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We calculate the capture (fusion) cross sections for nine reactions involving spherical nuclei: 16 O + 16 O, 28 Si, 92 Zr, 144 Sm, 208 Pb; 28 Si + 28 Si, 92 Zr, 208 Pb; 32 S + 208 Pb. For six of them precision data are available in the literature. Analysis of these precision data within the framework of the single-barrier penetration model based on the Woods-Saxon profile for the strong nucleus-nucleus interaction potential (SnnP) gave rise to the problem of the apparently large diffuseness of the SnnP [Newton et al., Phys. Rev. C 70, 024605 (2004)]. Our fluctuation-dissipation trajectory model is based on the double-folding approach with the density-dependent M3Y NN forces including the finite-range exchange part. For the nuclear matter density the Skyrme-Hartree-Fock approach including the tensor interaction is applied. The resulting nucleus-nucleus potential possesses rather small (normal) diffuseness. The strength of the radial friction K R is used as the free parameter of the model. It turns out that for four of the five reactions induced by 16 O (except 16 O + 208 Pb) the calculated cross sections cannot be brought into agreement with the data within the experimental errors. This suggests that the calculated nuclear density is incorrect for 16 O. For the reactions not involving 16 O and, surprisingly, for the 16 O + 208 Pb reaction the agreement with the data within 2-5% is achieved at K R = 1.2 × 10 −2 to 3.0 × 10 −2 MeV −1 zs which is in accord with the previous works.

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We have compared the results of dynamical modeling of the fission process with predictions of the Kramers formulas. For the case of large dissipation, there are two of them: the integral rate R I and its approximation R O . As the ratio of the fission barrier height B f to the temperature T reaches 4, any analytical rate is expected to agree with the dynamical quasistationary rate R D within 2%. The latter has been obtained using numerical modeling with six different potentials. It has been found that the difference between R O and R D sometimes exceeds 20%. The features of the potentials used that are responsible for this disagreement are identified and studied. It is demonstrated that it is R I , not R O , that meets this expectation regardless of the potential used.

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Systematic calculations of the Coulomb barrier parameters for collisions of spherical nuclei are performed within the framework of the double folding approach. The value of the parameter = ((which estimates the Coulomb barrier height) varies in these calculations from 10 MeV up to 150 MeV. The nuclear densities came from the Hartree-Fock calculations which reproduce the experimental charge densities with good accuracy. For the nucleon-nucleon effective interaction two analytical approximations known in the literature are used: the M3Y and Migdal forces. The calculations show that Migdal interaction always results in the higher Coulomb barrier. Moreover, as increases the difference between the M3Y and Migdal barrier heights systematically increases as well. As the result, the above barrier fusion cross sections calculated dynamically with the M3Y forces and surface friction are in agreement with the data. The cross sections calculated with the Migdal forces are always below the experimental data even without accounting for the dissipation.

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.

In the present work, the influence of the nuclear matter density on the DF potential and on the Coulomb barrier parameters is studied systematically for collisions of spherical nuclei. The value of the parameter = ( 1 3 ⁄ + 1 3 ⁄ ) ⁄ (estimating the Coulomb barrier height) varies in these calculations from 10 MeV up to 150 MeV. We have introduced self-consistent relativistic mean field (RMF) density in the present analysis. For the nucleon-nucleon effective interaction, the M3Y forces with the finite range exchange term and density dependence are employed. The above barrier fusion cross sections are calculated within the framework of the trajectory model with surface friction. Results are compared with the previous study in which the nuclear density came from the Skyrme Hartree-Fock (HF) calculations and with the high precision experimental data. This comparison demonstrates that i) agreement between the theoretical and experimental cross sections obtained with RMF and HF densities is of the same quality and ii) the values of the only adjustable parameter (friction strength) obtained with RMF and HF densities strongly correlate with each other.where is the mass number and ( ⊥ , ) is the deformed density. The total binding energy and other observables are also obtained by using the standard relations, given in Ref. [50]. We apply the widely used NL3 [54] interaction parameter set for the present analysis. It is worth mentioning that the interaction parameters are able to describe the bulk properties of the nuclei reasonably good from the β-stable region to the drip-line [35,38,42,[44][45][46][47]. To deal with the open-shell nuclei, one has to consider the pairing correlations in their ground as well as excited states [33,35,38,42,[44][45][46][47]. The constant gap BCS approach is adopted for the present study and more details of the paring can be found in Ref. [31][32][33][34][35][36][37][38][39][40][42][43][44][45][46][47][48][49][50][51][52][53][54]. The trajectory fluctuation-dissipation model Dynamical equations and cross-sectionsThe physical picture of our dynamical model is similar to that of Ref.[55] the detail description of the model can be found in [22]. The fictitious particle with the reduced mass runs experiencing the action of the conservative, dissipative, and random (fluctuating)