A new model is proposed for fusion mechanisms of massive nuclear systems where so-called fusion hindrance exists. The model describes two-body collision processes in an approaching phase and shape evolutions of an amalgamated system into the compound nucleus formation. It is applied to 48 Ca-induced reactions and is found to reproduce the experimental fusion cross sections extremely well, without any free parameter. Combined with the statistical decay theory, residue cross sections for the superheavy elements can be readily calculated. Examples are given.PACS numbers: 25.60.Pj, 25.70.Jj How many elements exist in the nature or what is the heaviest element has been an intriguing question since the periodic table was proposed for the chemical elements. The heaviest element that exists in the nature is now known to be Uranium with atomic number Z being 92. But the discovery of the magic numbers in atomic nuclei and their understanding by the shells of nucleonic motion [1] suggest that much heavier atomic nuclei might exist, stabilized by extra-bindings due to possible shells next to the largests known, i.e., Z=82 and N=126. Actually, many theoretical calculations have been made, predicting the next double closed shell nucleus to be with Z=114, 120, or 126 and N=184 [2]. Naturally, enormous experimental efforts have been devoted to finding out traces of existence of the corresponding superheavy atomic nuclei and to synthesizing them with nuclear reactions, especially with heavy-ion fusion reactions [3]. But what combination of ions is favorable as entrance channels and what incident energy is the optimum for residues are not predicted well, and thus, the experiments have been performed according to the results of systematic studies done so far. This is due to the lack of our knowledge of reaction mechanisms.Based on the theory of compound nucleus reactions, the residue cross sections are given as follows,where λ − is the inverse of the wave number and J is the total angular momentum quantum number. P fusion and P surv denote the fusion and the survival probabilities, respectively. The latter is given by the statistical theory of decay, i.e., by competitions between neutron emission and fission decay. Essentially unknown is the fusion probability, i.e., fusion mechanism of massive systems, although there are ambiguities in the parameters in the properties of heavy and superheavy nuclei which give rise to uncertainties in calculating the survival probability.In lighter systems, the fusion probability is well determined by the barrier defined with the Coulomb and the nuclear attraction between nuclei in the entrance channel, but in massive systems, the situation is not so simple. It has been well known experimentally that there is the fusion-hindrance [4], which is often described with socalled extra-push energy which is required for a system to fuse in addition to the barrier height [5]. A physical origin or mechanism is not yet well clarified. There are two possible interpretations proposed. They both attribute i...

The fusion process of 48 Ca induced reactions is studied with the two-step model. In this model, the fusion process is devided into two stages: first, the sticking stage where projectile and target come to the touching point over the Coulomb barrier from infinite distance, and second, the formation stage where the di-nucleus formed with projectile and target evolve to form the spherical compound nucleus from the touching point. By the use of the statistical evaporation model, the residue cross sections for different neutron evaporation channels are analyzed. From the results, optimum reactions are given to synthesize Z = 117 element with 48 Ca induced reactions.

A two-step model is proposed for the fusion mechanism of massive heavy-ion systems which is the most unknown part in the reaction theory for the synthesis of the superheavy elements. It consists of the approaching phase of incident ions and the dynamical shape evolution of the amalgamated system toward the spherical compound nucleus. Preliminary results are presented.

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