Production of 100 Sn in fusion reactions via cluster emission channels

The possibilities of production of the doubly magic nucleus Sn in complete fusion and quasifission reactions with stable and radioactive ion beams are investigated within a dinuclear system model. The excitation functions for production of the exotic nuclei 100−103Sn via cluster emission channels are predicted for future experiments.


Introduction
100 Sn can be produced both in light particle and the cluster emission channels in fusion reactions.In Ref. [1], these possibilities were studied by measuring the production cross sections of very neutron-deficient isotopes of nuclei near 100 Sn in the reactions 58 Ni+ 50 Cr and 58 Ni+ 58 Ni.In these reactions both the evaporation and the cluster emission channels lead to similar production cross sections of exotic nuclei near 100 Sn.Because the probability of cluster emission increases with decreasing N/Z ratio of the compound nucleus (CN) [2], the cluster emission channels might become more important in the reactions with neutron-deficient radioactive ion beams.For instance, to produce 100 Sn in the 12,14 C emission channels, one can employ the reactions leading to the CN 112 Ba or 114 Ba.In the present work, the excitation functions for production of the exotic nuclei channels in the fusion and quasifission reactions are predicted.Our calculations are based on the dinuclear system (DNS) model [2,3].The DNS model was successfully applied for the description of charge and mass distributions of products of the fusion and quasifission reactions.The model was able to reproduce the absolute cross sections for individual isotopes within a factor of 2-3 in the considered reactions so far [2,3].

Model
Here, we briefly present the main ingredients of the model and the more details can be found in Refs.[2,3].DNS model describes an evolution of the charge and mass asymmetry degrees of freedom, which are defined here by the charge and mass (neutron) numbers Z 1 and A 1 (N 1 ) of light nucleus of the DNS, and relative distance R coordinate.According to the model, there are nucleon drift and nucleon diffusion between the DNS nuclei, which lead to the formation of excited CN and DNS configurations (DNS with different Z 1 and A 1 ) with probabilities depending on the potential energy surface and temperature of the system.The cross section of the residual nucleus with certain mass number A and charge number Z is given as where σ cap is the partial capture cross section which is calculated using the Hill-Wheeler formula.The probability for the production of certain residual nucleus (Z,A) from the excited entrance channel DNS in a distinct decay channel is described by W sur Z,A (E c.m. , J).To calculate W sur Z,A (E c.m. , J), one has to find the formation-emission probability W Z 1 ,A 1 (E c.m. , J) of a certain light particle or cluster (Z 1 ,A 1 ) from the excited system [2].Formation probabilities and decay barriers are calculated using the double folding nucleus-nucleus potential with Skyrme-type density dependent effective nucleon-nucleon forces [4].Angular momentum dependence of barriers are determined from centrifugal component of potential energy of DNS and CN configurations.

Results
The difficulties of the production of 100 Sn in fusion-evaporation reactions are mainly related with the drastically small probability of neutron emission  The production of 100 Sn in the fusion and quasifission reactions via cluster decay channels is mainly connected with the emission of 12,14 C due to the largest emission probability of carbon among heavy clusters.Hence, we consider the reactions 56,58 Ni + 58 Ni and 72 Kr + 40 Ca leading to the CN of barium.In Fig. 1, we present the calculated excitation functions for the production of 100−103 Sn in the reactions 56,58 Ni + 58 Ni.It is seen that the excitation function becomes wider with increasing amount of evaporated particles.The excitation functions may have several maxima which correspond to different decay channels.The cluster decay channels are realized at low bombarding energies.With increasing bombarding energy, the light particle evaporation channels become dominant.For the reactions 58 Ni + 58 Ni at 5.6 -5.8 MeV/nucleon [ 56 Ni + 58 Ni at 4.8 -5.0 MeV/nucleon], the main decay channels leading to the production of 100 Sn are 12 C4n (40%) and 14 C2n (60%) [ 12 C2n (20%) and 14 C (80%)].For the reactions 58 Ni + 58 Ni and 56 Ni + 58 Ni, the maximum production cross sections are about 5 and 75 nb, respectively.
For the 72 Kr + 40 Ca reaction with the radioactive beam, we present the excitation functions for production of exotic nuclei 100−103 Sn (Fig. 2).One can observe that the excitation function for 100 Sn has two maxima at energies 4.0 and 4.8 MeV/nucleon which correspond to the decay channels 12 C and 3α, respectively.The maximum production cross sections corresponding to the emission channels 12 C and 3α are 1 μb and 130 nb, respectively.In conclusion, we have presented the DNS model predictions for the excitation functions for production of exotic nuclei 100−103 Sn in the reactions 58,56 Ni + 58 Ni and 72 Kr + 40 Ca.The predicted maximum value of production cross section for 100 Sn in cluster emission channels are 5nb and 1 μb for the reactions with stable and radioactive ion beams, respectively.

Figure 2 :
Figure 2: The same as in Fig. 5, but for the 72 Kr + 40 Ca reaction.