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Extension of superasymmetric fission theory from cluster decay to nanophysics
Nuclear Physics A 834 (2010) 163c–166c www.elsevier.com/locate/nuclphysa
Extension of superasymmetric fission theory from cluster decay to nanophysics Dorin N. Poenarua,b and Walter Greinera a
Frankfurt Institute for Advanced Studies (FIAS), J. W. Goethe Universitaet, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main, Germany b
Horia Hulubei National Institute of Physics and Nuclear Engineering (IFIN-HH), P.O. Box MG-6, RO-077125 Bucharest-Magurele, Romania The experimental half-lives of cluster emitters are in good agreement with our predictions within the analytical superasymmetric fission model. We extended the macroscopicmicroscopic approach to study metallic cluster physics. Charged metallic clusters are ideal emitters of singly ionized trimers because both LDM and shell correction are reaching a minimum for the same mass asymmetry corresponding to the emission of a charged particle with two delocalized electrons. Maximum Q-value is obtained for transition metal clusters (high surface tension and low Wigner-Seitz radius). 1. INTRODUCTION The superasymmetric fission theory we have used to predict cluster radioactivities [1] is based on the macroscopic-microscopic method, which have been adapted to study atomic cluster physics [2–8]. This interdisciplinary approach is valid because the delocalized elctrons of a metallic cluster may be viewed as a Fermi liquid, like the nucleons in a nucleus. Consequently their collective properties are well accounted for within a Liquid Drop Model (LDM), while the quantum behavior comes out from the shell correction method [9] having as input data the energy levels of a deformed single-particle shell model, e.g. the two-center shell model [10,11]. By using the analytical superasymmetric fission (ASAF) model we published comprehensive tables to guide the experiments [12]. Potential energy surfaces (PES) of cluster emitters, are showing deep valleys due to the strong shell effect of the doubly magic daughter 208 Pb. The experiments [13] performed in Oxford, Moscow, Orsay, Berkeley, Argonne, Dubna, Milano, Wien, and Beijing [14] confirmed the half-lives predicted with the ASAF model (for more details see the books [15] and the systematics [16]). Unlike the nucleons, the atomic clusters may be viewed with ultrasensitive microscopes (e.g. Atomic Force Microscope) [17]. The images of deposited clusters suggest that one of the simplest approximation is a hemispheroid. Its shape is prolate if the interaction with the substrate may be neglected or it is otherwise oblate. Analytical relationships for the deformation-dependent Liquid Drop Model (LDM) energies of oblate and prolate hemispheroidal atomic clusters have been obtained. A superdeformed prolate hemispheroid 0375-9474/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2009.12.029
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226
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30
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25
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log10 T(s)
log10 T(s)
22 20 18 16 14 Fr Ra Ac
12 10
14
C
32
20
20
32
Si Mg Ne 20 O 14 C 28
15
34
Si Mg 26 Ne 22 Ne
24
10 25
30
35
40
30
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30
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30 28
20
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0
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26 24 22 Th Pa U
20 18 228
24
230 232 234
A
Ne 236
10
20
30
- log10 Ps
40
0.4
0.5
-1/2
Q
0.6
-1/2
(MeV
0.7
)
Figure 1. LEFT: ASAF model predictions (lines) and experimental confirmations (points) of the half-life vs. mass number of the emitter nucleus for 14 C (top) and 24 Ne (bottom) radioactivities. RIGHT: Universal curves for cluster radioactivities (top) and α-decay (bottom left). Geiger-Nuttal like plot for α-decay (bottom right).
is the most stable hemispheroidal shape within LDM [18,19]. It is also the shape with maximum degeneracy of quantum states of the hemispheroidal harmonic oscillator [20] used to compute the shell and pairing corrections [19,21]. The valleys on PES produced by the shell corrections played an important role in the production and study of superheavy nuclei, and of cluster radioactivity. Such cold valleys were used in the sixtieth by one of us (WG) to motivate the search for superheavies, and the development of Heavy Ion Physics worldwide and in Germany, where GSI was built. We have shown that even an alpha valley may be seen [22,23]. Nevertheless , in the majority of these nuclear studies the minimum of shell corrections is placed on the steepest ascending or descending Businaro-Gallone mountain so that the final result is a shallower valley on the total deformation energy. One exception is the neutron rich 264 Fm [24] which was not produced until now. From this point of view a fissioning positively charged metallic cluster [25] with z charges equal or higher than 2 is an ideal emitter of an “alpha” particle (meaning a single-charged trimer) as both the LDM and the shell correction are contributing to a deeper valley for this decay mode. Compared to nuclei, in which the electric charge of protons is assumed to be homogeneously distributed in the volume, in ionized metallic atomic clusters the excess charge of electrons produced by ionization is concentrated on the surface. 2. HEAVY PARTICLE RADIOACTIVITIES Up to now the following heavy particle radioactivities have been experimentally confirmed in heavy nuclei with Z = 87 − 96: 14 C, 20 O, 24,25 Ne, 28,30 Mg, and 32,34 Si; lower limits for 18 O, 23 F and 26 Ne are available. As can be seen in the left-hand side of figure 1 the strong shell effects of the doubly magic daughter 208 Pb are responsible for bringing
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D.N. Poenaru, W. Greiner / Nuclear Physics A 834 (2010) 163c–166c
12 10 8 6 4 2 0
Au
Q2 (eV)
E (eV)
1.0
0.5 ELDM ELDM + E
0.0 0
2
4
ne1
6
8
2 4 0
200
400
12 10 8 6 z=10 4 8 2 0 400 600
Cs
600
6 200
ne
Figure 2. LEFT: The large asymmetry part of scission point deformation energies, ELDM (dotted line) and ELDM +δE (full line), for z = 9 of the Cs9+ 209 cluster emitting a singly ionized trimer Cs+ . RIGHT: Q-value for singly charged trimer emission from Au2+,4+,6+,8+,10+ 3 and Cs2+,4+,6+,8+,10+ atomic clusters with spherical shapes.
the half-lives of the majority of cluster decay modes in the measurable range. The universal curves [26,27] in the right-hand side of this figure are able to reproduce quite well the experimental data, even for the region of superheavy nuclei [28,23]. Geiger-Nuttal plots for α-decay are showing much scattered behaviour. From a systematic analysis [16] we have seen that magicity of the daughter 208 Pb was not fully exploited so that new experimental searches can be successfully performed. Also a new kind of fine structure [29] in which the emitted cluster is in an excited state may be experimentally confirmed. Up to now only the fine structure similar to that of α-decay was reported [30].
3. METALLIC CLUTERS — IDEAL EMITTERS The left-hand side of the figure 2 shows a minimum of the LDM deformation energy taking place at the same mass asymmetry (ne1 = 2) as the minimum of shell corrections, illustrating the “ideal” character of singly ionized trimer emission. The number of delocalized electrons of the light fragment is denoted by ne1 . It happens that not only 2 is a magic number but also 198, so that both fragments are contributing to a deep minimum of the shell correction energy. Possible applications in nanotechnology may be envisaged in which the kinetic energy of the singly charged trimer can be used in analogy with the wide spread applications of nuclear α-decay. The Q-value for metallic cluster fission increases with the charge z (see the right-hand side of the figure 2). It is large when the surface tension is large and the Wigner-Seitz radius is small (larger for transition metallic clusters as Cu, Au, Ag and smaller for alkali metal clusters Cs, K, and Na). Also when the number of delocalized electrons of the two fragments are magic the total Q-value has a local maximum.
Acknowledgements This work is supported by Deutsche Forschungsgemeinschaft (DFG) and partially within IDEI Programme under contract 123/01.10.2007 with UEFISCSU, Bucharest. One of us (DNP) is grateful to DFG for the Mercator Guest Professorship.
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D.N. Poenaru, W. Greiner / Nuclear Physics A 834 (2010) 163c–166c
REFERENCES 1. A. S˘andulescu, D.N. Poenaru, W. Greiner, Sov. J. Part. Nucl. 11 (1980) 528. http://www.britannica.com/EBchecked/topic/465998/, New Encyclopaedia Britannica, 15th Edition, 1995, V. 15, p. 371. 2. W.D. Knight et al. Phys. Rev. Lett. 52 (1984) 2141. 3. Nuclear Physics Concepts in the Study of Atomic Cluster Physics, edited by R. Schmidt et al. Lecture Notes in Physics, Springer, Berlin, Vol. 404 (1992). 4. W.A. de Heer, Rev. Mod. Phys. 65 (1993) 611. 5. M. Brack, Rev. Mod. Phys. 65 (1993) 677. 6. U. N¨aher et al. Phys. Rep. 285 (1997) 245. 7. C. Yannouleas and U. Landman, Rep. Prog. Phys. 70 (2007) 2067. 8. J.P. Connerade, A.V. Solov’yov, W. Greiner, Europhysics News 33 (2002) 200. 9. V.M. Strutinsky, Nucl. Phys. A 95 (1967) 420. 10. W. Greiner, J.A. Maruhn, Nuclear Models, Springer, Berlin, 1996. 11. R.A. Gherghescu, W. Greiner, Phys. Rev. C68 (2003) 044314; C67 (2003) 014309. 12. D.N. Poenaru et al. Atomic Data Nuc. Data Tab. 34 (1986) 423; 48 (1991) 231. 13. R. Bonetti, A. Guglielmetti, Rom. Rep. Phys. 59 (2007) 301; A. Guglielmetti et al., J. Phys.: Conf. Ser. (JPCS) 111 (2008) 012050. 14. Q. Pan et al. Phys. Rev. C 62 (2000) 044612. 15. Nuclear Decay Modes, ed. D.N. Poenaru, Institute of Physics Publishing, Bristol, 1996; Handbook of Nuclear Properties, eds. D.N. Poenaru, W. Greiner, Clarendon, Oxford, 1996; Experimental Techniques in Nuclear Physics, eds. D.N. Poenaru, W. Greiner, Walter de Gruyter, Berlin, 1997. 16. D.N. Poenaru, Y. Nagame, R.A. Gherghescu, W. Greiner, Phys. Rev. C 65 (2002) 054308, erratum: C66.049902. 17. K. Seeger, R.E. Palmer, Appl. Phys. Lett. 74 (1999) 1627. 18. D.N. Poenaru, R.A. Gherghescu, A.V. Solov’yov, W. Greiner, EPL 79 (2007) 63001. 19. D.N. Poenaru et al. Europ. Phys. J. D 47 (2008) 379. 20. D.N. Poenaru, R.A. Gherghescu, A.V. Solov’yov, W. Greiner, Phys. Lett. A 372 (2008) 5448. 21. R.A. Gherghescu, D.N. Poenaru, A.V. Solov’yov, W. Greiner, Int. J. Mod. Phys. B 22 (2008) 4917. 22. D.N. Poenaru, R.A. Gherghescu, W.Greiner, Phys. Rev. C 73 (2006) 014608. 23. D.N. Poenaru, I.H. Plonski, R.A. Gherghescu, W. Greiner, J. Phys. G: Nucl. Part. Phys. 32 (2006) 1223. 24. D.N. Poenaru, R.A. Gherghescu, W. Greiner, J. Phys. G: Nucl. Part. Phys. 36 (2009) in print. 25. C. Br´echignac, P. Cahuzac, F. Carlier, J. Leygnier, Phys. Rev. Lett. 63 (1989) 1368. 26. D.N. Poenaru, W. Greiner, Physica Scripta 44 (1991) 427. 27. C. Qi, F.R. Xu, R.J. Liotta, R. Wyss, Phys. Rev. Lett. 103 (2009) 072501. 28. D.N. Poenaru, I.H. Plonski, W. Greiner, Phys. Rev. C 74 (2006) 014312. 29. Martin Greiner, W. Scheid, J. Phys. G: Nucl. Phys. 12 (1986) L229. 30. L. Brillard et al. C. R. Acad. Sci. Paris 309 (1989) 1105; E. Hourany et al. Phys. Rev. C 44 (1991) 1424.
Extension of superasymmetric fission theory from cluster decay to nanophysics Dorin N. Poenarua,b and Walter Greinera a
Frankfurt Institute for Advanced Studies (FIAS), J. W. Goethe Universitaet, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main, Germany b
Horia Hulubei National Institute of Physics and Nuclear Engineering (IFIN-HH), P.O. Box MG-6, RO-077125 Bucharest-Magurele, Romania The experimental half-lives of cluster emitters are in good agreement with our predictions within the analytical superasymmetric fission model. We extended the macroscopicmicroscopic approach to study metallic cluster physics. Charged metallic clusters are ideal emitters of singly ionized trimers because both LDM and shell correction are reaching a minimum for the same mass asymmetry corresponding to the emission of a charged particle with two delocalized electrons. Maximum Q-value is obtained for transition metal clusters (high surface tension and low Wigner-Seitz radius). 1. INTRODUCTION The superasymmetric fission theory we have used to predict cluster radioactivities [1] is based on the macroscopic-microscopic method, which have been adapted to study atomic cluster physics [2–8]. This interdisciplinary approach is valid because the delocalized elctrons of a metallic cluster may be viewed as a Fermi liquid, like the nucleons in a nucleus. Consequently their collective properties are well accounted for within a Liquid Drop Model (LDM), while the quantum behavior comes out from the shell correction method [9] having as input data the energy levels of a deformed single-particle shell model, e.g. the two-center shell model [10,11]. By using the analytical superasymmetric fission (ASAF) model we published comprehensive tables to guide the experiments [12]. Potential energy surfaces (PES) of cluster emitters, are showing deep valleys due to the strong shell effect of the doubly magic daughter 208 Pb. The experiments [13] performed in Oxford, Moscow, Orsay, Berkeley, Argonne, Dubna, Milano, Wien, and Beijing [14] confirmed the half-lives predicted with the ASAF model (for more details see the books [15] and the systematics [16]). Unlike the nucleons, the atomic clusters may be viewed with ultrasensitive microscopes (e.g. Atomic Force Microscope) [17]. The images of deposited clusters suggest that one of the simplest approximation is a hemispheroid. Its shape is prolate if the interaction with the substrate may be neglected or it is otherwise oblate. Analytical relationships for the deformation-dependent Liquid Drop Model (LDM) energies of oblate and prolate hemispheroidal atomic clusters have been obtained. A superdeformed prolate hemispheroid 0375-9474/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2009.12.029
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220 222 224
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log10 T(s)
log10 T(s)
22 20 18 16 14 Fr Ra Ac
12 10
14
C
32
20
20
32
Si Mg Ne 20 O 14 C 28
15
34
Si Mg 26 Ne 22 Ne
24
10 25
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- log10 Ps
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26 24 22 Th Pa U
20 18 228
24
230 232 234
A
Ne 236
10
20
30
- log10 Ps
40
0.4
0.5
-1/2
Q
0.6
-1/2
(MeV
0.7
)
Figure 1. LEFT: ASAF model predictions (lines) and experimental confirmations (points) of the half-life vs. mass number of the emitter nucleus for 14 C (top) and 24 Ne (bottom) radioactivities. RIGHT: Universal curves for cluster radioactivities (top) and α-decay (bottom left). Geiger-Nuttal like plot for α-decay (bottom right).
is the most stable hemispheroidal shape within LDM [18,19]. It is also the shape with maximum degeneracy of quantum states of the hemispheroidal harmonic oscillator [20] used to compute the shell and pairing corrections [19,21]. The valleys on PES produced by the shell corrections played an important role in the production and study of superheavy nuclei, and of cluster radioactivity. Such cold valleys were used in the sixtieth by one of us (WG) to motivate the search for superheavies, and the development of Heavy Ion Physics worldwide and in Germany, where GSI was built. We have shown that even an alpha valley may be seen [22,23]. Nevertheless , in the majority of these nuclear studies the minimum of shell corrections is placed on the steepest ascending or descending Businaro-Gallone mountain so that the final result is a shallower valley on the total deformation energy. One exception is the neutron rich 264 Fm [24] which was not produced until now. From this point of view a fissioning positively charged metallic cluster [25] with z charges equal or higher than 2 is an ideal emitter of an “alpha” particle (meaning a single-charged trimer) as both the LDM and the shell correction are contributing to a deeper valley for this decay mode. Compared to nuclei, in which the electric charge of protons is assumed to be homogeneously distributed in the volume, in ionized metallic atomic clusters the excess charge of electrons produced by ionization is concentrated on the surface. 2. HEAVY PARTICLE RADIOACTIVITIES Up to now the following heavy particle radioactivities have been experimentally confirmed in heavy nuclei with Z = 87 − 96: 14 C, 20 O, 24,25 Ne, 28,30 Mg, and 32,34 Si; lower limits for 18 O, 23 F and 26 Ne are available. As can be seen in the left-hand side of figure 1 the strong shell effects of the doubly magic daughter 208 Pb are responsible for bringing
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D.N. Poenaru, W. Greiner / Nuclear Physics A 834 (2010) 163c–166c
12 10 8 6 4 2 0
Au
Q2 (eV)
E (eV)
1.0
0.5 ELDM ELDM + E
0.0 0
2
4
ne1
6
8
2 4 0
200
400
12 10 8 6 z=10 4 8 2 0 400 600
Cs
600
6 200
ne
Figure 2. LEFT: The large asymmetry part of scission point deformation energies, ELDM (dotted line) and ELDM +δE (full line), for z = 9 of the Cs9+ 209 cluster emitting a singly ionized trimer Cs+ . RIGHT: Q-value for singly charged trimer emission from Au2+,4+,6+,8+,10+ 3 and Cs2+,4+,6+,8+,10+ atomic clusters with spherical shapes.
the half-lives of the majority of cluster decay modes in the measurable range. The universal curves [26,27] in the right-hand side of this figure are able to reproduce quite well the experimental data, even for the region of superheavy nuclei [28,23]. Geiger-Nuttal plots for α-decay are showing much scattered behaviour. From a systematic analysis [16] we have seen that magicity of the daughter 208 Pb was not fully exploited so that new experimental searches can be successfully performed. Also a new kind of fine structure [29] in which the emitted cluster is in an excited state may be experimentally confirmed. Up to now only the fine structure similar to that of α-decay was reported [30].
3. METALLIC CLUTERS — IDEAL EMITTERS The left-hand side of the figure 2 shows a minimum of the LDM deformation energy taking place at the same mass asymmetry (ne1 = 2) as the minimum of shell corrections, illustrating the “ideal” character of singly ionized trimer emission. The number of delocalized electrons of the light fragment is denoted by ne1 . It happens that not only 2 is a magic number but also 198, so that both fragments are contributing to a deep minimum of the shell correction energy. Possible applications in nanotechnology may be envisaged in which the kinetic energy of the singly charged trimer can be used in analogy with the wide spread applications of nuclear α-decay. The Q-value for metallic cluster fission increases with the charge z (see the right-hand side of the figure 2). It is large when the surface tension is large and the Wigner-Seitz radius is small (larger for transition metallic clusters as Cu, Au, Ag and smaller for alkali metal clusters Cs, K, and Na). Also when the number of delocalized electrons of the two fragments are magic the total Q-value has a local maximum.
Acknowledgements This work is supported by Deutsche Forschungsgemeinschaft (DFG) and partially within IDEI Programme under contract 123/01.10.2007 with UEFISCSU, Bucharest. One of us (DNP) is grateful to DFG for the Mercator Guest Professorship.
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D.N. Poenaru, W. Greiner / Nuclear Physics A 834 (2010) 163c–166c
REFERENCES 1. A. S˘andulescu, D.N. Poenaru, W. Greiner, Sov. J. Part. Nucl. 11 (1980) 528. http://www.britannica.com/EBchecked/topic/465998/, New Encyclopaedia Britannica, 15th Edition, 1995, V. 15, p. 371. 2. W.D. Knight et al. Phys. Rev. Lett. 52 (1984) 2141. 3. Nuclear Physics Concepts in the Study of Atomic Cluster Physics, edited by R. Schmidt et al. Lecture Notes in Physics, Springer, Berlin, Vol. 404 (1992). 4. W.A. de Heer, Rev. Mod. Phys. 65 (1993) 611. 5. M. Brack, Rev. Mod. Phys. 65 (1993) 677. 6. U. N¨aher et al. Phys. Rep. 285 (1997) 245. 7. C. Yannouleas and U. Landman, Rep. Prog. Phys. 70 (2007) 2067. 8. J.P. Connerade, A.V. Solov’yov, W. Greiner, Europhysics News 33 (2002) 200. 9. V.M. Strutinsky, Nucl. Phys. A 95 (1967) 420. 10. W. Greiner, J.A. Maruhn, Nuclear Models, Springer, Berlin, 1996. 11. R.A. Gherghescu, W. Greiner, Phys. Rev. C68 (2003) 044314; C67 (2003) 014309. 12. D.N. Poenaru et al. Atomic Data Nuc. Data Tab. 34 (1986) 423; 48 (1991) 231. 13. R. Bonetti, A. Guglielmetti, Rom. Rep. Phys. 59 (2007) 301; A. Guglielmetti et al., J. Phys.: Conf. Ser. (JPCS) 111 (2008) 012050. 14. Q. Pan et al. Phys. Rev. C 62 (2000) 044612. 15. Nuclear Decay Modes, ed. D.N. Poenaru, Institute of Physics Publishing, Bristol, 1996; Handbook of Nuclear Properties, eds. D.N. Poenaru, W. Greiner, Clarendon, Oxford, 1996; Experimental Techniques in Nuclear Physics, eds. D.N. Poenaru, W. Greiner, Walter de Gruyter, Berlin, 1997. 16. D.N. Poenaru, Y. Nagame, R.A. Gherghescu, W. Greiner, Phys. Rev. C 65 (2002) 054308, erratum: C66.049902. 17. K. Seeger, R.E. Palmer, Appl. Phys. Lett. 74 (1999) 1627. 18. D.N. Poenaru, R.A. Gherghescu, A.V. Solov’yov, W. Greiner, EPL 79 (2007) 63001. 19. D.N. Poenaru et al. Europ. Phys. J. D 47 (2008) 379. 20. D.N. Poenaru, R.A. Gherghescu, A.V. Solov’yov, W. Greiner, Phys. Lett. A 372 (2008) 5448. 21. R.A. Gherghescu, D.N. Poenaru, A.V. Solov’yov, W. Greiner, Int. J. Mod. Phys. B 22 (2008) 4917. 22. D.N. Poenaru, R.A. Gherghescu, W.Greiner, Phys. Rev. C 73 (2006) 014608. 23. D.N. Poenaru, I.H. Plonski, R.A. Gherghescu, W. Greiner, J. Phys. G: Nucl. Part. Phys. 32 (2006) 1223. 24. D.N. Poenaru, R.A. Gherghescu, W. Greiner, J. Phys. G: Nucl. Part. Phys. 36 (2009) in print. 25. C. Br´echignac, P. Cahuzac, F. Carlier, J. Leygnier, Phys. Rev. Lett. 63 (1989) 1368. 26. D.N. Poenaru, W. Greiner, Physica Scripta 44 (1991) 427. 27. C. Qi, F.R. Xu, R.J. Liotta, R. Wyss, Phys. Rev. Lett. 103 (2009) 072501. 28. D.N. Poenaru, I.H. Plonski, W. Greiner, Phys. Rev. C 74 (2006) 014312. 29. Martin Greiner, W. Scheid, J. Phys. G: Nucl. Phys. 12 (1986) L229. 30. L. Brillard et al. C. R. Acad. Sci. Paris 309 (1989) 1105; E. Hourany et al. Phys. Rev. C 44 (1991) 1424.