Fig. 1. Sorption of from 0.27 M HF by various anion exchange resins as a function of the HNO 3 concentration. Fig. 2. Sorption of Ta from 0.27 M HF by various anion exchange resins as a function of the HNO 3 concentration. and Ta from 0.27 M HF as a function of the HNO 3 concentration was investigated for various anion-exchange resins in batch experiments with long lived tracer activities. The nitrate ion acts as a counter ion that competes for the binding sites of the exchanger more or less effectively, depending on its concentration. Apart from the strongly basic anion exchanger Dowex 1x8, a number of non-commercial products on the basis of a polystyrene-divinylbenzene (DVB) co-polymer with different functional groups as well as products on the basis of polyacryl amide-dvb, i.e. with a preferentially aliphatic matrix, were used. A number of data characterizing these different anion-exchange resins is given in Table 1 showing the functional groups, the capacities, and the apparent exchange constants K of the anion exchange of the - and Ta complex ions against the counter ion NO 3.K is calculated according to K (, Ta/NO 3 ) K d [NO 3 ] n [capacity] n (3) where n is the charge of the complex. The last column in Table 1 gives the resulting separation factors. It is apparent that the latter depend strongly on the type of the polymer matrix and on the functional group. The underlying K d values of and Ta for a selected number of these resins are shown in Figs. 1 and 2 as a function of the HNO 3 concentration. In most cases, one observes a linear dependence on the counter-ion concentration of slope 1, which points to the fact that, in the investigated range of HNO 3 concentrations and in the presence of 0.27 M HF, anionic complexes with an average charge of 1 are formed, probably O 2 F 3 or OF 5 as well as TaF 6. In the case of, sorption on the different anion exchangers decreases in the sequence Dowex 1x8 Y17 SNL 36 HB 36 I/92 Kr 146/12 HS 36 I/92. At the same HNO 3 concentration, the difference in the K d values for Dowex 1x8 and HS 36 I/92 is about an order of magnitude. This result points to the possibility to influence the K d value and the expected retention time in future on-line experiments not only by the HNO 3 concentration and the weight of the exchanger in the chromatographic column but also by the choice of a resin with a most suitable functionality. This will be particularly important for the future experiments with seaborgium. For Ta, one observes an almost inverted sequence of K d values HB 36 I/92 Kr 146/12 HS 36 I/92 SNL 36 Dowex 1x8 BioRad AG1 Y17. Especially for Y17, the influence of the polymer matrix becomes visible as anion exchangers with an aliphatic polyacryl amide DVB are characterized by a strongly reduced selectivity for anions such as MX 6 [14]. This shows that the separation factor for the /Ta separation can decisively be influenced by the choice of the anion exchanger. The preference for Ta as compared to at the same composition of the aqueous solution apparently increases with an increased hydrophobic character of the functional group as is shown by comparison of the K d values on Dowex 1x8 and on Kr 146/12 with the functional group N (CH 3 ) 3 and N (n- C 4 H 9 ) 2 (CH 3 ), respectively. This is also reflected by the apparent equilibrium constants K in Table 1 for the ion exchange reactions of the TaF 6 and O 2 F 3 (or OF 5 ) complexes against NO 3 and by the resulting separation factors K (Ta/) for 0.27 M HF HNO 3. hile for Y17 a low separation factor of 2 is observed, the value for Dowex 1x8 is 56, and that for Kr 146/12 and HS 36 I/92 exceeds 2 10 3. For the on-line chromatography of short lived isotopes, the following conclusions can be drawn: 1. As anion exchanger for columns F and C, a resin is selected that shows a sufficiently large sorption for Ta while the K d for is only on the order of 10 10 2 ml/g.

276 G. Pfrepper, R. Pfrepper, J. V. Kratz et al. Fig. 4. Schematic representation of the experiment for the on-line chromatography with, produced at the U-400 cyclotron. Fig. 3. Sorption of and Ta by HS 36 and BioRad AG1 from 0.27 M HF as a function of the HNO 3 concentration. The weight of that resin in column F is minimized such that the retention time for is small while Ta is still completely retained. Column C serves at the same time for a quantitative sorption of the Ta daughter nuclei (activity N 1 ) that grow in during the retention time t R. Therefore, the choice of an exchange resin for columns F and C is SNL 36 or HS 36 I/92 (both with a N (C 2 H 5 ) 3 functional group) for which in the range of 0.03 0.2 M HNO 3 a separation factor of about 320 or 2300 (Table 1) is found, respectively, and K d values of 10 10 2 ml/g for and 3 10 3 3 10 4 ml/g for Ta (Figs. 1 and 2). 2. For column D, an anion-exchange resin is selected that shows sufficiently large K d values for both Ta and in order to sorb both elements until complete decay of the activity has occurred. This requirement is fulfilled by Dowex 1x8 or BioRad AG1 with K d values of 10 2 10 3 ml/g for and 10 3 10 4 ml/g for Ta. For a safe retention of the relatively long-lived (t 1/2 29 min), the weight of the exchanger in column D can be increased accordingly. In Fig. 3, a comparison is made of the K d values for and Ta with the resins HS 36 and BioRad AG1 in 0.27 M HF in the interesting range of HNO 3 molarities. 2.3 Experimental scheme Fig. 4 shows a scheme of the experimental apparatus used at the Flerov Laboratory for Nuclear Reactions of the JINR Dubna. 6.7-min and 29-min were produced in 2 3 h bombardments of a natural Sm target with 190 MeV 24 Mg at the U400 cyclotron. The reaction products were transported with an Ar/KCl gasjet system at a flow rate of 0.8 1 l/min to a degassing unit where it was transferred into the eluent solution with a yield of 80%. The eluent solution was continuously transported into the chromatographic system consisting of three subsequent columns F, Fig. 5. Degassing unit for the dissolution of the activity bearing KCl aerosols into the continuously flowing aqueous phase. C, and D with a flow rate of 0.35 0.2 ml/min depending on the HNO 3 concentration. The columns C and D with the Ta fractions N 1 and N 2, after the complete decay of the isotopes in column D, were washed with 0.27 M HF and were assayed directly for the γ-ray activity of the daughters 37-min Ta and 1.04-h Ta. In the experiments with the shorter lived isotope 145-s produced at the Philips Cyclotron of the Paul Scherrer Institute (PSI) in the nat. Dy( 18 O, xn) reaction, an analogous system of columns was used. The reaction products were transported by a He/ KCl gas jet at a flow rate of 2 l/min to the degassing unit shown in Fig. 5 where the KCl aerosols were dissolved in mixed HNO 3 /HF solutions containing 0.1 M HF and 0.5 M HF, respectively, that were pumped at 1 ml/min by a HPLC pump. The transport of the aqueous solution leaving the degassing unit into the column system was performed by another HPLC pump. After the on-line experiment, the γ- ray activities of 6.76-min Ta on columns C and D were determined. 3. Results and discussion The retention times t R and K d values of resulting from the ratio of the Ta daughter activities are listed in Table 2. As there is only a week dependence (if any) on the HF concentration above 0.1 M HF, Table 2, besides values ap-

Continuous on-line chromatography of short lived isotopes of tungsten 277 Table 2. Determination of K d values of HNO3 Eluent Daughter γ-energy t R K d complexes on the anion exchanger HS36 from [mol/l] [ml/min] isotope nuclide [kev] [min] [ml/g] 0.27 M HF/HNO 3 by on-line chromatography using the multi-column technique. Some data for 0.1 M HF/HNO 3 and 0.5 M HF/HNO 3 are also included. 0.01* 0.750 Ta 101 5.6 536 221 6.9 650 0.01* 0.780 Ta 101 5.1 506 0.03 0.300 Ta 214 12.1 145 Ta 207 17.4 199 0.05** 0.925 Ta 101 3.3 98 221 4.1 122 0.05** 0.792 Ta 101 3.6 105 221 3.3 96 0.05 0.238 Ta 95 9.9 89 214 8.4 75 Ta 207 11.0 99 0.10 0.146 Ta 95 7.2 37 Ta 91 6.6 34 207 7.3 38 0.2 0.120 Ta 95 3.2 13 214 3.4 14 Ta 207 7.2 30 *: with 0.1 M HF; **: with 0.5 M HF. plying for 0.27 M HF, also contains some values for 0.1 M HF and for 0.5 M HF. One observes that the values of t R and K d for different isotopes with different half lives are consistent, and the values of t R and K d decrease with increasing HNO 3 concentration as expected. In Fig. 6, the K d values resulting from the on-line experiments with and in HNO 3 /0.27 M HF are compared to the results of batch experiments with the long lived tracer 187. There is good agreement between the two sets of data. In Fig. 7, the K d values resulting from the online experiments with the short lived in HNO 3 /0.1 M HF are compared to the results of batch experiments also using the tracer 187. Also here, good agreement between the two sets of data is observed. One can conclude that the isotopes produced in heavy-ion reactions and studied in on-line chromatography experiments with mixed HNO 3 /HF solutions, adopt the valence state 6. The slope of the linear regression in Fig. 6 is 1.19 0.15 for the on-line data and 1.08 0.2 for the data from the batch experiment. In Fig. 7, the slopes are 1.08 0.22 and 0.94 0.11, respectively. This means that, in the presence of HF, in the range 0.1 M through 0.5 M HF, forms anionic complexes with an electric charge of 1, most probably O 2 F 3 or OF 5. For the application of the continuous on-line chromatography to seaborgium and for the determination of its K d values in mixed HNO 3 /HF solutions, the results of the present work give several hints. As in this case, a fast and effective Sg/Rf separation is necessary, the concept devel- Fig. 6. Intercomparison of the results of batch experiments ( 187 ) and of on-line experiments on the sorption of (, ) from 0.27 M HF by Dowex 1x8 and HS 36 as a function of the HNO 3 concentration. Fig. 7. Same as Fig. 6 for the sorption of 187 (batch) and (online) from 0.1 M HF on HS 36.

278 oped for in the present form is not suited. However, in principle, the cation exchange separation of Sg and Rf performed in the ARCA experiments [3] appears to be applicable if it is combined with a suitable anion exchanger as chromatographic column. On this column, Rf must not be sorbed, and the anionic Sg complexes must show a weak sorption with K d values of the order of 10 ml/g. For a safe retention of Rf on a cation exchanger, concentrations of 10 3 M HF and 0.1 M HNO 3 should be used resulting in special requirements for the choice of the anion exchanger. From Fig. 1 and Table 1 it follows that Dowex 1x8 with values of K (/NO 3 )of 3.4 in 0.1 HNO 3 yields K d values of 10 2 ml/g which are too large for the Sg experiments. Among the resins with quaternary ammonium groups, primarily HS 36 appears to be suitable because of its K d value of 10 ml/g resulting from its reduced capacity and its K (/NO 3 ) value of 0.99. Based on their strong nitrate selectivity, also resins with strongly hydrophobic tertiary ammonium groups like Kr 146/7 or Kr 146/17 as well as HB 36 appear to be suitable (see Table 1). The final decision will rest on the values of K (/Mo) that are presently being determined for various resins. Preliminary results show that no significant separation of and Mo is achieved with Kr 146/17, for example, while a separation factor of 3 is obtained with HB 36 ( Mo). This is a desired feature for the Sg experiments that should aim at a differential characterization of the sorption of Sg on an anion exchanger with respect to that of Mo and. Acknowledgments. G. P. and R. P. thank the FLNR Dubna for its hospitality and for assistance during the experiments. The experiments in Dubna were supported by the Bundesministerium für Forschung und Technologie under contract 211-4006-06LZ122. The Mainz/GSI group thanks A. Türler and associates for providing their infrastructure to perform the experiments at the Philips Cyclotron of the Paul Scherrer Institute. The Mainz group acknowledges financial support by the Deutsche Forschungsgemeinschaft under contract KR 1458/4-1. G. Pfrepper, R. Pfrepper, J. V. Kratz et al. References 1. Lazarev, Yu. A., Lobanov, Yu. V., Oganessian, Yu. T., Utyonkov, V. K., Abdullin, F. Sh., Buklanov, G. V., Gikal, B. N., Iliev, S. M., Mezentsev, A. N., Polyakov, A. N., Sedykh, I. M., Shirokovsky, I. V., Subbotin, V. G., Sukhov, A. M., Tsyganov, Yu. S., Zhuchko, V. E., Lougheed, R.., Moody, K. J., ild, J. F., Hulet, E. K., McQuaid, J. H.: Phys. Rev. Lett. 73, 624 (1994). 2. Schädel, M., Brüchle,., Dressler, R., Eichler, B., Gäggeler, H.., Günther, R., Gregorich, K. E., Hoffman, D. C., Hübener, S., Jost, D. T., Kratz, J. V., Paulus,., Schumann, D., Timokhin, S., Trautmann, N., Türler, A., irth, G., Yakushev, A.: Nature (London) 388, 55(1997). 3. Schädel, M. Brüchle,., Schausten, B., Schimpf, E., Jäger, E., irth, G., Günther, R., Kratz, J. V., Paulus,., Seibert, A., Thörle, P., Trautmann, N., Zauner, S., Schumann, D., Andrassy, M., Misiak, R., Gregorich, K. E., Hoffman, D. C., Lee, D. M., Sylwester, E. R., Nagame, Y., Oura, Y.: Radiochim. Acta 77, 149 (1997). 4. Schädel, M., Brüchle,., Jäger, E., Schausten, B., irth, G., Paulus,., Günther, R., Eberhardt, K., Kratz, J. V., Seibert, A., Strub, E., Thörle, P., Trautmann, N., aldek, A., Zauner, S., Schumann, D., Kirbach, U., Kubica, B., Misiak, R., Nagame, Y., Gregorich, K. E.: Radiochim. Acta 83, 163 (1998). 5. Türler, A., Dressler, R., Eichler, B., Gäggeler, H.., Jost, D. T., Schädel, M., Brüchle,., Gregorich, K. E., Trautmann, N., Taut, S.: Phys. Rev. C57, 1648 (1998). 6. Baes, C. F., Mesmer, R. E.: The Hydrolysis of Cations, John iley (1976). 7. Szeglowski, Z., Bruchertseifer, H., Domanov, V. P., Gleisberg, B., Guseva, L. J., Hussonnois, M., Tikhomirova, G. S., Zvara, I., Oganessian, Yu. Ts.: Radiochim. Acta 51, 71(1990). 8. Pfrepper, G., Pfrepper, R., Yakushev, A. B., Timokhin, S. N., Zvara, I.: Radiochim. Acta 77, 201(1997). 9. Pfrepper, G., Pfrepper, R., Krauss, D., Yakushev, A. B., Timokhin, S. N., Zvara, I.: Radiochim. Acta 80, 7(1998). 10. Pfrepper, G., Pfrepper, R., Krauss, D., Yakushev, A. B., Timokhin, S. N., Zvara, I.: FLNR Scientific Report, Heavy Ion Physics, E7-95-227, Dubna (1995) p. 147. 11. Kronenberg, A., Kratz, J. V., Nähler, A., Brüchle,., Jäger, E., Schädel, M., Schausten, B., Schimpf, E., Jost, D. T., Türler, A., Gäggeler, H.., Pfrepper, G.: PSI Annual Report (1998) p. 7. 12. Kraus, K. A., Moore, G. E.: J. Am. Chem. Soc. 73, 2900 (1951). 13. Caletka, R., Krivan, V.: J. Radioanal. and Nucl. Chem. 142, 359 (1990). 14. Pfrepper, G.: Habilitationsschrift, Leipzig, ZfI-Mitteilungen 107, 1 292 (1985).