Journal of Nuclear and Radiochemical Sciences, Vol. 8, No. 2, pp. 63-67, 2007

Peculiarities of Nuclear Fusion in Synthesis of Superheavy Elements
A. K. Nasirov,*, a,b G. Giardina,c A. I. Muminov,b G. Mandaglio,c and R. K. Utamuratova,baJoint Institute for Nuclear Research, Dubna, 141980, Moscow region, Russia
Heavy Ion Physics Department, Institute of Nuclear Physics, 100214, Tashkent, Uzbekistanc
INFN, Sezione di Catania, and Dipartimento di Fisica dell’Universita di Messina, 98166, Messina, Italyb

Received: December 20, 2006; In Final Form: April 23, 2007
The role of entrance channel for reactions with massive nuclei is discussed by comparison of experimental data ofreactions with different mass (charge) asymmetry and leading to different isotopes of the superheavy element Z =112. Three stages (capture, complete fusion, and formation of evaporation residues) of the so called “cold” and“hot” fusion reactions are considered for 70Zn + 208Pb and 48Ca + 238U reactions which were used to synthesize
superheavy elements Z = 112. It is shown that the collisions by the orientation angles 30° < αP < 60° for projectile
and 30° < αT < 45° for the target nucleus lead to the largest cross section in synthesis of superheavy element in the48* = 35 MeV.
Ca + 238U reaction at ECN

1. Introduction
The small probabilities of synthesis of new superheavy elements at GSI (Darmstadt, Germany), Joint Institute for Nuclear
Research (Dubna, Russia), and RIKEN (Wako, Japan) during
the last decade stimulate the experimental and theoretical studies of the nuclear reaction mechanism.1– 4 In preparation ofthese experiments, the main aim is to reach maximum crosssections of the yield of evaporation residues (ER) as a result of
the de-excitation of the heated compound nucleus which isformed in complete fusion of the projectile and target nuclei.
Because the ER excitation function in the synthesis of superheavy elements has very narrow width for “cold fusion” reactions (5–10 MeV) with 208Pb and 209Bi targets5 and the width of
the “hot fusion” reactions with 48Ca projectile on actinide targets6 is more wider (15–20 MeV). It is interesting to compare* > 30 MeV) and “cold” (ECN
* < 25 MeV) fusion reac“hot” (ECN
tions. In the “hot fusion” 30Si + 238U reaction, sufficiently low
ER cross section 70 pb for the synthesis of superheavy element263
Sg in 5n-channel was observed while the isotope 260Sg was
obtained with large cross section 2500 pb in the “cold fusion”
54
Cr + 208Pb reaction. The smallness of the ER cross section in
the “hot fusion” 30Si + 238U reactions is explained by the small
survival probability of the compound nucleus with the excitation energy 50 MeV at de-excitation of 5 neutrons.1,2 The useof the 48Ca beam leads to the relatively high cross section of theevaporation residues due to large binding energy of 48 Ca.
Therefore, the maximum of cross section of the yield of superheavy elements corresponds to 35 MeV while in the “hotfusion” reactions the maximum value of evaporation residues
yield is observed at 50 MeV.7-9
So, for experiments it is important to know the favorable
range of beam energy before experiments. The use of the “coldfusion” reactions with projectiles 50Ti, 54Cr, 56Fe, 64Ni, and 70Zn
on the 208Pb and 209Bi targets succeeded in synthesizing superheavy elements Z = 102, 104, 106, 108, 110, 111, and 112 in
GSI while the use of 48Ca projectile and actinide targets allows
one to synthesize more heavy superheavy elements Z = 114,
115, 116, and 118 in JINR. The last experiments of “coldfusion” reactions were performed in RIKEN where the newelement Z = 113 was observed in the 70Zn + 209Bi reaction.10 Z*Cor responding author. E-mail: nasirov@jinr.r u. Fax: +749621-65084.

= 113 seems to be a heaviest superheavy element which was
obtained in “cold fusion” reaction due to drastic decrease of
fusion probability with increase of the projectile charge number in reactions with 208Pb and 209Bi targets.
The way to obtain nucleus as possible less excited seems tobe preferable but in this case amount of formed compound
nuclei may be very small due to a hindrance at its formation,i.e., very small complete fusion cross section. As a result yieldof superheavy elements will be extremely small to be observed.
Therefore, it is important to increase fusion cross section byincrease of the beam energy. But the survival probability of a
hot compound nucleus should not decrease so much by increaseof excitation energy to avoid decreasing of the yield of ER.
Note we should avoid the large values of compound nucleus
angular momentum (l) which decreases strongly its survival
probability. The actinide nuclei are mainly prolate deformed.
The distribution in the space of the orientation angles of their
axial symmetry axis α to the beam direction is arbitrary. The
dependence of the complete fusion probability on α allows us
to calculate the beam energy providing a large partial fusioncross section with small angular momentum of compound
nucleus. In this work we will analyse the role played by shellstructure and orientation angles of the symmetry axis of colliding nuclei in formation of ER.
The rotated dinuclear system (DNS) is formed as intermediate stage in deep-inelastic collisions, quasiﬁssion, complete
fusion, and fast-ﬁssion reactions with the different lifetime.
The complete fusion of nuclei occurs through the stage of formation of DNS which can evolve to the hot compound nucleus
in competition with breaking up after the intense nucleon transfer between its constituents (quasiﬁssion). In reactions withmassive nuclei, the contributions of the quasiﬁssion fragments
are dominate in comparison with ones of fusion-ﬁssion mechanism. The mass distribution of the quasiﬁssion fragments canhave different shapes including the symmetric shape of fusionﬁssion reaction fragments as a function of the beam energy,
initial mass asymmetry, and shell structure of reacting nuclei.
In the analysis of experimental data there are diffculties in separation of fragments according to their origination to estimate
the experimental cross sections of different mechanisms. It is
important to study all three stages of reaction with massive
nuclei in synthesis of superheavy elements to determine theoptimal beam energy providing as possible larger values of the
ER cross sections.

© 2007 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 10/19/2007

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J. Nucl. Radiochem. Sci., Vol. 8, No. 2, 2007

TABLE 1: Comparison of the main characteristics of the“cold” and “hot” fusion in case of the 70Zn + 208Pb and 48Ca
+ 238U reactions used to synthesize superheavy element Z =112
Zn + 208Pb

δW / MeV

–5.08

122

30

40

1

10

Ca + 238U

50

48

60

Ca +

238

–5.94

7.14

6.95

* / MeV
ECN

12

35

+1.8
0.5 +1.1–0.5 (Reference 5) 2.5 –1.5 (Reference 6)

σ theorER / pb
σ fus / nb

0.7 (Reference 11)

5.2 (Reference 12)

0.3

50

σ cap / mb

2.5

40

δW: shell corrections to binding energy of compound nucleus.
* : excitation energy of comSn: neutron separation energy. ECN
pound nucleus. σER: maximum values of the evaporation residue cross section. σfus and σcap : theoretical complete fusionand capture cross sections, respectively.

2. Three Stages of the Evaporation Residues Formation
The three stages are: (a) capture of projectile-nucleus by
nucleus of target and formation of the molecular-like dinuclear
system, (b) complete fusion which is transformation of thedinuclear system into a hot compound nucleus in competition
with the quasiﬁssion process, and (c) formation of the ER after
emission of neutrons and charged particles from the heatedcompound nucleus in competition against ﬁssion. The experiments of synthesis of superheavy elements in the Flerov
Laboratory of Nuclear Reaction showed that to synthesize theelement Z = 112 the “hot fusion” 48Ca + 238U reaction6 is more
preferable than so called “cold fusion” 70Zn + 208Pb reaction.5
It is seen in comparison of the measured cross sections for the
ER for these reactions presented in Table 1. Theoreticalresults11,12 obtained in description of this experimental data
allows us to estimate the dependence of the synthesis probability of Z = 112 element on each stage of the reaction mechanism,for example, capture and fusion cross sections, σcap and σfus,
respectively. Their maximal values are presented in Table 1.
The advantage of the “hot fusion” reaction in comparison with“cold fusion” at synthesis of the superheavy element Z = 112
seems to be clear according to experimental data. It is
explained by the calculated larger values of capture σcap andfusion σfus cross sections for the 48Ca + 238U reaction in comparison with that for the 70Zn + 208Pb reaction (Table 1). The
shell corrections to binding energy of compound nucleus 286112
is larger by 0.9 MeV in comparison with one of 278112. The
neutron separation energies of the formed compound nuclei arecomparable. But the surviving probability of the compound
nucleus 286112 formed in the former reaction is smaller thanthat of the compound nucleus 278112 formed in the 70Zn + 208Pb
reaction due to large excitation energy E*CN. The main factor
which provides the observable cross section of the ER is thelarge fusion probability of nuclei in the 48Ca + 238U reaction. In
Figure 1, we compare the experimental and calculated crosssections of capture, complete fusion, and formation of ER after
neutron emission from the compound nucleus for the 48Ca +238
U reaction. The capture cross section is, qualitatively, ingood agreement with experimental data whereas the calculated
fusion cross section is much smaller than the extracted values
for fusion from the measured data of reaction fragments. It
seems to us that the experimental data for ﬁssion fragments cancontain a contribution of the quasiﬁssion fragments which are

286

80
6

112

Capture (Exp. Oganessian et. al.)Fusion (Exp. Oganessian et. al.)Capture (DNS-theory)
Fusion (DNS-theory)
Ev.Res.(ASM-calc)
Oganessian et al

-1

10

112

70

U=

286

Sn / MeV

σ exp
ER / pb

20

-3

10

Bfis

4

2

-5

10

-7

10

Bfis / MeV

Compound nucleus

278

48

10

σ /mb

70

E* /MeV
3

0

-9

10

-2

-11

10

220

230

240

250

260

270

280

290

ELab. /MeV

Figure 1. Comparison of the experimental6 (symbols) and calculated12 (lines) excitation functions of capture, complete fusion, andformation of evaporation residues after neutron emission from theexcited compound nucleus for the 48Ca + 238U reaction (left axis).
Fission barrier of the excited and rotated compound nucleus as afunction of beam energy (right axis) is also shown.

formed without formation of compound nucleus but their mass
distribution may have a shape of the one of ﬁssion fragments.
Unfortunately, in analysis of the experimental data, it is diffcult
to separate the pure fusion-ﬁssion fragments from the fragments of quasiﬁssion. Due to full momentum transfer in bothreactions their fragments have similar total kinetic energy distribution. As a function of the initial orbital angular momentum and beam energy of the projectile the mass distribution of
the quasiﬁssion fragments can be overlapped with the one offusion-ﬁssion fragments. In these experiments the angular distribution was not measured and, therefore, there is an ambiguity in extraction of fusion cross section from the measured
binary fragments of full momentum reactions. Theoretical
calculations are not free from some assumptions and freeparameters as a radius parameters r0. Therefore, the exact ratioof contributions of quasiﬁssion and complete fusion fragments
into measured data is still questionable.
In Figure 1, the ﬁssion barrier of the heated compound
nucleus is also presented as a function of excitation energy.
The cross sections of evaporation residues formation are
described well by use of the advanced statistical model. In thismodel, the damping of the nuclear shell correction by increaseof angular momentum of compound nucleus is taken into
account. The spin distribution of compound nucleus plays thedecisive role in calculation of survival probability. It is formedby the partial fusion cross sections which are determined by
the features of potential energy surface13,14 of DNS and friction
coeffcients (radial, tangential)15 for the given value of the beamenergy and initial orbital angular momentum L 0 . Note thepotential energy surface is a function of the orientation anglesof the axial symmetry axis of reacting nuclei.16 The small crosssection at synthesis of the 277112 element in the 70 Zn + 208Pb
reaction is explained by the large hindrance for complete fusion(see Figure 2) in “cold fusion” reactions. The strong hindrance
to fusion is connected with the location of the initial charge
asymmetry of this reaction in the valley corresponding to themagic nucleus 208Pb which is seen in Figure 5. In the next section we will compare the capture and fusion cross sections forreactions under discussion.
2.1. Peculiarities of capture and fusion in hot and cold
fusion reactions. In our model (see References 13 and 14), thecapture occurs if the heavy-ion collision path is in the potential
well after overcoming of the Coulomb barrier and dissipationof the main part of the relative kinetic energy. In the deep
inelastic collisions projectile or projectile-like fragment over-Peculiarities of Nuclear Fusion in Synthesis of Superheavy Elements
E* /MeV
100

8

10

12

16

18

6

1.5

0.01

5

Zn +

208

Pb =

278

3

112

1E-6

2

1E-8

1

1E-10

0

1E-12
336

338

340

342

344

346

348

350

55
50

45

E 40
CN
/M35 30
eV
25 0

10

20

30

30

50

40

0.0

L0/ h

(L)

(mb/h)

projectile 45°

projectile 30°

1.5target 30°

55

50

45

CN

30

40

/M 35
eV 30

20
10

25

40

50

(L)

dσfus/dL(mb/h) 1.5

target 0°

1.0

1.0

0.5

0.5

0.0

55
50
45

E 40 35
CN/M 30
eV 25 0

/h
L0

10

30

20

40

50

0.0

L0/ h

0

Figure 3. Dependence of the partial fusion cross sections on the orientation angles of symmetry axis of colliding nuclei ( β2 (238U) = 0.21;
β2 (2 + -excitation 48Ca) = 0.1 from Reference 17) as a function of theinitial orbital angular momentum L 0 and excitation energy of com*.
pound nucleus ECN

48(mb/h)

projectile 60°
target 30°

55
50

45

0

10

20

30
L0

50

11
10
9
8
7
6
5
4
3
2
1
0

(L)

dσcap/dL 11(mb/h)

projectile 30°
target 75°
55
50
45
40
35
30
25

eV
/M

E 40
35
CN
/M 30
eV 25

40

238

Ca+ U

(L)

dσcap/dL

E CN

comes the Coulomb barrier from inner part to outside (exitchannel) due to the smallness of dissipation of kinetic energy(see ﬁgure 1 in Reference 11). It is clear that deep inelastic
collision occurs at higher energies of projectile above the
Coulomb barrier than in the case of capture for a given value ofthe orbital angular momentum, because the friction coeffcient
is not strong to trap all trajectories into potential well.16 The
amount of energy above the Coulomb barrier determines whichof these two processes occurs. If capture occurs, then we calculate the competition between quasiﬁssion and complete
fusion. In collision of deformed nuclei with different orientations proportion between contributions of deep inelastic collisions and capture, as well as proportion between quasiﬁssion
and complete fusion are different at the same beam energy andorbital angular momentum. To reach an agreement with theexperimental data for capture cross section we take into
account the deformation parameters connected to the 2 +and 3−
collective excitations in the spherical nuclei. It was done byuse of the mean-square values of the deformation parameters17,18 corresponded to above mentioned excitations. The partial fusion cross-sections, which are used to calculate the ER
cross-section along the de-excitation cascade of compound
nucleus, are obtained by averaging over all orientations (indetail see Reference 16). Analysis of the dependence of thepartial cross sections of complete fusion on the orientation
angles of colliding nuclei showed that large fusion probability
with the small values of compound nucleus angular momentum
is observed in the range 30°–60° for the orientation angles ofsymmetry axis for projectile and 60°–75° for ones of the target
nucleus. Some examples are shown in Figure 3 for the 48Ca +238
U reaction. So the large fusion probability is obtained at thesmall values of angular momentum in heavy ion collisions
when orientation angles of the projectile and target symmetry
axis are in the corresponding above mentioned ranges. Thiscase is shown on the right top panel of Figure 3. It is seen thatpartial fusion cross section is small for the around tip–tip (0°–0°) and side–side (90°–90°) orientations. In the former casequasiﬁssion is a dominate channel while in the latter case capture cross section is small due to shallow potential well. It isseen from Figure 4. The maximum cross sections corresponds
to those values of beam energy at which the three events ofsynthesis of superheavy element Z = 112 was observed in the
Flerov Laboratory of Nuclear Reactions (see Figure 1). We

10

0

20

dσfus/dL

E

Figure 2. Comparison of the experimental data of the evaporation
residues5 (symbols) and calculated11 (lines) excitation functions of
capture, complete fusion, and formation of evaporation residues after
neutron emission from the excited compound nucleus for the 70Zn +208
Pb reaction (left axis). Fission barrier of the excited and rotatedcompound nucleus as a function of beam energy (right axis).

0.5
55
50
45
40
35
30
25

h
L 0/

-1

Ebeam / MeV

1.0

target 75°

0.0

50

40

1.5

projectile 30°

0.5

4

Bfis
70

1.0

Bfis /MeV

CaptureComplete fusion
Ev.Res. theor
Exp. (Hofmann)(L)dσfus/dL(mb/h)eV/M
E CN

Cross sections /mb

1

238

Ca+ U

dσfus/dL(mb/h)

projectile 60°
target 30°

1E-4

48

(L)

14

65

J. Nucl. Radiochem. Sci., Vol. 8, No. 2, 2007/h(L)

dσcap/dL

11
10
9
8
7
6
5
4
3
2
1
0
50
40

target 30°

55

50

45

E

CN

40

/M 35
eV 30

10
25

0

20

30

/h
L0

40
30
L0/ h

20

50

(L)

dσcap/dL(mb/h)
projectile 45°

0

10

10
9
8
7
6
5
4
3
2
1
0

(mb/h) 11

projectile 0°target 45°

55

50

45

20
E 40 35
CN /M
10
eV 30 25 0

30

10
9
8
7
6
5
4
3
2
1
0
50
40
/h
L0

Figure 4. Same as in Figure 3 but for the partial capture cross sections.

Figure 5. Potential energy surface (left panel) and driving potential(right panel) for the cold and hot fusion reactions leading to Z = 112.
The nucleus-nucleus potential (l = 0) for the 70Zn + 208Pb reaction anddriving potential for the dinuclear system are showed by arrows.
Intrinsic fusion barrier (B*fus (Zn)) for the “cold” fusion is sufficiently
larger than the one (B*fus (Ca)) for the “hot” fusion reaction.

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J. Nucl. Radiochem. Sci., Vol. 8, No. 2, 2007

came to our conclusion that this beam energy value Elab = 235
MeV is favorable to observe the largest cross section of evaporation residues due to relatively large values of the partial
fusion cross section with small angular momentum (L < 25h)of compound nucleus is obtained.
We calculate the cross section of ER formed after each step
x of the de-excitation cascade after the emission from the hot
CN of particles ν (x)n + y(x)p + k(x) α + s(x) (where ν, y, k, ands are numbers of neutrons, protons, α-particles, and γ -quanta)
by formula(x)
σ ER(Ec.m.) =ld

Σ (2l+1) σ

(x−1)
l

(Ec.m.)W (x−1)
sur (E c.m. + Qgg,l),

(1)

l=0

where σl(x−1)(Ec.m.,l) is the partial formation cross section of theexcited intermediate nucleus of the (x−1)th step and W (x−1)
sur (E c.m.
+ Qgg,l) is the survival probability of the (x−1)th intermediate
nucleus against ﬁssion along the de-excitation cascade of CN.
It is clear that σl(0)(Ec.m.,l) = σl(fus)(Ec.m.,l). Our method of calculation (also including the advanced statistical method19,20) of
the ER cross sections takes into account the damping of theshell correction in the ﬁssion barrier as a function of the excitation energy and orbital angular momentum. This is accounted
for the various steps of the de-excitation cascade of the compound nucleus leading to the ﬁssion fragments or the ER nuclei
in the exit channel.13,14,21
The fusion cross section is related to the number of events
corresponding to the transformation of the dinuclear system
into compound nucleus in competition with the quasi-ﬁssion
process. It is deﬁned by the product of the partial capture crosssection and the related fusion factor PCN which allows to take
into account the competition between the complete fusion andquasiﬁssion processes:
(l)
σ (l)
fus (E c.m.) = σ capture (E c.m.)PCN (E c.m.,l).

(2)

The capture cross section is calculated by solution of the
dynamical equations of motion for radial distance and orbital
angular momentum (details see in References 13, 14, and 16).
Calculations showed that a “window” of the l values leading tocapture may appear. For example, there is no capture with thevalues l < 30 of angular momentum at Elab > 225 MeV (E CN =28.1 MeV) for the small orientation angles of target and projectile symmetry axis as shown in the right bottom panel of Figure
4.
During the formation of the dinuclear system at the capture
stage there is an intense nucleon exchange between reacting
nuclei. In the quasiﬁssion and fusion processes, an intense
mass transfer takes place and, in depending on the entrance
channel, the mass asymmetry degree of freedom may be fullyor partially equilibrated.22 As a result, while DNS exists, wehave an ensemble {Z} of the DNS conﬁgurations which contribute to the competition between complete fusion andquasiﬁssion with the probabilities {Y Z}. Position of the maximum of the mass distribution is determined by the peculiaritiesof the nuclear shell structure and lifetime of the dinuclear system.16 Therefore, the statistical calculation of PCN (E*DNS,l) is
performed by the formula:* ,l) =
PCN(EDNS

Zmax

Σ Y (E* ,l)P (E* ,l),
Z

DNS

(Z)
CN

DNS

(3)

Z=Zsymwhere Y Z (E*DNS,l) is the probability of population of the DNS
conﬁguration (Z, Z tot − Z) at E*DNS (Z) and l; Z sym = (Z1 + Z 2)/2;
Z max corresponds to the charge asymmetry where the driving
potential reaches its maximum (B*fus (Z max) = 0) (see References
13 and 14);* ,l) =P (EDNS(Z)
CN

ρ(E*DNS(Z) – B*fus (Z,l)),*ρ(E DNS(Z) – B*fus (Z,l)) + ρ(E*DNS(Z) – Bqf (Z,l))(4)

where the intrinsic fusion barrier B*fus (Z,l) being a function of
the charge asymmetry and angular momentum of DNS is foundfrom the driving potential13,14,16 (see Figure 5). The quasiﬁssion
barrier B qf (Z,l)) for the considered fragment depends on its
charge number and is determined by the depth of potential wellof the nucleus-nucleus interaction of the DNS fragment with its
partner nucleus. Therefore, transformation of the DNS into
compound nucleus by complete fusion is a function of thecharge asymmetry of the DNS constituents.
In eq 4, ρ(E*DNS(Z) – B*K(Z,l)) is the DNS level density calculated on the quasiﬁssion and intrinsic fusion barriers (BK = Bqf,
B*fus). For more details see Reference 16.
Both characteristics of the fusion excitation function,
namely, its maximum value and width (energy window for thecomplete fusion) are related to the ratio between B*fus and Bqf for
the given reaction.
3. Conclusion
Hot fusion reactions with the 48Ca-projectile can be successfully used in synthesis of superheavy elements due to reducingof excitation energy of compound nucleus up to 35–40 MeV.
The loss of events by high intensity of ﬁssion should be compensated by large fusion cross section in comparison with 70Zn
+ 208Pb reaction. Advantage of the use of the double magic48
Ca projectile allowed us to decrease of 15 MeV excitationenergy of compound nucleus in synthesis of superheavy elements up to Z = 118. The observable values of the evaporation
residues is provided by the large partial fusion cross section atas possible as low excitation energy and angular momentum ofcompound nucleus.
In our calculations, E*CN = 35 MeV corresponds to the beamenergy which is 5–10 MeV higher than interaction barriers at
the projectile orientation angles 30° < αP < 60° and that 30° <αT < 45° for the target nucleus. These angles are taken relative
to the beam direction. In case of the 30Si + 238U reaction, E*CN =50 MeV corresponds to the similar intermediate orientation
angles. The equatorial collisions make relatively small contributions in comparison with the above mentioned angles.
Acknowledgement. One of authors (A.K.N.) thanks Drs. Y.
Aritomo, K. Hagino, H. Ikezoe, A. Iwamoto, K. Morita, K.
Nishio, M. Ohta, T. Ohtsuki, N. Tagikawa, W. Scheid, V. V.
Volkov, and T. Wada for fruitful discussions and he is gratefulto the Japan Society for the Promotion Science for support his
research in collaboration with scientists of Japan Atomic
Energy Agency and to Drs. Katsuhisa Nishio and Yoshihiro
Aritomo, as well as Japanese colleagues in the Advanced
Science Research Center of JAEA, RIKEN, and Konan andTohoku Universities for warm hospitality.
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