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Gamow peak describes the most effective energy E₀ for a nonresonant nuclear reaction to occur. At astrophysical low energies much lower than the Coulomb barrier, the ability of the interacting nuclei to tunnel through the barrier depends on the primitive probability which is proportional to the Gamow factor. The reaction rate will then be determined by the primitive tunneling probability and the astrophysical S-factor. In the literature, tables on the thermonuclear reaction rates are compiled for many reactions of interest in astrophysics by using this low energy approximation. In this paper, we describe a method to obtain E₀ by using the exact tunneling probability that is valid for higher energy. We illustrate the method by using three major reactions in the proton-proton chain, ³He(³He, 2p)⁴He, ³He(⁴He, γ)⁷Be and ⁷Be(γ, p)⁸B. In all cases, E₀ starts to divert to lower values than the low energy approximation limit at around T = 10⁹K and hence generate lower reaction rates. This result might be significantly important for the thermonuclear reactions in the advanced stages of the evolution of massive stars.

Recent experimental results for the fusion of the weakly bound nucleus ⁹Be with spherical targets are analyzed by dynamical classical trajectories approach. In this approach, the Proximity model has been used to calculate the nuclear part of interaction potentials. Having determined the breakup functions and interaction potentials for ⁹Be + ¹²⁴Sn, ⁸⁹Y, ¹⁴⁴Sm and ²⁰⁸Pb reactions, the complete and incomplete fusion (ICF) cross-sections are calculated by classical trajectories model and our results show a good description of the experimental data. We have stressed on the ICF probability (P_ICF) for chosen reactions. The obtained results show that the (P_ICF) based on our calculations are in a good agreement with both experimental data and empirical predictions [J. Hinde et al., Phys. Rev. Lett.89, 272701 (2002)].

The barrier characteristics, barrier height and position, are systematically studied using Prox. 2010 potential for wide range of fusion systems with mass numbers from 6 to 238. We present a pocket formula which reproduces the exact values of the barrier height and its position within the accuracy of ±1%.

We have studied the fusion of ¹¹Be with ²⁰⁹Bi and ¹⁵C with ²³²Th in the energy region around the barrier within the framework of quantum diffusion approach and have found enhancement in fusion cross-section in deep sub-barrier region and a very minor suppression in the above barrier energy region with respect to the corresponding experimental observations. The fusion cross-section is found to be slightly increased for reactions involving ¹¹Be and ¹⁵C nuclei in comparison to those involving the stable ¹⁰Be and ¹²C isotopes, respectively.

The ${}^{26}\mathrm{\text{Mg}}{(n,\gamma )}^{27}\mathrm{\text{Mg}}$ reaction plays a crucial role in the process of nucleosynthesis in stars. It occurs primarily in massive stars during their late evolutionary stages or during explosive events like supernovae. This paper focuses on investigating discrepancies in the ANC values of the ${}^{26}\mathrm{\text{Mg}}{(n,\gamma )}^{27}\mathrm{\text{Mg}}$ reaction by analyzing experimental angular distributions of ${}^{26}\mathrm{\text{Mg}}{(d,p)}^{27}\mathrm{\text{Mg}}$ using the DWBA, ADWA and CDCC methods for both ground and first excited states. We then use a mirror nucleus procedure to extract information on the ANCs of the ground state ${}^{26}\mathrm{\text{Si}}{(p,\gamma )}^{27}\mathrm{\text{P}}$ reaction. The Hauser–Feshbach formalism of the statistical Compound Nucleus (CN) model was applied in this study to perform a compound-nucleus analysis of the ${}^{26}\mathrm{\text{Mg}}{(d,p)}^{27}\mathrm{\text{Mg}}$ reaction. The ${}^{26}\mathrm{\text{Mg}}{(d,p)}^{27}\mathrm{\text{Mg}}$ reaction has almost fulfilled the condition of peripherality, which is necessary for understanding the magnitude of the direct reaction contribution. ANCs for the ${}^{27}\mathrm{\text{Mg}}\to {}^{26}\mathrm{\text{Mg}}+n$ virtual decay system were obtained. Moreover, according to charge symmetry of mirror nuclei, the square of proton ANC for a ${}^{27}\mathrm{\text{P}}\to {}^{26}\mathrm{\text{Si}}+p$ is determined and comparison between the values of the presented ANCs.

In this work, we delved into the intriguing realm of nuclear physics by investigating fusion reactions initiated by ${}^{70}$Zn projectiles colliding with various stable isotopes of thorium nuclei, including ${}^{227-232,234}$Th. Our primary objective was the synthesis of the superheavy element $\mathrm{\text{Z}}=120$. To achieve this, we employed an advanced statistical model to evaluate the evaporation residue cross-sections. Remarkably, we observed that the fusion reaction between ${}^{70}$Zn and ${}^{231}$Th exhibited the highest evaporation residue cross-sections, reaching a peak value. Furthermore, the 3n channel within this fusion reaction yielded substantially larger evaporation cross-sections, with a notable value of 0.89 picobarns. The predicted cross-sections fall within the measurable range, making them highly valuable for experimental endeavors aimed at synthesizing the superheavy element $\mathrm{\text{Z}}=120$. This research not only contributes to our understanding of nuclear reactions but also holds promise for expanding our knowledge of the heaviest elements in the periodic table, potentially opening new frontiers in nuclear science.

We assume a simple model to describe the ion–ion potential with dynamical change in its surface diffuseness. In particular, this model is used to calculate the heavy-ion fusion cross-section using different values of the surface diffuseness. Both the static and dynamic nuclear Woods–Saxon potentials with diffuseness values ranging between 0.65 fm and 1.3 fm are used to reproduce the fusion cross-sections data of the ¹⁹F+²⁰⁸Pb and ¹⁶O+¹⁵⁴Sm reactions. The results estimate that there are different physical processes which could contribute to the fusion cross-section with different weights at each energy value. Each of these processes has its own nuclear potential.

The reactions including the stable weakly bound nucleus ⁹Be have been studied using the classical trajectory model accompanied with the experimental breakup function and the Aage-Winther interaction potential (AW95). In these calculations, the no-capture breakup and the incomplete fusion cross-sections as well as their competition at around the Coulomb barrier have been investigated. Our calculations showed that at a given far-Coulomb-barrier energy the incomplete fusion reaction in different distributions of angular momentum and energies can dominate the no-capture breakup reaction. This dominating process is reversed at the near-barrier energies.

The effects of the projectile deformation and orientation on the total potential characteristic have been studied for the reactions between weakly bound nucleus, ⁹Be, as the projectile and different targets. In this paper, the double-folding model is used to calculate the nuclear potentials and deformation of projectile included. It is shown that applying the deformation effects can modify the potential barrier height and depth in the interior regions of the potential. It is also shown that the gradient variation of the potential barrier height is linearly increased when the angle between the projectile and the target nuclei increases. The rate of the variation is constant in different reactions with ⁹Be. In order to study the possible effect of these deformation dependent potentials, application is made in the calculation of cross-sections of the different reactions. It is observed that the deformation and orientation are of important role in the dynamics of such reactions and improve the agreement with the experimental results.

By changing the neutron and nuclear matter incompressibility constant $K$, we investigate the isotopic behavior of the fusion barriers for the collision of large number of different isotopes with condition of $0.7\le N/Z\le 1.36$. Here, the double folding (DF) model which is accompanied by density-dependent (DD) versions of M3Y interactions is adopted as a basic heavy ion–ion potential. We show that the selected DD potentials predict a linear behavior for the calculated fusion barrier heights as a function of $(N/Z-1)$ for both proton- and neutron-rich systems. Moreover, the results indicate that the isotopic behavior of these values depend linearly on the change in the $K$ constant. The isotopic studies conducted on the fusion cross-section also shows that the properties of the nuclear matter in the range of energy which is below the fusion barrier will quite affect the fusion process.

Fusion and direct processes have been studied for the ⁶He + ⁶⁴Zn reaction at energies around the Coulomb barrier, in order to investigate the effects of the projectile halo structure on the reaction mechanisms. As comparison, the ⁴He + ⁶⁴Zn reaction was also studied. No effect has been observed on the fusion cross section for the ⁶He when compared with the reaction induced by the stable well bound isotope, whereas a large yield for direct reactions due to transfer and break-up events has been evidenced.

We present a statistical-model description of fission, in the framework of compound-nucleus decay, which is found to simultaneously reproduce data from both heavy-ion-induced fusion reactions and proton-induced spallation reactions around 1 GeV. For the spallation reactions, the initial compound-nucleus population is predicted by the Liège intranuclear cascade model. We are able to reproduce experimental fission probabilities in the all reactions with the same parameter set. We also discuss the need for fission transients, which are expected to have a significant effect on the spallation reactions.

Use of fusion reactions for synthesis and studying new superheavy nuclei is considered in the paper. Perspectives of synthesis of new elements with Z > 118 are discussed. The gap of unknown SH nuclei, located between the isotopes which were produced earlier in the cold and hot fusion reactions, can be filled in fusion reactions of ⁴⁸Ca with available lighter isotopes of Pu, Am, and Cm. Cross sections for the production of these nuclei are predicted to be rather large. The found area of β⁺-decaying SH nuclei with 111 ≤ Z ≤ 115 located to the “right” (more neutron-rich) to those synthesized recently in Dubna in ⁴⁸Ca-induced fusion reactions gives a unique chance to synthesize in fusion reactions the most stable SH nuclei located at the center of the island of stability.