Detail study of application of the relativistic mean-field effective NN forces for heavy-ion fusion within a dynamical model

Abstract

In the analysis of the heavy-ion above-barrier fusion cross-sections of complex nuclei, the relativistic effects are usually ignored. In the present work, we undertake a step toward accounting for these effects. Namely, the nucleus–nucleus interaction potential is obtained using the double-folding model with six different effective nucleon–nucleon (NN) forces coming from the relativistic mean field (RMF) theory. We also compare our present results with the ones obtained with the non-relativistic M3Y NN-forces. In all calculations, the nuclear densities resulting from the Hartree–Fock approach with the SKX-Skyrme forces accounting for the tensor part are used. Our calculations show that four sets of the considered RMF forces cannot be used for describing heavy ion fusion. Of the remaining two sets, one results in the barriers which are too high not leaving any room for the dissipative effects. Only the potentials calculated using the NL2 NN-forces allow us to reproduce the experimental cross-sections within the framework of the fluctuation–dissipation trajectory model with surface friction with a typical accuracy of 3%–5%. The values of the variable parameter of the model which defines the friction strength resulting from the present calculations are systematically lower than those obtained earlier with the M3Y NN-forces.

Experimental nuclear charge density and theoretical description of the above-barrier light heavy-ion fusion process*

“…That is why in the rest of the paper all calculations are performed only with FE-densities. Here we provide only a brief description of the options employed; all the details about the version of the double-folding model utilized in the present work can be found in [13,15].…”

“…Three spherical even-even nuclei with are employed: 12 C, 16 O, and 40 Ca. Although there is some experimental information on the deformed shape of 12 C (see, for example, [28,29] and references therein), this nucleus is considered a spherical one in many studies [14,20,21,30,31]. Moreover, it is well established that at above barrier collision energies, structure effects, such as nuclear deformation, do not significantly manifest themselves [32].…”

“…It is difficult to decide which collision energies to use from the experimental dataset for detailed quantitative comparison with calculations. In [13,14] the criterion mb was chosen following Ref. [32]; this ap- proximately corresponds to .…”

“…This criterion was formulated in [32] based on the coupled-channel calculations for the 16 O + 154 Sm reaction. Accordingly, in [13,14], reactions were considered in which one of the colliding nuclei was 92 Zr or heavier. For such relatively heavy nuclei, the energies of the lowest excited states are at most 1 MeV, and the barrier energies are approximately 40 MeV or larger.…”

“…However, there are two shortcomings of this approach: (i) it is very computer-time consuming and (ii) it is difficult to account for fluctuations of the nucleus shape. Therefore, in the literature simplified dynamical approaches are widely used like the quantum diffusion approach [5][6][7][8], the coupled-channels method [9][10][11][12] or the trajectory model with the surface friction [13][14][15][16].…”