Fission barriers of super-heavy nuclei obtained from experimental data

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Nuclear

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Fission Barriers of Super-Heavy Nuclei obtained from Experimental Data Jean Peter” * a LPC Caen, ENSICAEN, 6 boulevard du Mar&ha1 Juin, 14050 Caen, Prance Excitation functions of super-heavy evaporation residues formed in cold fusion reactions were analysed with the aim of getting information on the fission barrier of these nuclei. The method uses only the location of the maximum of In (and 2n) excitation functions. The results are compared to available theoretical predictions. 1. Data

Analysis.

The fission barrier value of a super-heavy nuclei is a fundamental characteristics, since the existence of a fission barrier is the condition for the existence of such a nucleus. The excitation functions of residual nuclei formed at Dubna in hot fusion reactions were used in cases where the compound nucleus cross sections had been experimentally measured [I]. The survival probability was calculated via usual statistical formulas. By fitting the calculated xn excitation functions to the experimental ones, lower limits of fission barrier values were obtained for isotopes of elements 112, 114 and 116 [2]. In this paper, we want to extract the fission barrier of residues formed in the In or 2n de-excitation channels of nuclei formed at GSI and RIKEN in cold fusion reactions [3,4]. Since the compound nucleus cross sections are not known experimentally and theoretical calculations differ by orders of magnitude, the above method cannot be used. Here we rely on the peals locations of In and 2n excitation functions, E*max(ln) and E*max(2n), measured for Z=104 to 112 nuclei formed in fusion between “‘Pb or “‘Bi and projectiles ranging from 50Ti to 70Zn. These compound nuclei have two common features: i) all of them have an even neutron number; ii) the incident energy which corresponds to E*max(ln) is much smaller than the Bass barrier VB (Coulomb barrier) at Z=104 and moves up to Vg at Z N 110; the incident energy for E*max(2n) is slightly smaller or close to VB for Z=104-107 (and was not measured for Z>lOS). 1.1.

Simulated

excitation

functions.

Experimental In excitation functions were simulated in three steps: fig. 1. In the first step, only the competition between fission and the first neutron evaporation is studied: it is described with the usual (l?f/I’n) statistical formula. It depends on the neutron separation energy and fission barrier of the compound nucleus and In evaporation residues, Sn(CN) and Bf(CN), Sn(CN-ln) and Bf(CN-ln). The level density parameters an and af do not play any role on E*max(ln) values. Monte Carlo calculations were performed with a large number of events at each excitation energy E*, in 0.1 MeV steps. The maxwellian *e-mail:

jpeterQin2p3,fr

037.S9474/$ - see front matter doi:10.1016/j.nuclphysa.2004.01.032

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Figure 1. Simulated In excitation functions. Left: survival probability. Center: survival probability multiplied by the slope of the complete fusion cross section. Right: same distribution simulating an experiment: data taken at 1.5 MeV intervals with a target thickness covering 3 MeV.

kinetic energy distribution of evaporated neutrons was taken into account. Left panel exhibits the excitation function. Its maximum is located in the 0.1 MeV step just above Sn(CN) + [the smallest one of Bf(CN-1 n ) and Sn(CN-ln)]. It was assumed previously that the average neutron kinetic energy should be added (~1 MeV)[5], but the present Monte Carlo calculation invalidates this assumption. Second step: each point of this survival probability must be multiplied by the corresponding fusion cross section. We are not interested here in the absolute value of the fusion cross section, but only on its variation with energy. Since this range of energy is well below the Bass barrier, the fusion cross section decreases exponentially with decreasing energy: more than two orders of magnitude on 5 MeV were measured on the system 48Ca + “‘Pb [6]. Theoretical calculations give similar slopes [7,8]. The resulting excitation function is shown in the center panel. Of course, the points at low E* are more depressed than those at high E*. The effect of interest for us is a displacement of E*max(ln) to a higher value, DEl: 0.8 MeV in this example. Third step: in order to compare this shape and E*max(ln) to experimental data, t,he energy resolution of these data has to be taken into account. The projectile energy decreases through the target thickness. The corresponding excitation energy variation is 2.5 MeV to 3.5 MeV [3,4]. In the shown example, 3 MeV was used and the simulated points are plotted at mid-target energy as in experimental data. They exhibit a gaussian shape, like the data. The FWHM of these distributions decreases from 3.2 MeV (left) to 2.8 MeV (center) and of course increases at right: 4.5 MeV. This value is close to FWHM observed with the same target thickness [3]. 1.2. Mass tables and extraction of Bf values. Experiments determine In and 2n excitation functions in the center-of-mass system. The rea,ction Q value is subtracted to get E*. It depends on the projectile and target

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Fission barrier values obtained for In and 2n evaporation residues from the nuclei listed at left. Dotted line triangles at Z=104-106 indicate lower limits ER (see text). Dashed line triangles for Z=llO and 112 indicate very low “Max-Min tables”: maximum difference due to different adjusted mass tables.

masses, which are known, and the compound nucleus mass, found in mass tables. Mass tables predictions differ by up to a few MeV. E*max( In) and Bf(CN-ln) values would differ by this same amount. For the 13 masses experimentally known for Z 1 102, the differences between measured and calculated values, DM(A,Z), were observed to be systematically either negative [9,11,12,14], or positive [10,13,15]. Moreover, in each table DM(A,Z) do not exhibit a significant variation as a function of Z or A. Average values, , were then calculated. They vary from -1.36 to +0.46 MeV. Adjusted masses for superheavy nuclei in each table were obtained by adding of this table. These adjusted masses are much closer to each other. The uncertainties on E* and Bf values due to the remaining differences are listed in fig. 2. For each reaction, the In excitation function was simulated as described above. Sn(CN), Sn(CN-In) and Sn(CN-2n) were taken as the average values of the different mass tables. In the third step, the excitation energies and energy width of each simulated point were the same as in the actual data. Bf(CN-ln) was chosen to get agreement between simulated and measured E*max( ln) values. 2. Results

and

conclusion

Fig. 2 exhibits the results obtained by this method. The width of each symbol represents the estimated uncertainty on experimental data. When Sn(CN-ln) is smaller than Bf(CN-ln), it determines the location of E*max(ln). For Z=104-106, values obtained from the In analysis (dotted line triangles in fig. 2) are indeed very close to Sn(CN-In) values (-6.3 hIeV for these odd-N nuclei). Then the same method was applied to 211 excitation functions. They offer two advantages: i) since the

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incident energy which corresponds to E*max(Zn) is close to Vg, DE2 is smaller; ii) since these residues are even-N nuclei, Sn(CN-2n) is >8 MeV and Bf(CN-2n) can be measured up to this value. Bf(CN-2n) values are indeed found to be -7 MeV for Z=104-106. For Z 2 108, Bf values are obtained for In residues and are smaller than 6 MeV, which is consistent with the vanishing of 2n cross sections relative to In (This is also due to a much smaller reduction of the In cross section than at smaller Z’s when the incident energy becomes closer to or larger than V,). For Z = 110 and 111, different E*max(ln) values were obtained at GSI and RIKEN [3,4]. The beam energies have to be exactly known. For Z=112, the two dashed line triangles are indicative only since they come from 1 event only at each of two incident energies [3]. Remark: in fission barrier tables [10,17,18], the differences between neighbouring isotopes are smaller than the experimental uncertainties in fig. 2. These fission barrier values are not accurate. Nevertheless they may be compared to fission barrier theoretical predictions [10,16-181. [17] g’Ives values which are systematically smaller than the data, by 2 to 3 MeV. [10,16] predict a rather constant value, 5-6 MeV, for the nuclei studied here; they underpredict the data by -1.5 MeV for Z=104-106 and may be in agreement for Z 2 108. An overall agreement is observed for [18]. It has to be confirmed by more accurate data on Z=llO-112. However, the lower limits for Bf of 112, 114 and 116 isotopes obtained in [2] are larger than the values predicted in [18] and in agreement with (i.e. smaller than the values predicted in) [10,17]. One cannot conclude about the overall validity of any fission barrier table for super-heavy nuclei.

REFERENCES 1. M. G. Itkis et al., Proc. on Fusion Dynamics at the Extremes, Dubna, Russia, 2000, ed. by Y. Oganessian and V. Zagrebaev, World Sci.,2001. 2. M. G. Itkis et al., Phys. Rev. C 65, 044602 (2002) 3. S. Hofmann G. Miinzenberg, Rev. Mod. Phys. 72, 733(2000), this conference and private communication. 4. K. Morita et al., Riken Accel. Prog. Rep. 36 (2003), this conf. and private communication. 5. J. Peter et al., Proc. Int. Symposium EXON 2001, Baikal, Russia, ed. by YU. Penionzhkevic and E. Cherepanov, World Sci., p. 41. 6. M. G. Itkis et al., Nuovo Cimento All1 (1998) 783. 7. Y. Aritomo and M. Ohta Proc. on Fusion Dynamics at the Extremes, Dubna, Russia, 2000, World Sci.,2001, and private communication. 8. B. Bouriquet, Y. Abe and D. Boilley, preprint (2003) and private communication. 9. W.D. Myers, W.J. Swiatecki, Nut. Phys A601 (1996) 141 and report LBL-36803 (1994) 10. P. Miiller, J.R. Nix, W.D. Myers, W.J. Swiatecki, At. Data Nucl. Data Tab 59 (1995)185 11. A. Mamdouh et al., Nut. Phys. A 644 (1989) 389 and M. Rayet, private communication. 12. H. Koura, M. Uno, T. Tachibana, M. Yamada Nut. Phys. A 674 (2000) 47 13. S. Liran, A. Marinov, N. Zeldes, Phys. Rev C 62 (2001) 047301 14. S. Goriely. F. Tondeur, J.M. Pearson, At. Data Nucl. Data Tables 77 (2001) 311 15. I. Muntian, Z. Patyk, A. Sobiczewski, Yad. Fiz. (Phys. At. Nucl.) 66 (2003) 16. G. Giardina et al., Eur. Phys. J. A. 8 (2000) 205 and private communication. 17. A. Mamdouh, J.M. Pearson, M. Rayet, F. Tondeur, Nut. Phys. A 679 (2001) 337 18. I. Muntian, Z. Patyk, A. Sobiczewski, Acta Phys. Pol. B34 (2003)