Above-barrier heavy-ion fusion cross-sections using the relativistic mean-field approach: Case of spherical colliding nuclei

Abstract

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)

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

“…with 𝑠 𝐴𝐺 = 1.5840 fm, 𝐹 𝐴𝐺 = 4/3 for 12 C and 𝑠 𝐴𝐺 =1.7410 fm, 𝐹 𝐴𝐺 =2 for 16 O. However, this type of density profile is not known to us for 40 Ca.…”

“…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].…”

“…The idea of the present work is to make use of the experimental NCDs for obtaining the correct NDs which are then implemented in the double folding potential. Three spherical even-even nuclei with 𝑁 = 𝑍 are employed: 12 C, 16 O, and 40 Ca. Although there is some experimental information on the deformed shape of 12 C (see, e.g.…”

“…Following [21] we assume that 𝜌 𝑍 = 𝜌 𝑁 for these nuclei and propose a novel approach for parametrizing the NDs. These densities are used for evaluating the above-barrier capture cross-sections for 12 C+ 12 C, 16 O; 16 O+ 16 O, 40 Ca; and 40 Ca+ 40 Ca reactions.…”

Theoretical Inspecting of ²¹¹At Radionuclide via Coupled-Channel Model for Fusion Reaction of Stable Nuclei

“…Fusion mechanisms of heavy-ion interactions have attracted big attention experimentally and theoretically as they reveal the interaction between the nuclear structure and reaction mechanisms [1][2][3][4]. Fusion processes at energies near the Coulomb barrier can be considered as a multidimensional barrier penetration problem [5][6][7][8]. The multidimensional barrier penetration part can be explained by disentangling the coupled channel (CC) model equations [9][10][11][12][13].…”