ANALYSIS OF YIELDS OF FUSION-FISSION AND QUASIFISSION FRAGMENTS
IN HEAVY ION COLLISIONS
A. K. Nasirov 1,2, G. Giardina3, F. Hanappe4, S. Heinz5, S. Hofmann5,
G. Mandaglio3, M. Manganaro3, A. I. Muminov2, W. Scheid6
1
Joint Institute for Nuclear Research, Dubna, Moscow region, Russia
2
Institute of Nuclear Physics, Tashkent, Uzbekistan
3
INFN, Sezione di Catania, and Dipartimento di Fisica dell’Università di Messina, Italy
4
Université Libre de Bruxelles, Bruxelles, Belgium
5
Gesellschaft für Schwerionenforschung, Darmstadt, Germany
6
Institut für Theoretische Physik der Justus-Liebig-Universität, Giessen, Germany
The decrease of the evaporation residues yield in reactions with massive nuclei is explained by increase of the
competition between quasifission and complete fusion processes and by the decrease of the survival probability of the
heated and rotating compound nucleus against fission. The experimental data on the yields of evaporation residues,
fusion-fission and quasifission fragments in the 48Ca + 154Sm reaction are analyzed simultaneously in the framework of
the theoretical method based on the DNS concept and advanced statistical model. The measured yields of evaporation
residues and fission fragments for the 48Ca + 154Sm reaction have been well reproduced by using the partial fusion and
quasifission cross sections obtained in the DNS model. Such way of calculation is used to find optimal conditions for
the synthesis of the new element Z = 120 (A = 302).We compare the excitation functions of evaporation residues of the
three reactions 54Cr + 248Cm, 58Fe + 244Pu, and 64Ni + 238U. Our estimations show that the 54Cr+248Cm reaction is
preferable in comparison with the two others because the excitation function of the evaporation residues is some orders
of magnitude higher and the optimal energy for the synthesis is lower than that for the 58Fe + 244Pu and 64Ni + 238U
reactions.
1. Introduction
The correct estimation of the fusion probability is not an easy task for the reactions with massive nuclei. Different
theoretical models use different assumptions about the fusion process they can give different cross sections. The
experimental methods of estimating the fusion probability depend on the unambiguity of identification of the complete
fusion reaction products. The problem is that quasifission fragments can be considered as fusion-fission fragments when
there is overlap of their mass (charge) and angular distributions. As a result the complete fusion cross sections may be
overestimated. We know that quasifission fragments show anisotropic angular distributions [1-2] and this is a way to
separate them from the fusion-fission fragments which should have isotropic angular distribution. But fission fragments in
reactions with heavy ions also show anisotropic angular distributions which is explained by the assumption that an
equilibrium K-distribution is not reached (K is the projection of the total spin of the compound nucleus on its axial
symmetry axis). Our recent calculations have shown that, at some values of the orbital angular momentum, the angular
distribution of quasifission fragments may be isotropic. This is discussed in Section 2. As example, we consider the
48
Ca + 154Sm reaction which was experimentally studied in detail in Ref. [3]. In Section 3, we present results of estimation
of the evaporation residue yields to find the preferable reactions for synthesizing the superheavy element Z = 120.
2. About overlaps of the fusion-fission, quasifission and fast-fission fragments distributions
All reaction channels with the full momentum transfer take place through the stage of the dinuclear system (DNS)
formation and can be called capture reactions. The formation of the compound nucleus (CN) in reactions with massive
nuclei has a hindrance: not all of the dinuclear systems formed at capture of the projectile by the target-nucleus can be
transformed into CN. The decay of the DNS into two fragments without passing the stage of the CN formation we call
quasifission. In the fast-fission reactions a mononucleus is formed with very large angular momentum LCN and its
fission barrier disappears. Therefore, the fast rotating mononucleus goes immediately to fission forming two fragments
without reaching of the equilibrium stage of a CN.
Fig. 1 taken from Ref. [3] shows the overlap of the measured mass distributions of the 48Ca+154Sm reaction products
in the mass range 55 < A < 145. Upper panel presents the data for the beam energy corresponding to excitation energy
*
of CN of ECN
= 63 MeV and lower panel corresponds to the excitation energy 49 MeV. In Ref.[3], the measured data
approximated by the solid Gaussian lines of Fig.1 are interpreted as fusion-fission products. The variances of the mass
distribution of fission fragments were calculated simply by using the saddle point temperature T by formula (1)
σ M2 = (98.1 ± 15.1)T + (0,05 ± 0.01) <I2>
(1)
The large open circles correspond to the symmetric part of the mass-angular distributions, i.e. to the isotropic
angular distribution. The calculations performed in the framework of the DNS model [see Refs. 5 - 6] showed that at
lower energies the contribution of fusion-fission (dashed line in the lower panel of Fig. 2) to the yield of binary
fragments is small in comparison with quasifission. At low energies the projectile-like fragments (A < 55) give a large
342
Fig. 1. (from Ref. [3]). Mass distributions obtained for
the 48Ca + 154Sm reaction (small solid circles) for the two
beam energies corresponding to excitation energies of
*
compound nucleus ECN
= 49 and 63 MeV. Solid lines
are Gaussians with variances according to Eq. (1), large
open circles correspond to the symmetric part of the
mass-angular distributions; solid squares represent the
quasifission component and dashed lines are the
Gaussian fits to the quasifission component.
Fig. 2. Comparison of the DNS model results for the
capture, complete fusion, quasifission, fast-fission and
evaporation residues cross sections with the measured data
of fusion-fission and quasifission obtained from Ref. [3] and
with data of evaporation residues obtained from [4].
contribution to the quasifission cross section since the excitation energy of the DNS is small. According to the results of
this work the quasifission (thick solid line) is the dominant channel in comparison with the fusion-fission, total
evaporation residues (dashed-dot-dot line) and fast-fission (thin solid line) channels. At lower energies, our capture
cross section overestimates the experimental data because in the analysis of the reaction products the authors of Ref. [3]
considered the restricted mass range 55 < A < 145 with the result that they lost a part of the captures related to
contributions of the quasifission fragments with Aqf < 55 :
σ c( ae xp p ) ( E c . m . ; A q f ) = σ E( eRx p ) ( E c . m . ) + σ
(exp)
fis s
( E c . m . ) + σ q( efisx ps ) ( E c . m . , A q f ) .
(2)
The experimental and theoretical capture cross sections come closer by increase of the beam energy due to a shift of
the maximum of the DNS mass distribution to the complete fusion region or to the mass symmetric region: the amount
of the lost part of the capture cross section decreases. Our capture cross section includes the fast-fission contribution
too. Our opinion is that the data on the fusion-fission cross section included some part of the quasifission fragments
which overlap with the mass and angular distributions of the former one. To show this we calculated the angular
distribution of the quasifission fragments. The angular distributions of the quasifission fragment 58Cr calculated as
function of the orbital angular momentum by the method presented in Ref. [7] are presented in Fig. 3. At
*
Ec.m .= 138 MeV ( ECN
= 48 MeV) for LDNS > 35 = the rotational angle is sufficiently large and the angular distribution
may be nearly isotropic. The partial cross sections for the decay of DNS after rotation on the given angle are presented
in Fig. 3, c for this energy. The maximum of the angular distribution moves to small angles at larger energies: at
*
Ec.m = 154 MeV ( ECN
= 63 MeV) the largest part of the fragments goes to the forward and backward angles (see
Fig. 3, b) and the maximum of the angular distribution is concentrated around ϕ DNS = 15o in the center of mass system.
This conclusion is confirmed by our analysis of the measured angular momentum distributions of the CN in Ref. 3.
Results of the comparison are presented in Fig. 4. The deviation of the results for < LCN > of this work from
experimental data at Ec.m.= 138 MeV is explained by the large contribution of quasifission fragments.
343
Fig. 3. The rotational angle of the dinuclear system as a function of the orbital angular momentum (a) and (b), and the
angular distribution of the yield of quasifission fragments (c) and (d) at energies Ec.m. = 138 and 154 MeV,
corresponding to the excitation energies of the compound nucleus ECN = 49 and 63 MeV.
This way of the analysis of the experimental data was
used to estimate and make predictions which of the
reactions 54Cr + 248Cm, 58Fe + 244Pu, and 64Ni + 238U is
preferable to synthesize the superheavy element Z = 120.
The results of the calculations and discussions are
presented in the next Section 3.
3. The role of charge asymmetry and nuclear shell
structure in the yield of reaction products
The advantage of the cold fusion reactions is a large
survival probability by emission of one or two neutrons
from the heated CN. This way was used to obtain the
first superheavy elements Z = 110 (darmstatdium), 111
(roentgenium) and 112 (see Refs. [8]), as well as element
Z = 113 [9]. The grave disadvantage of “cold fusion”
Fig. 4. Comparison of the calculated angular momentum reactions is the dominance of the quasifission process as
channel causing hindrance in transforming the DNS into
distribution of a compound nucleus with the experimental
data from Ref. [3]. The presence of the quasifission a compound nucleus. According to the DNS model, for
the more mass symmetric reactions, the intrinsic fusion
contribution in the measured data is noticeable at low
barrier is larger in comparison with mass asymmetric
energies.
ones. But the quasifission is not such a strong hindrance
in mass asymmetric “hot fusion” reactions. The events proving the synthesis of the more heavy new elements Z = 114,
115, 116, 118 were observed in the reactions with 48Ca ions on the actinide targets 244Pu, 243Am, 248Cm and 249Cf,
respectively, at the Flerov Laboratory of Nuclear Reaction in Dubna [10]. The interaction time and dynamics of the
initial stage play a crucial role for the formation of reaction products at the final stage of the process. Our analysis
showed that the potential energy surface and friction coefficient are important quantities to determine the angular
momentum and excitation energy distributions between fragments forming the DNS. In the DNS model the capture and
fusion stages are studied in detail to describe or to interpret experimental data. The observed hindrance of complete
fusion in reactions with massive nuclei is connected with the intrinsic fusion barrier B *fus which is sensitive to the mass
asymmetry and shell structure of the nuclei in the entrance channel. It is determined by the peculiarities of the potential
energy surface U(Z, A, R) [5, 6] calculated as a function of a fragment charge Z for the DNS leading to Z = 120 and
A = 302.. In Ref. [6], we discussed the difference in the yields of evaporation residues in different reactions leading to
*
and barrier
the same CN. It was shown that the relationship between the excitation energy of dinuclear system E DNS
B *fus indicates which reaction is better in comparison to the other two ones to obtain an expected evaporation residue
344
with larger cross section. The potential energy surface is
calculated as a sum of the mass balance for DNS
fragments and the nucleus-nucleus interaction potential
Vnuc-nuc(Z, R):
U(Z, A, R) = B1(Z) + B2(Ztot - Z) +
+ Vnuc-nuc(Z, R) - BCN(Ztot),
Fig. 5. Potential energy surface calculated for the DNS
configurations leading to formation of the compound
nucleus Z = 120 and A = 302 and quasifission fragments as
a function of charge number of a fragment and the relative
distance between the centers of fragments. The initial
points for the dinuclear systems formed in the 54Cr +
+ 248Cm, 58Fe + 244Pu, and 64Ni + 238U reactions are shown
by circle, X and ∇, respectively.
(3)
where B1(Z), B2(Ztot - Z) and BCN(Ztot) are the ground
state binding energy of the DNS fragments 1 and 2, and
compound nucleus, respectively [5, 6]. The potential
energy surface for the reaction leading to the CN 302120
is presented in Fig. 5. Our calculation and analysis
showed that among the three 54Cr + 248Cm, 58Fe + 244Pu,
and 64Ni + 238U reactions the first one is preferable to
synthesis of the superheavy element Z = 120. The results
of calculation of capture, complete fusion and
evaporation residue formation are presented in Fig. 6.
From these figures it is seen that the 54Cr + 248Cm
reaction is advantageous due to the small intrinsic fusion
barrier B *fus because it is placed close to the maximum
(“saddle point”) to the way of fusion valley (to small values of Z). The second reason is that the quasifission barrier for
this reaction is larger because it is a more charge asymmetric one. The relatively better mass balance leads to formation
of a compound nucleus with smaller excitation energy which allows it to survive against fission and to be observed as a
new superheavy element Z = 120.
Fig. 6. Calculated capture and fusion cross sections for the 54Cr + 248Cm, 58Fe + 244Pu, and 64Ni + 238U reactions (upper
panels) and evaporation residue cross sections in the 2n, 3n, 4n, and 5n channels (lower panels).
4. Conclusions
It is important to analyze more accurately the experimental yields of binary fragments to establish more realistic
fusion and quasifission cross sections. The overlaps of angular distributions of their fragments and their mass
distributions may be strong. The information about the fusion mechanism can be very useful to estimate the preferable
reaction for the synthesis of superheavy elements by the experimental study of fusion-fission fragments. Among the
three reactions 54Cr + 248Cm, 58Fe + 244Pu, and 64Ni + 238U the first one is preferable for the synthesis of the element
Z = 120.
Acknowledgments
This work was performed partially under the financial support of the DFG, RFBR and INTAS which are thanked.
Authors AKN and GG are also grateful to the Fondazione Bonino-Pulejo of Messina for the support received in the
collaboration between the Dubna and Messina groups.
345
REFERENCES
1. Toke J. et al. Quasi-fission - the mass-drift mode in heavy-ion reactions // Nuclear Physics A. - 1985. - Vol. 440. P. 327 - 365.
2. Shen W.Q. et al. Fusion and quasifission in U-induced reactions // Phys. Rev. C. - 1987. - Vol. 36. - P. 115 - 142.
3. Knyazheva G.N. et al. Quasifission processes in 40,48Ca + 144,154Sm reactions // Phys. Rev. C. - 2007. - Vol. 75. P. 064602(13).
4. Stefanini A.M. et al. Fusion-evaporation cross-sections for 48Ca + 154Sm near the Coulomb barrier// Eur. Phys. J. A. 2005. - Vol. 23. - P. 473 - 480.
5. Fazio G. et al. Formation of heavy and superheavy elements by reactions with massive nuclei // Eur. Phys. J. A. 2004. - Vol. 19. - P. 89 - 104.
6. Fazio G. et al. Strong influence of the entrance channel on the formation of compound nuclei 216,222Th and their
evaporation residues // Phys. Rev. C. - 2005. - Vol. 72. - P. 064614(14).
7. Nasirov A.K. et al. Angular anisotropy of the fusion-fission and quasifission fragments // Eur. Phys. J. A. - 2007.
Vol. 34. - P. 325 - 339.
8. Hofmann S., Munzenberg G. The discovery of the heaviest elements // Rev. Mod. Phys. - 2000. - Vol. 72. - P. 733 777.
9. Morita K. et al. Experiment on the Synthesis of Element 113 in the Reaction 209Bi(70Zn, n)278113 // J. Phys. Soc.
Japan. - 2004. - Vol. 73. - P. 2593 - 2596.
10. Oganessian Yu. Ts. et al. Measurements of cross sections and decay properties of the isotopes of elements 112, 114,
and 116 produced in the fusion reactions 233,238U, 242Pu, and 248Cm + 48Ca // Phys. Rev. C. - 2004. - Vol. 70. P. 064609(14).
346