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Register a new userStudy of fusion reactions of light nuclei at low energies using complex nucleon-nucleus potential function
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Nuclear fusion reactions, at energies, far below the Coulomb barrier play a significant role in the synthesis of light elements in the primordial nucleosynthesis as well as in the interior of compact stellar objects. Many different kinds of nuclear reactions are occurring simultaneously inside the stellar core depending upon the density and temperature conditions of the nuclear plasma along with other relevant parameters of these stars. Nuclear fusion reactions in the energy range ($Esim$ 1 eV to few keV) can be explained successfully by quantum mechanical tunneling through the mutual Coulomb barrier of interacting nuclei. The measurement of the cross-sections at extremely low energy is quite difficult because of the larger width of the Coulomb barrier, which results in a very small value of the reaction cross-section. Hence, any improvement in the data on astrophysical S-factors for the light nuclei fusion may give a better picture of the elemental abundance in nucleosynthesis. In this work, we have theoretically investigated the energy dependence of fusion cross-sections and astrophysical S-factors for fusion reaction of light nuclei like D-D and p-$^{11}$B using complex Gaussian nuclear potential with adjustable depth and range parameters plus the mutual Coulomb interaction of the interacting nuclei. Numerical computation of the observables is done in the framework of the selective resonant tunneling model approach. The results of our calculation are compared with those found in the literature.
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Applying a macroscopic reduction procedure on the improved quantum molecular dynamics (ImQMD) model, the energy dependences of the nucleus-nucleus potential, the friction parameter, and the random force characterizing a one-dimensional Langevin-type description of the heavy-ion fusion process are investigated. Systematic calculations with the ImQMD model show that the fluctuation-dissipation relation found in the symmetric head-on fusion reactions at energies just above the Coulomb barrier fades out when the incident energy increases. It turns out that this dynamical change with increasing incident energy is caused by a specific behavior of the friction parameter which directly depends on the microscopic dynamical process, i.e., on how the collective energy of the relative motion is transferred into the intrinsic excitation energy. It is shown microscopically that the energy dissipation in the fusion process is governed by two mechanisms: One is caused by the nucleon exchanges between two fusing nuclei, and the other is due to a rearrangement of nucleons in the intrinsic system. The former mechanism monotonically increases the dissipative energy and shows a weak dependence on the incident energy, while the latter depends on both the relative distance between two fusing nuclei and the incident energy. It is shown that the latter mechanism is responsible for the energy dependence of the fusion potential and explains the fading out of the fluctuation-dissipation relation.
Complete fusion excitation functions of reactions involving breakup are studied by using the empirical coupled-channel (ECC) model with breakup effects considered. An exponential function with two parameters is adopted to describe the prompt-breakup probability in the ECC model. These two parameters are fixed by fitting the measured prompt-breakup probability or the complete fusion cross sections. The suppression of complete fusion at energies above the Coulomb barrier is studied by comparing the data with the predictions from the ECC model without the breakup channel considered. The results show that the suppression of complete fusion are roughly independent of the target for the reactions involving the same projectile.
The recent experimental data obtained by the OBELIX group on $bar{p}$D and $bar{p}^4$He total annihilation cross sections are analyzed. The combined analysis of these data with existing antiprotonic atom data allows, for the first time, the imaginary parts of the S-wave scattering lengths for the two nuclei to be extracted. The obtained values are: $Im a^{sc}_0 = [- 0.62 pm 0.02 ({stat}) pm 0.04 ({sys})] fm$ for $bar{p}$D and $Im a^{sc}_0 = [- 0.36pm 0.03({stat})^{+0.19}_{-0.11}({sys})] fm$ for $bar{p}^4$He. This analysis indicates an unexpected behaviour of the imaginary part of the $bar{p}$-nucleus S-wave scattering length as a function of the atomic weight A: $|Im a^{sc}_0|$ ($bar{p}$p) > $|Im a^{sc}_0|$ ($bar{p}$D) > $|Im a^{sc}_0|$ ($bar{p}^4$He).
The real part of the optical potential for the nucleon-nucleus scattering at lower energies (E_i<100MeV) has been calculated including nucleonic and mesonic form factors by a double folding approach. Realistic density- and energy-dependent effective NN-interactions DDM3Y, BDM3Y and HLM3Y based on the Reid and Paris potentials are used in this respect. The effects of the nucleon density distribution and the average relative momentum on the folded potential have been analysed. A good agreement with the phenomenological potential of Lagrange-Lejeune, as well as with the parametrization of Jeukenne-Lejeune-Mahaux for both neutron and proton double-folded potentials is obtained. The results indicate that the strongly simplified model interactions used in preequilibrium reaction theory neglect important dynamical details of such processes.
The present understanding of reaction processes involving light unstable nuclei at energies around the Coulomb barrier is reviewed. The effect of coupling to direct reaction channels on elastic scattering and fusion is investigated, with the focus on halo nuclei. A list of definitions of processes is given, followed by a review of the experimental and theoretical tools and information presently available. The effect of couplings on elastic scattering and fusion is studied with a series of model calculations within the coupled-channels framework. The experimental data on fusion are compared to bare no-coupling one-dimensional barrier penetration model calculations. On the basis of these calculations and comparisons with experimental data, conclusions are drawn from the observation of recurring features. The total fusion cross sections for halo nuclei show a suppression with respect to the bare calculations at energies just above the barrier that is probably due to single neutron transfer reactions. The data for total fusion are also consistent with a possible sub-barrier enhancement; however, this observation is not conclusive and other couplings besides the single-neutron channels would be needed in order to explain any actual enhancement. We find that a characteristic feature of halo nuclei is the dominance of direct reactions over fusion at near and sub-barrier energies; the main part of the cross section is related to neutron transfers, while calculations indicate only a modest contribution from the breakup process.
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