ON THE LIIMITS OF POSSIBILITIES OF SUPERHEAVY ELEMENT SYNTHESIS
IN NUCLEAR REACTIONS WITH HEAVY IONS
V.L. Mikheev
Flerov Laboratory of Nuclear Reactions
Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia
Abstract
Experimental data on the bombarding energies of heavy ions with 10  Z  30 in 36 fusion
reactions with evaporation of 1-4 neutrons at irradiation of targets with 82  Z  98 have been
compared with fusion barriers calculated according to different theoretical models. The
experimental fusion barrier was defined as the minimum value of the heavy ion bombarding
energy at which neutron evaporation residues were really observed to form. Corrections to the
theoretical fusion barriers have been found by least-squares linear fit of calculated and
experimental barrier values. The corrected values of the fusion barriers B were calculated for
the fusion of 208Pb, 238U, 248Cm, 249Cf with heavy ions with the atomic numbers 6  Z  46.
These fusion barriers B were compared with the ground state Q-values for the complete
fusion. According to the criterion (B+Q)  0 for complete fusion, the extreme atomic number
for the elements producible in complete fusion reactions involving heavy ions is 134.
1. Introduction
In the last years, considerable progress has been achieved in the synthesis of superheavy
elements. The elements with atomic numbers 114 and 116 were synthesized [1-3].
Experiments to produce element 118 in a 249Cf + 48Ca nuclear reaction were carried out at the
Flerov Laboratory of Nuclear Reactions, JINR, Dubna [4]. The results concerning the
production of elements 104-112 can be found in surveys [5-8].
The periodic table currently contains 23 man-made elements, of which the latest 14
elements were produced using fusion nuclear reactions involving heavy ions (HI). This raises
the question on limits to producing superheavy elements in laboratory conditions. The main
restricting factors are: 1) the instability of nuclei first of all with respect to spontaneous
fission and 2) the entrance channel limitations for the fusion of the nuclei used to produce
new heavy elements.
The nuclear properties of superheavy elements were analyzed in many works. According to
work [9], the most heavy nuclide with a shell stabilized fission barrier which can be produced
using the really available isotopes of elements in the Mendeleev’s Table is 329134. In work
[10] the spontaneous fission half-lives larger than 0.1 s were calculated for the elements with
atomic numbers up to 120. The alpha and beta decay properties of the nuclei with atomic
numbers up to 136 have been estimated in work [11].
By now, a large body of data on the complete fusion of heavy ions with heavy targets has
been accumulated. One of the key factors to be dealt with in planning and analyzing
experiments is the fusion barrier, which basically owes its existence to Coulomb repulsion.
The fusion barrier is known to be the minimum value of entrance channel energy for colliding
nuclei to overcome their mutual Coulomb repulsion and fuse. Below the fusion barrier,
complete fusion can occur only with a low probability owing to the quantum-mechanical
penetrability of a potential barrier. The nucleus-nucleus interaction potential and the near
barrier fusion cross section are determined by many factors [12-14]. For heavy targets,
experimental values for fusion barriers are usually deduced from the corresponding excitation
functions for fusion-fission and for the summary yield of evaporation residues. For most
heavy systems target + heavy ion, the problems connected with fast fission, incomplete
fusion-fission and the sharply decreasing fusion cross section make identification of real
complete fusion-fission events very difficult. An event of complete fusion can be most
reliably identified by direct registration of neutron evaporation residues with Z=Z1+Z2, where
Z1 and Z2 are the atomic numbers of target and projectile nuclei. In this work, the
experimental fusion barrier B(exp) is defined as a minimum value of heavy ion bombarding
energy at which neutron evaporation residues corresponding to the minimum number of
evaporated neutrons were really observed to form. This definition is not so rigorous. But it
permits to extract B(exp) values from the data on the synthesis of the heaviest elements when
the measurements were performed at one value of projectile energy and the number of
registered events was a few units. Comparing the experimental values of fusion barriers
derived from (HI, xn) reactions with existing theoretical calculations allows corrections to be
found to the initial theoretical barrier values. Due to that, it is possible to obtain more reliable
estimations of fusion barriers for various combinations of targets and projectiles.
The aim of the present work is to estimate what is the maximum Z value of the element
which can be synthesized in fusion reactions from the really available quantities ( ~1 mg) of
initial atoms of the elements (natural or man-made) required for producing targets and beams.
For this purpose, a comparison of the fusion barriers and the compound nucleus ground state
Q-values was made for different target + projectile combinations.
2. Calculated and experimental fusion barriers
Potential energy calculations can be carried out now in multidimensional approaches using
many parameters. But one-dimensional models allow to reveal more clearly the general
tendencies in changing fusion barriers for the wide ranges of Z1 and Z2. From among many
approaches to calculating entrance channel potential (see, for example, [14] and the references
cited therein) those approaches were chosen that use a minimum number of adjustable
parameters.
The classical potential model by Bass [15] is much used to calculate the fusion barriers for
heavy ion reactions,.
Heavy ion collisions were analysed in detail by W. Wilcke et al. [16]. The fusion barriers
have been calculated for s-waves using the BSS Coulomb potential [17] and the nuclear
proximity potential [18]. Myers and Swiatecki [19] have revised the nuclear parameters used
for proximity potential calculations. However for heavy targets, the results of works [16,18]
and [19] differ only slightly. This work makes use of the parameterization from works
[16,18].
K. Siwek-Wilczynska and J. Wilczynski [20] suggested for the description of fusion barriers
the adiabatic fusion potential with the nuclear part of the Woods-Saxon shape.
The fusion barriers can be expressed in terms of the Coulomb potential alone,
B(Coul.)=Z1Z2e2/r0(A11/3+A21/3). The radius parameter r0 is a handy variable for comparing
fusion barriers for various combinations of nuclei. In this work r0 =1.44 fm.
The experimental and calculated fusion barriers are listed in Table 1. The used experimental
data include 36 nuclear reactions involving heavy ions with 10  Z  30 and heavy targets
with 82  Z  98. Only those experiments were selected in which the incident energy in the
middle of the thin target was exactly determined. The data have been arranged corresponding
to the experimental fusion barrier magnitudes.
Table 1
Fusion barriers (MeV) deduced from the experimental data on (HI,xn) reactions, compared
with the Coulomb barriers and with the barriers calculated by theoretical models [15, 16, 20].
Reaction
Ref.
B(exp) B(Coul)
B(Bass) B(Wilcke) B(Wilcz.)
208
22
Pb( Ne, 4n)
21
92
94.0
92.5
95.8
89.8
232
Th(22Ne,4n)
22
92
100.6
99.6
103.1
92.9
208
20
Pb( Ne, 4n)
21
93
94.9
93.6
95.9
92.5
238
22
U( Ne,4n)
23
96
102.2
101.3
104.9
94.6
242
22
Pu( Ne,4n)
24
99
104.1
103.2
106.9
97.1
236
U(22Ne,4n)
25
102
102.4
101.5
103.5
95.1
243
22
Am( Ne,4n)
26
103
105.1
104.3
108
98.1
248
22
Cm( Ne,4n)
27
107
105.7
105.0
107.3
98.5
232
Th(26Mg, 4n)
25
117
118.6
118.5
122.6
110.2
207
Pb(34S,3n)
28
138
143.3
144.7
149.3
139.1
206
40
Pb( Ar,2n) 29,30
155
158.3
160.5
165.6
155.5
208
40
Pb( Ar,2n)
5,30
157
157.9
160.1
165.3
155.3
209
Bi(40Ar,2n)
31
159
157.8
162
167.2
157.4
208
48
Pb( Ca,1n)
32
171
171.6
174.5
180.0
174.5
206
48
Pb( Ca, 2n)
28
173
171.9
174.8
180.3
174.5
204
Pb(48Ca,2n)
28
173
172.3
175.2
180.7
174.3
207
48
Pb( Ca,2n)
28
174
171.7
174.6
180.2
174.6
208
50
Pb( Ti,1n)
6,33
185
187.7
191.9
198.1
189.5
209
50
Bi( Ti,1n)
33
187
189.8
194.2
200.4
192.2
232
Th(48Ca,3n)
34
189
184.1
188
194.0
183.6
238
48
U( Ca,3n)
34
192
187.2
191.3
197.3
187.4
242
48
Pu( Ca, 3n)
34
196
190.6
195.0
201.3
191.8
244
48
Pu( Ca,3n)
1
197
190.2
194.7
201.0
191.1
209
Bi(51V,2n)
35
199
198
203
209.5
198.4
248
48
Cm( Ca,4n)
3
201
193.6
198.4
204.7
195.6
208
54
Pb( Cr,1n)
6
202
202.8
208.1
214.8
205.1
249
Cf(48Ca, 3n)
4
206
197.5
202.6
209
201.4
209
54
Bi( Cr,1n)
36
208
205.1
210.6
217.3
208.3
207
58
Pb( Fe,1n)
6,37
218
217.9
224.7
231.6
221.8
208
58
Pb( Fe,1n)
6,37
219
217.6
224.4
231.4
221.4
209
Bi(58Fe,1n)
6
223
220.1
227.2
234.1
223.4
208
64
Pb( Ni,1n)
6
236
231.3
239.3
246.6
237.0
208
62
Pb( Ni,1n)
6
237
232.3
240.6
247.8
236.0
207
Pb(64Ni,1n)
38,39
239
231.6
239.6
246.9
237.5
209
64
Bi( Ni,1n)
6,39
240
233.9
242.2
249.5
240.1
208
70
Pb( Zn,1n)
6,39
255
244.9
254.1
261.8
252.6
Fig. 1(a) shows the difference between the experimental fusion barriers and the barriers
calculated by theoretical models [15,16,20] as well as the Coulomb barriers. It is seen this
difference to be as much as ~13 MeV. To decrease this discrepancy, least squares linear fit of
calculated and experimental fusion barriers was made. The formulae for calculating the
corrected fusion barriers are as follows:
B(Coul. corr.)= -10.61 + 1.068 B(Coul.); standard deviation SD=3.2MeV
B(Bass corr.)= -2.54 + 1.00B(Bass); SD=3.1 MeV
B(Wilcke corr.)= -2.61+ 0.97B(Wilcke); SD=3.3 MeV
B(Wilcz. corr.)=5.60+ 0.974B(Wilcz.); SD=3.3 MeV
30
[B(calc. corr.) - B(exp)] / MeV
[B(calc) -B(exp)] / Mev
25
80
100
120
140
160
180
200
220
240
260
B(Bass)
B(Coulomb)
B(Wilcke)
B(Wilczynski)
(a)
20
15
(1)
30
25
20
15
10
10
5
5
0
0
-5
-5
-10
-10
-15
-15
-20
30
-20
30
25
25
(b)
20
20
15
15
10
10
5
5
0
0
-5
-5
-10
-10
-15
-15
-20
80
100
120
140
160
180
200
220
240
260
-20
B(exp) / MeV
Fig.1 (a) The difference between the calculated and experimental fusion barriers versus
B(exp) values for the nuclear reactions from Table 1.
(b) The same as in (a), but the theoretical barriers are corrected by formulae (1).
Fig. 1(b) demonstrates the effect of introducing corrections to the initial theoretical fusion
barriers. Based on experimental data, these corrections include possible effects of extra push
energy, nuclear static and dynamic deformations, different entrance channels coupling and so
on. The fusion barriers calculated by formulae (1) differ from the experimental fusion barriers
by no more than 5 MeV. An essential part of this difference may be aroused owing to the
errors in the B(exp) values connected with target thickness, incomplete measurement of the
excitation function, the accuracy of HI energy measurement.
Table 2
Number of evaporated
neutrons
1
2
3
4
Dissipated energy,
MeV
6.32.2
9.13.5
10.83.7
13.36.1
Table 2 shows the mean values of dissipated energy E* for presented in Table 1 (HI, xn)
reactions
x
E*=(B(exp) + Q -
 Bi ),
i 1
x
where
 Bi
is the binding energy of evaporated neutrons.
i 1
The Q-values and neutron binding energies were calculated using mass tables [40-42].
According to the way experimental fusion barriers were determined, the E* value for x=1
corresponds to the maximum of the excitation function and that for x 1 corresponds to the
low energy edge of the excitation function or the sole projectile energy at which the
evaporation residue was observed.
3. Fusion barriers and Q-values for the synthesis of nuclei with the highest Z numbers
The up-to-date theoretical approaches [43-45] are not capable of predicting the values of
the formation cross sections of superheavy elements with a good accuracy [43]. Therefore,
from the practical point of view, while planning experiments to produce superheavy elements,
it is very important to choose an optimal target + projectile combination and the value of
incident energy. The only question arises then on the maximum sensitivity of experiments.
The Q-value is the very important parameter in nuclear processes. The use of the
corresponding Q-values and Coulomb barriers allows unified systematization of the
probabilities of spontaneous fission, alpha decay and cluster decay of heavy nuclei [46]. To
some extent, the fusion of heavy ion with a target nucleus is the inverse process to the cluster
decay [47]. It seems reasonable to analyze the entrance channels of nuclear reactions leading
to superheavy elements by comparing the entrance fusion barriers and the Q-values for the
compound nuclei formed.
3.1 Main points of approach proposed
1) The necessary condition for fusion to occur is (B+Q)  0 (Q  0 for all the considered
nuclear reactions), which provides a gradient of potential (driving force) between the
initial double nuclear system and the final compound nucleus. In terms of statistical
model, it means that compound nucleus excitation energy is greater than zero for the
incident energy equal to B.
2) Formulae (1) are used to calculate the B value that does correspond to the complete
fusion.
3) The sum of Coulomb and nuclear potentials must have a pocket on the way of radial
motion towards fusion. The only s-wave absorption is considered owing to the fact that
the nuclear systems involved in the formation of superheavy nuclei are highly fissionable.
4) At (B+Q)  0, an increase in the initial kinetic energy over B will not result in compound
nucleus formation. The additional kinetic energy is thermalized [20].
5) Since superheavy elements have small formation cross sections ( pb), only the isotopes
of elements available in quantities no less than ~1 mg are considered to make it possible to
produce the targets and beams required.
3.2
Calculations for 208Pb, 238U, 248Cm, 249Cf
These nuclides were chosen as the most suitable targets for producing the elements with Z
much greater than 100. 252Cf and 254Es can be used also, but they give no appreciable
advantage in comparison with 248Cm and 249Cf. Moreover, 252Cf produces an extremely high
spontaneous fission background and 254Es, available in small quantities (~0.1 mg) only, has a
half-life less than 1 year.
Figs. 2-5 show the (B+Q) values as a function of the atomic number of the projectile, the
projectile being either the heaviest or the lightest isotope of the element with Z number
plotted. As can be seen from the figures, the (B+Q) values with B calculated by the various
models and corrected by formulae (1) are close to one another. The increasing projectile Z
number results finally in cold fusion for all the targets considered.
50
0
40
4
8
12
16
20
24
28
32
40
44
48
B(Bass)
B(Coulomb)
B(Wilcke et al)
B(Wilczynski)
(a)
30
(B + Q) / MeV
36
20
40
30
20
10
10
0
0
-10
-10
208
Pb +
the heaviest projectile isotopes
-20
-30
-20
-30
-40
50
-40
50
40
(B + Q) / MeV
50
40
(b)
30
30
20
20
10
10
0
0
-10
-10
208
Pb +
the lightest projectile isotopes
-20
-30
-40
0
4
8
12
16
20
24
28
-20
-30
32
36
40
44
48
-40
Projectile Z number
Fig. 2. (a) The sum of the fusion barriers calculated by formulae (1) and the Q-values for the
fusion of 208 Pb (arbitrary taken to be the target) and the heaviest isotope of the elements
with the Z numbers plotted on the horizontal axis.
(b) The same as in (a) for the lightest isotope
60
0
50
4
8
12
16
20
24
28
36
40
44
60
B(Bass)
B(Coulomb)
B(Wilcke et al)
B(Wilczynski)
(a)
40
(B + Q) / MeV
32
30
50
40
30
20
20
10
10
0
0
238
U+
the heaviest projectile isotopes
-10
-10
-20
60
-20
60
(B + Q) / MeV
50
50
(b)
40
40
30
30
20
20
10
10
0
Fig. 3. The same as in Fig. 2, but
the target is 238U
0
238
U+
the lightest projectile isotopes
-10
-20
0
4
0
4
8
12
16
20
24
-10
28
32
36
-20
44
40
Projectile Z number
60
50
8
12
16
20
24
28
(B + Q) / Mev
36
40
B(Bass)
B(Coulomb)
B(Wilcke et al)
B(Wilczynski)
(a)
40
30
60
50
40
30
20
20
10
10
0
0
248
Cm +
the heaviest projectile isotopes
-10
-20
-10
-20
-30
-30
60
60
50
(B + Q)/ MeV
32
50
(b)
40
40
30
30
20
20
10
10
0
0
248
-10
-20
-30
-10
Cm +
the lightest projectile isotopes
0
4
8
12
16
20
24
-20
28
Projectile Z number
32
36
40
-30
Fig. 4. The same as in Fig. 2,
but the target is 248Cm
0
4
8
12
16
20
24
28
(a)
40
30
(B + Q) / MeV
32
36
40
B(Bass)
B(Coulomb)
B(Wilcke et al)
B(Wilczynski)
50
40
30
20
20
10
10
0
0
249
Cf +
the heaviest projectile isotopes
-10
-20
-10
-20
-30
-30
50
50
(b)
40
(B + Q) / MeV
50
40
30
30
20
20
10
10
0
0
249
-10
-20
-30
-10
Cf +
the lightest projectile isotopes
0
4
8
12
16
20
24
-20
28
32
36
40
-30
Projectile Z number
Fig. 5. The same as in Fig. 2, but the target is 249Cf.
Reaction with the
heaviest isotope
208
Pb +82Se
238
U + 88Sr
248
Cm + 82Se
249
Cf+82Se
Table 3
Compound
Reaction with the lightest
nucleus
isotope
290
208
116
Pb +84Sr
326
238
130
U + 90Zr
330
248
130
Cm+84Sr
331
249
132
Cf+78Kr
Compound
nucleus
292
120
328
132
332
134
327
134
Table 3 shows the combinations of nuclei that satisfy the criterion (B+Q)  0 and result in
producing compound nuclei with the largest Z values. The results obtained for odd Z
projectiles are similar to the results for even Z projectiles shown in Figs. 2-5 and didn’t
provide for the possibility of the synthesis of elements with Z134. From entrance channel
consideration, combinations of a light isotope of the less heavy element and a heavy isotope of
the heavier element are a bit more advantageous for producing nuclei with the extreme atomic
number in complete fusion reactions.
Fig. 6 shows the driving potential per one projectile mass unit (B+Q)/Aproj. for fusion
reactions involving heavy targets. As can be seen, it is close to zero for the projectile mass
number A ~80. The calculations were carried out using the Wilczynski model [20]. The
other models give similar results.
[B(Wilcz.)+Q]/A, MeV/(m. u.)
4.0
0
10
20
30
40
50
60
70
80
90 100 110 120
4.0
3.6
3.6
3.2
3.2
2.8
208
b
Pb
2.4
238
U
248
Cm
1.6
Cf
1.2
2.0
1.6
249
1.2
2.8
2.4
2.0
0.8
0.8
0.4
0.4
0.0
0.0
-0.4
-0.4
0
10
20
30
40
50
60
70
80
90 100 110 120
Projectile mass number A
Fig. 6. Driving potential per one projectile mass unit versus Aproj.. The B was calculated by
the Wilczynski model and corrected by formulae (1). The targets were 208Pb, 238U, 248Cm and
249
Cf .For every projectile Z, there are two dots referring to the heaviest and the lightest
isotopes.
4. Conclusion
Formulae (1) allow us to obtain fusion barrier values based on a large body of experimental
data on (HI, xn) reactions including those used for the synthesis of the heaviest elements
produced up to now. Analysis based on the (B+Q) criterion ensures an optimum choice of
fusion reaction intended to be used for producing new elements. It can be illustrated with the
situation about element 118, which was intended to be produced in a 208Pb(86Kr,1n) reaction.
The production cross section was predicted to be 670 pb [45]. The observed events
corresponded to cross section of ~2pb [48] and were retracted later [49]. From the standpoint
of our approach, these experiments had very little chance for success since (B+Q)  0 for that
reaction and fusion process is suppressed (see Fig. 2(a)).
According to the calculations presented in section 3, the extreme atomic number for nuclei
producible in the form of neutron evaporation residues in complete fusion reactions involving
heavy ions is 134. In the nuclear reactions 248Cm +84Sr and 249Cf+78Kr, compound nuclei can
be produced at (B+Q)=0÷15 MeV and will be de-excited most probably by evaporating one
neutron. The evaporation residues will be 331134 and 326134, respectively. These nuclei are
close to the boundary of stability against spontaneous fission [9]. It is remarkable that the
extreme atomic numbers deduced from the limitations imposed by the entrance channel of
complete fusion reactions are close to those deduced from the limitations imposed by nuclear
instability owing to spontaneous fission.
1.
2.
3.
4.
5.
6.
References
Yu.Ts. Oganessian et al., Phys. Rev. Lett., v. 83, 3154, 1999
Yu.Ts. Oganessian et al., Phys. Rev. C, v. 62, 041604(R), 2000
Yu.Ts. Oganessian et al., Phys. Rev. C, v. 63, 011301(R), 2000
Yu.Ts. Oganessian et al., Communications of JINR, D7-2002-287, Dubna, 2002
G. Münzenberg, Rep. Progr. Phys., v. 51, 57, 1988
S. Hofmann, Rep. Progr. Phys., v. 61, 639, 1998
7. P. Armbruster, Rep. Progr. Phys., v. 62, 465, 1999
8. S. Hofmann, G. Münzenberg, Rev. Mod. Phys., v. 72, No. 3, 2000.
9. W.D. Myers, Droplet model of atomic nuclei, IFI/Plenum, (N. Y.), 1977
10. R. Smolanczuk et al., Phys. Rev. C, v. 56, 812, 1997
11. P. Möller et al., Atomic Data and Nuclear Data Tables,
v. 66, No. 2, 1997
12. M. Beckerman, Rep. Prog. Phys., v. 51, 1047,1988
13. M. Dasgupta et al., Ann. Rev. Nucl. Part. Sci., v. 48, 401, 1998
14. V.Yu. Denisov, W. Nörenberg, Eur. Phys. J. A v. 15, 375, 2002
15. R. Bass, Lecture Notes in Physics, v. 117, 281, 1980
16. W.W. Wilcke et al., Atomic Data and Nuclear Data Tables, v. 25, 389, 1980
17. J.R. Bondorf et al., Phys. Rev. C, v.15, 83, 1974
18. J. Blocki et al., Annals of Physics, v. 105, 427, 1977
19. W.D. Myers, W.J. Swiatecki, Phys. Rev. C, v. 62, 044610, 2000
20. K. Siwek-Wilczynska, J. Wilczynski, Phys. Rev. C, v. 64, 024611, 2001
21. R.N. Sagaidak et al., J. Phys. G: Nucl. Part. Phys., v. 24, 611, 1998
22. E.D. Donets et al., JETP, v. 43, 11, 1962 (in Russian)
23. E.D. Donets et al., Yad. Fiz., v. 6, 1015, 1965 (in Russian)
24. G.N. Flerov et al., Physics Letters, v. 13, 73, 1964
25. A.N. Andreyev et al., Z. Phys. A, v. 345, 389, 1993
26. G.N. Flerov et al., Nucl. Phys. A, v. 160, 181, 1971
27. Yu.A. Lazarev et al., Phys. Rev. Lett., v. 73, 624, 1994
28. Yu.Ts. Oganessian et al., Phys. Rev. C, v. 64, 054606, 2001
29. H. Gäggeler et al., in: Proc. Int. School-Seminar on Heavy ion Physics, Alushta, USSR,
1983, Dubna, JINR, D7-83-644, p. 41, 1983
30. G. Münzenberg et al., Z. Phys. A, v. 302, 7, 1981.
31. V. Ninov et al., Z. Phys. A, v. 356, 11, 1996.
32. A.V. Eremin et al., JINR Rapid Communications, 6[92]-98, Dubna, 1998, p. 21.
33. F.P. Heßberger et al., Eur. Phys, J. A, v.12, 57, 2001
34. Yu.Ts. Oganessian et al., FLNR Scientific Report 1999-2000, p. 25, JINR, Dubna, 2001
35. F.P. Heßberger et al., Z. Phys. A, v. 359, 415, 1997
36. G. Münzenberg et al., Z. Phys. A, v. 300, 107,1981
37. G. Münzenberg et al., Z. Phys. A, v. 328, 49, 1987
38. S. Hofmann et al., Eur. Phys. J. A, v. 10, 5, 2001
39. S. Hofmann et al., Eur. Phys. J. A, v. 14, 147, 2002
40. G. Audi et al., Nucl. Phys. A, v. 624, 1, 1997
41. W.D. Myers, W.J. Swiatecki, Nucl. Phys. A, v. 601, 141, 1996
42. P. Möller et al., Atomic Data and Nuclear Data Tables, v. 59, 181, 1995
43. V.I. Zagrebaev et al., Phys. Rev. C, v. 65, 014607, 2001
44. A.S. Zubov et al., Phys. Rev. C, v. 65, 024308, 2002
45. R. Smolanczuk, Phys. Rev. C, v. 59, 2634, 1999
46. V.L. Mikheev et al., Yad. Fiz., v. 62, 1231, 1999 (in Russian).
47. V.L. Mikheev et al., Proc. 9th Int. Conf. on Nucl. Reaction Mechanisms, Varenna, Italy,
2000, Ed. by E. Gadioli, Universita Degli Studi Di Milano, Ricerca Scientifica ed
Educazione Permanente, Supplemento, No 115, p. 601, 2000
48. V. Ninov et al., Phys. Rev. Lett., v. 83, 1104, 1999
49. V. Ninov et al., Phys. Rev. Lett., v. 89, 039901, 2002