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This study focusses on identification and analysis of possible isotopes of the superheavy element Roentgenium (Z = 111) by studying competition between the decay modes of the 259-300Rg isotopes. It is also parameterized an equation for the fusion barrier height and position. After this we have also identified the possible projectile-target combinations to synthesize 268-279Rg by studying compound nucleus formation probability, survival probability, and evaporation residue cross sections. The selected projectile-target combinations to synthesize the superheavy element Z = 111 with the combinations are 58Ni+210Bi, 59,60Co+210Po,35,36Cl+236Pu, 35Cl+239-242Pu, 36Cl+238,242,244Pu. The present work is compared with the experimental values available in literature.

The excitation function for quasielastic scattering of the weakly bound projectile $^{6}\mathrm{Li}$ on a $^{159}\mathrm{Tb}$ target, at large backward angle, has been measured at energies around the Coulomb barrier. The corresponding quasielastic barrier distribution has been extracted from the experimental cross sections, both including and excluding the $\ensuremath{\alpha}$ particles produced in the reaction. The quasielastic scattering cross sections, excluding the $\ensuremath{\alpha}$ particles, have been analyzed in the framework of coupled channels calculations. The centroid of the quasielastic barrier distribution, including the $\ensuremath{\alpha}$ particles, is found to shift towards higher energy relative to the centroid of the fusion barrier distribution for the system. This has been attributed to the low $\ensuremath{\alpha}$-breakup threshold of the nucleus $^{6}\mathrm{Li}$.

The role of the nuclear structure degrees of freedom associated with the colliding nuclei and the energy dependence in the nucleus–nucleus interaction potential in fusion dynamics of various projectiles (16O, 27Al and 37Cl) with the Ge-isotopes (74,76Ge) has been investigated. Fusion cross-sections obtained through energy dependent interaction potential (EDWSP model) and coupled channel theory show quite similar behavior in near and above barrier energy regions. In coupled channel view, the couplings to inelastic surface excitations associated with the fusing nuclei results in large fusion enhancement at sub-barrier energies. The consideration of spherical shape for targets (74,76Ge-isotopes) along with their relevant internal structure degrees of freedom in coupled channel approach is sufficient to get a good description to observed fusion enhancement of the studied reactions. In contrast, the energy dependent interaction potential modifies the barrier profile of interaction barrier and subsequently reduces the effective fusion barrier between the colliding systems, henceforth, predicts substantially large fusion enhancement at below barrier energies in comparison to the expectations of the one dimensional barrier penetration model. Furthermore, χ 2 -analysis and the ratio plots σ T h σ E x p for outcomes of the EDWSP model suggested that the model calculations provide a consistent fit to fusion data within 10%. For the chosen reactions, only at 6 fusion data points out of 75 fusion data points does the deviation exceed 5% while 69 fusion data points lie within 5% and hence, the EDWSP model reasonably explained the above barrier fusion data within 5% with a probability more than 90%.

We have studied the Ti-induced fusion reactions for the synthesis of superheavy elements with atomic number in the range 104 ≤ Z ≤ 130 for all projectile target combinations. We have obtained a semi-empirical formula for fusion barrier heights (VB), positions (RB), curvatures of the inverted parabola (ħω) of Ti-induced fusion reactions for the synthesis of superheavy nuclei with atomic number in the range 104 ≤ Z ≤ 130 for all projectile target combinations. The present pocket formula produces fusion barrier characteristics of Ti-induced fusion reactions for the synthesis of superheavy nuclei with the simple inputs of the mass number (A) and the atomic number (Z) of the projectile and the target. We have also studied the compound nucleus formation probability, survival probability, and evaporation residue cross-sections of all possible Ti-induced fusion reactions to synthetize superheavy element. The fusion reaction having high survival probability and evaporation residue cross-sections is considered to be possible fusion reaction to synthetize superheavy elements. We have identified the most probable Ti-induced fusion reactions to synthesize superheavy elements of atomic number in the range Z = 104–126. Our predictions may be a guide for the future experiments in the synthesis of more superheavy elements using Ti-induced fusion reactions.

Fusion excitation functions at energies above the fusion barrier for 12−15C + 12C are examined. From these excitation functions the average fusion cross-section, σ F > , is calculated. For this isotopic chain, the measured dependence of σ F > on neutron excess is compared with static barrier penetration models. The more rapid increase observed for the experimental cross-sections above the geometric increase predicted by the static models suggests that the stronger dependence on neutron-excess measured may be attributable to dynamics. Calculations with a time-dependent Hartree-Fock model also fail to describe the observed trend suggesting that for neutron-rich nuclei, neutron dynamics may play a larger role than is presently accounted for.

We study the quasifission and fusion-fission lifetimes for a number of fusion reactions used to synthesize the superheavy element $Z=120$ using a statistical method within the framework of the dinuclear system model. In particular, influence of the target orientation and angular momentum on such lifetimes have been investigated. The quasifission and fusion-fission lifetimes have been compared very well with that of available experiments on successful superheavy element synthesis. We notice further the predicted quasifission and fusion-fission lifetimes of the projectile-target combinations used for the synthesis of the superheavy element $Z=120$ also show the similar trend. Furthermore, the fusion-fission lifetime is seen to somewhat decrease with the increase of the angular momentum as well as beam energy. Little effect is seen on fusion barrier of the reaction and fission barrier of superheavy compound nucleus. Variation of quasifission lifetime is also not much with orientation angle, beam energy and fission barrier of the superheavy compound nuclei. Hence, this lifetime study does not provide any good reason why the attempted reactions have failed to synthesize the superheavy nuclei $Z=120$. Furthermore, consideration of the fusion barrier, fissility, mass asymmetry, deformation parameter, fission barrier, etc., leads us to reveal that optimal colliding energy is important to have the largest evaporation residue cross section for any chosen reaction so that it is well within the measurable limit for a specific experimental set up.

Quasielastic scattering excitation function at large backward angle has been measured for the weakly bound system $^{7}\mathrm{Li}+^{159}\mathrm{Tb}$ at energies around the Coulomb barrier. The corresponding quasielastic barrier distribution has been derived from the excitation function, both including and excluding the $\ensuremath{\alpha}$ particles produced in the reaction. The centroid of the barrier distribution obtained after inclusion of $\ensuremath{\alpha}$ particles was found to be shifted higher in energy, compared with the distribution excluding the $\ensuremath{\alpha}$ particles. The quasielastic data, excluding the $\ensuremath{\alpha}$ particles, have been analyzed in the framework of continuum discretized coupled-channels calculations. The quasielastic barrier distribution for $^{7}\mathrm{Li}+^{159}\mathrm{Tb}$, has also been compared with the fusion barrier distribution for the system.

International audience; The fusion and fission barriers have been determined with a Generalized Liquid Drop Model taking into account the proximity forces acting between surfaces in regard, the charge and mass asymmetry, the shell and pairing effects and quasimolecular shapes. The heights and positions of these barriers have been compared with the empirical results deduced from the experimental data. There is an overall agreement for the fusion barrier heights for most of the reactions. These fusion barrier heights may also be calculated from a proposed analytic formula or other formulas. The empirical fission barrier heights lie always between the values given by the GLDM and neglecting the microscopic effects in the fragments and the values determined in including the deformation and shell and pairing effects of the fragments.

Experimental above-barrier fusion cross-sections for $^{17}$F + $^{12}$C are compared to the fusion excitation functions for $^{16,18}$O, $^{19}$F, and $^{20}$Ne ions on a carbon target. In comparing the different systems both the differing static size of the incident ions and changes in fusion barrier are accounted for by examining the reduced fusion cross-section. Remaining trends of the fusion cross-section above the barrier which reflect the sensitive interplay of the sd protons and neutrons are observed. The experimental data are also compared to both a widely-used analytical model of near-barrier fusion, as well as a time-dependent Hartree-Fock model. Both models fail to describe the trends observed., Comment: 6 pages, 5 figures

The deformation and associated optimum/uniquely fixed orientations play an important role in the synthesis of compound nuclei via cold and hot fusion reactions, respectively, at the lowest and highest barrier energies. The choice of optimum orientation ( ) for the ‘cold or elongated’ and ‘hot or compact’ fusion configurations of quadrupole ( ) deformed nuclei depends only on the +/- signs of -deformation [J. Phys. G: Nucl. Part. Phys. 31, 631-644 (2005)]. In our recent study [Phys. Rev. C 101, 051601(R) 2020], we proposed a new set of (different from the values reported for quadrupole deformed nuclei) after the inclusion of octupole deformation (up to ) effects. Using the respective of -deformed nuclei for cold and hot optimum orientations, we analyzed the impact of the soft- and rigid-pear shapes of octupole deformed nuclei on the fusion barrier characteristics (barrier height and barrier position ). This analysis is applied to approximately 200 spherical-plus- deformed nuclear partners, that is, 16O, 48Ca+octupole deformed nuclei. Compared with the compact configuration, the elongated fusion configuration has a relatively larger impact on the fusion barrier and cross-sections owing to the inclusion of deformations up to . Its agreement with available experimental data for the 16O+150Sm reaction ( =0.205, =-0.055) also improves when the optimum orientation degree of freedom is fixed in view of octupole deformations. This reinforces the fact that nuclear structure effects play an important role in the nuclear fusion process. Thus, octupole deformed nuclei can be used for the synthesis of heavy and superheavy nuclei.

The neutron excess dependence of heavy ion fusion barrier parameters is investigated, guided by predictions of different heavy ion potentials. We develop parametrizations for the fusion barrier height and radius which explicitly involve the entrance channel mass asymmetry and neutron excess of the projectile and target. The developed expressions reproduce theoretical barrier parameters within 0.2%, which represents a big improvement over previous parametrizations. Furthermore, they provide a means to assess the importance of the neutron excess degree of freedom implied by each potential. Application of these expressions to systematics of experimental barrier parameters will be discussed.

In this paper, the cross section of the 4He + 64Zn and 6He + 64Zn reactions, at bombarding energies above and below the fusion barrier, has been investigated. Soft-core nucleon-nucleon interaction and the Monte Carlo method have been employed for studying the nuclear potential of the projectile-target system. One adjustable parameter has been chosen in this study. This parameter can change the depth of the soft-core potential. It has to be adjusted so that the calculated elastic scattering and fusion cross sections are in acceptable agreement with experimental data. Our results indicate that an increase in energy decreases the depth parameter of the soft-core nucleon-nucleon potential obtained from careful analysis the 4He + 64Zn and 6He + 64Zn reactions. Likewise, by comparing the results obtained from both reactions, one can observe that the calculated depth parameter for the reaction related to 6He is larger than that for 4He at the same energy, in particular at the sub-barrier energies. We try to explain this behavior.

Our previous study [Kumari R and Kaur S 2014 Chin. Phys. Lett. 31 112501] revealed that out of various proximity potentials, the parameterized forms derived using Proximity 1977 yield fusion barrier heights and positions in good agreement with empirical values for proton as well as helium induced reactions. Also, in an another study [Kumari R and Puri R K 2015 Nucl. Phys. A 933 135], we presented new parameterized forms for fusion barrier heights and positions using empirical data for more than 200 reactions. Our fits using these parameterized forms were found to be better than the others available in the literature. In the present study, all the above mentioned parameterizations are employed to calculate fusion barrier heights and positions for proton and helium induced reactions. Our findings show that our parameterized forms (based on empirical data and the one using Proximity 1977) yield results closer to the empirical values for helium induced reactions as compared to other parameterized forms. However, few deviations are observed in the present study in the case of proton induced reactions.

The role of barrier modifications and the relevant nuclear structure effects in the fusion of the $$ {}_8{}^{16}O+{}_{62}{}^{144,148,150,152,154}Sm $$ and $$ {}_3{}^{6,7}Li+{}_{62}{}^{152}Sm $$ systems is analyzed within the context of the energy-dependent Woods-Saxon potential model (EDWSP model) and the coupled channel model. For the $$ {}_8{}^{16}O+{}_{62}{}^{144,148,150,152,154}Sm $$ reactions, where the colliding pairs are stable against breakup, the collective excitations and/or static deformations are sufficient to account for the observed fusion enhancement. In contrast, the model calculations overpredict the complete fusion data at above - barrier energies for the $$ {}_3{}^{6,7}Li+{}_{62}{}^{152}Sm $$ systems, where the importance of projectile breakup effects has been pointed out. Due to the low threshold of the alpha-breakup channel, the weakly bound projectiles $$ \left({}_3{}^{6,7}Li\right) $$ break up into charged fragments before reaching the fusion barrier and consequently the complete fusion cross section is suppressed by 28% (25%) in the $$ {}_3{}^6Li+{}_{62}{}^{152}Sm\;\left({}_3{}^7Li+{}_{62}{}^{152}Sm\right) $$ reaction with respect to predictions of coupled channel calculations. However, the EDWSP model based calculations can minimize the suppression factor by as much as of 13% (8%) in the $$ {}_3{}^6Li+{}_{62}{}^{152}Sm\;\left({}_3{}^7Li+{}_{62}{}^{152}Sm\right) $$ reaction with reference to the predictions made by the coupled channel calculations. Therefore, the complete fusion data of the $$ {}_3{}^6Li+{}_{62}{}^{152}Sm\;\left({}_3{}^7Li+{}_{62}{}^{152}Sm\right) $$ reaction at above - barrier energies is reduced by 15% (17%) with respect to the expectations of the EDWSP model. The extracted suppression factors for the studied reactions are due to the modifications of the barrier profile as a consequence of the energy - dependence in nucleus-nucleus potential, and thus greater barrier modifications occur for more weakly bound system, which in turn, confirms the breakup of projectile in the incoming channel.

We develop a novel approach to fusion reactions for syntheses of superheavy elements, which combines the time-dependent Hartree-Fock (TDHF) method with a dynamical diffusion model based on the Langevin equation. In this approach, the distance of the closest approach for the capture process is estimated within the TDHF approach, which is then plugged into the dynamical diffusion model as an initial condition. We apply this approach to hot fusion reactions leading to formation of the element $Z=120$, that is, the $^{48}$Ca+$^{254,257}$Fm, $^{51}$V+$^{249}$Bk, and $^{54}$Cr+$^{248}$Cm reactions. Our calculations indicate that the distances of the closest approach for these systems are similar to each other and thus the difference in the probabilities of evaporation residue formation among those reaction systems originates mainly from the evaporation process, which is sensitive to the fission barrier height and the excitation energy of a compound nucleus., Comment: 5 pages, 2 figures, 1 table; published in Physical Review C as a Rapid Communication with Editors' Suggestion

Above-barrier complete fusion involving nuclides with low binding energy is typically suppressed by 30%. The mechanism that causes this suppression, and produces the associated incomplete fusion products, is controversial. We have developed a new experimental approach to investigate the mechanisms that produce incomplete fusion products, combining singles and coincidence measurements of light fragments and heavy residues in ^{7}Li+^{209}Bi reactions. For polonium isotopes, the dominant incomplete fusion product, only a small fraction can be explained by projectile breakup followed by capture: the dominant mechanism is triton cluster transfer. Suppression of complete fusion is therefore primarily a consequence of clustering in weakly bound nuclei rather than their breakup prior to reaching the fusion barrier. This implies that suppression of complete fusion will occur in reactions of nuclides where strong clustering is present.

Background: In heavy-ion induced reactions, the sub-barrier fusion cross sections are found to be higher as compared to the predictions of the one-dimensional barrier penetration model. Attempts have been made to explain sub-barrier fusion enhancement by including the static deformations, the couplings to inelastic excitations, and non-fusion channels.Purpose: To investigate factors which influence the sub-barrier fusion in the $^{37}\mathrm{Cl}+^{130}\mathrm{Te}$ system and to understand the interplay of couplings, the fusion excitation function was measured at energies from $10%$ below to $15%$ above the Bass barrier.Method: The fusion excitation function was measured by employing a recoil mass spectrometer, the Heavy-Ion Reaction Analyser (HIRA), at the Inter-University Accelerator Centre, New Delhi. To study the behavior of the fusion excitation function and the effect of couplings at sub-barrier energies, the excitation function was analyzed in the framework of the coupled-channels code ccfull.Results: In the present work, the fusion cross section was measured down to 1 $\ensuremath{\mu}\mathrm{b}$ at the lowest measured energy, i.e., $10%$ below the barrier. It was found that the inclusion of couplings of low-lying excited states along with the modified barrier between interacting nuclei satisfactorily reproduces the fusion excitation function of the $^{37}\mathrm{Cl}+^{130}\mathrm{Te}$ system. For better insight into the sub-barrier fusion, the fusion barrier distribution, the logarithmic derivative L(E) factor, and the astrophysical S factor were extracted from the analysis of the experimentally measured fusion excitation function.Conclusions: The analysis of the fusion excitation function in terms of the astrophysical S factor and the L(E) factor suggests the absence of fusion hindrance in the $^{37}\mathrm{Cl}+^{130}\mathrm{Te}$ system down to a 1 $\ensuremath{\mu}\mathrm{b}$ cross section achieved at the lowest measured energy. The excitation function of the present system is compared with the existing measurements in which $^{37}\mathrm{Cl}$ has been used as a projectile to understand the interplay of entrance-channel parameters in sub-barrier fusion enhancement.

Background: The density-constrained time-dependent Hartree-Fock method is currently a tool of choice to predict fusion cross sections. However, it does not include pairing correlations, which have been found recently to play an important role. Purpose: To describe the fusion cross section with a method that includes the superfluidity and to understand the impact of pairing on both the fusion barrier and cross section. Method: The density-constrained method is tested first on the following reactions without pairing, O16+O16 and Ca40+Ca40. A new method is developed, the density-constrained time-dependent Hartree-Fock-Bogoliubov method. Using the Gogny-TDHFB code, it is applied to the reactions O20+O20 and Ca44+Ca44. Results: The Gogny approach reproduces the experimental data well for reaction O16+O16 and Ca40+Ca40. The DC-TDHFB method is coherent with the TDHFB fusion threshold. The effect of the phase-lock mechanism is shown for those reactions. Conclusions: The DC-TDHFB method is a useful new tool to determine the fusion potential between superfluid systems and to deduce their fusion cross sections., SCOPUS: ar.j, info:eu-repo/semantics/published

A systematic calculation of barriers for heavy-ion fusion was performed on the basis of the double-folding model by employing two versions of an effective nucleon–nucleon interaction: M3Y interaction and Migdal interaction. The results of calculations by the Hartree–Fockmethod with the SKX coefficients were taken for nuclear densities. The calculations reveal that the fusion barrier is higher in the case of employing theMigdal interaction than in the case of employing the М3Y interaction. In view of this, the use of the Migdal interaction in describing heavy-ion fusion is questionable.

The role of three-parameter Fermi (3pF) and three-parameter Gaussian (3pG) density functions on the fusion dynamics has been explored in comparison to the two-parameter Fermi (2pF) within the semiclassical Skyrme Energy Density Formalism. For the case of the three-parameterized density functions (3pF and 3pG), an additional parameter ‘w’ influences the tail and nearby region, and hence the barrier characteristics get modified accordingly. In view of this, the role of 2pF, 3pF and 3pG density functions has been analyzed by calculating the fusion barrier height V B (and barrier position R B ) for a variety of nuclear reactions with the mass-asymmetry spread from symmetric to extreme asymmetric reaction partners, and the results are compared with the available data. In addition to this, the fusion cross-sections for 58Ni-based reactions are also calculated using extended l-summed Wong model and the collective effect of V B , R B and ħ ω B (barrier height, position and curvature respectively) for the use of above mentioned density distributions has been examined. It is found that 2pF density functional is more suitable for symmetric reactions, whereas 3pF and 3pG seems to be appropriate for asymmetric reactions.

This study focuses on using a semi-classical and quantum mechanical approach based originally on the theory of Winther and Alder that is used to explain the Coulomb excitation. This approach is called the coupled channels with continuum-discretised (CCCD), where the semi-classical and quantum models were used to investigate the channel coupling effects on the determination of the cross section for fusion σfus (mb) and the distribution of the fusion barrier Dfus (mb/MeV) for systems 14N+59Co, 16O+64Ni and 18O+64Ni. The comparison between the results of the semi-classical and quantum mechanical models along with the corresponding experimental data shows clearly that the adopted semi-classical model is very competitive to the quantum mechanical model and can be considered as efficient approach to study the properties of the fusion reactions.

Background: Several Time-Dependent Hartree-Fock-Bogoliubov (TDHFB) calculations predict that the super- fluidity enhances the fluctuations of the fusion barrier. This effect is not fully understood and not yet revealed experimentally. Purpose: The goal of this study is to investigate empirically the effect of the superfluidity on the fusion barrier width. Method: First, the local regression method is introduce and used to determine the barrier distribution more precisely. A second method that requires only the calculation of an integral of the cross section is developed to determine accurately the fluctuations of the barrier. A benchmark is done between this two methods and with the fitting method usually used. This integral method showing a better agreement in a test case, it is applied systematically in a selection of 115 fusion reactions. Results: The fluctuations of the barrier for superfluid systems are on average larger than for magic or semi-magic nuclei. This is due to the deformation effects and the effect of the superfluidity. To disentangle those two effects, we compare the experimental width to the width estimated from a model that takes into account the tunneling, the deformation and the vibration effect. The deviation of the experimental width from this theory for reaction between superfluid nuclei shows that the superfluidity enhance the fusion barrier width. Conclusions: This analysis shows that the predicted effect of the superfluidity on the width of the barrier is real and is of the order of 1 MeV., 11 pages, 14 figures

In the previous chapter, the mechanisms of breakup in interactions of \(^{7}\mathrm{Li}\) and \(^{9}\mathrm{Be}\) with targets ranging in Z from 6 to 83 were identified. In this chapter the importance of the structure of projectile-like nuclei in influencing reaction outcomes will be explored. In particular, the nature of the states populated in the projectile-like nucleus formed after transfer is a key factor in determining the extent to which transfer-triggered breakup can suppress complete fusion. At below-barrier energies, breakup that occurs prior to the nuclei reaching the distance of closest approach translates above the barrier into breakup that occurs prior to the nuclei passing the fusion barrier, reducing the probability of complete charge capture. Conversely, breakup that occurs after the nuclei reach the distance of closest approach translates into capture of the nuclei at above-barrier energies. Therefore, the locations of breakup are important. These locations are intimately connected to the lifetime of resonance states. In general, broad resonances populated in a reaction will quickly decay, resulting in breakup near to the target. This has the capacity to suppress complete fusion if it occurs prior to passing inside the fusion barrier radius. Transfer populating narrow resonances will break up asymptotically far from the target nucleus, long after the distance of closest approach, so cannot suppress complete fusion.

A systematic study is provided to analyze the behaviors of the interaction potential and complete fusion cross section which are influenced by the effects of the surface energy coefficients γ and temperature T. Our framework is restricted to the proximity formalism for fusion reactions induced by weakly bound projectiles 6Li, 7Li and 9Be. The different surface energy coefficients (γ-MN76, γ-MN95, γ-MS00 and γ-PD03) are used to study the role of the parameter γ in the proximity potentials AW 95 and BW 91. Comparison of the theoretical and the experimental values of the barrier characteristics (barrier heights and its positions) indicates that the modified versions AW 95 (γ-MS00) and BW 91 (γ-MS00) give the least deviations for fusion barrier heights. Moreover, it is shown that the temperature-dependence improves the calculated barrier heights based on the potentials AW 95 and BW 91. In the present study, the analysis of the mentioned effects on the complete fusion cross sections has been also discussed for the systems of interest. The obtained results reveal that the above-modified versions provide a more accurate description for behavior of the complete fusion cross sections than the original potentials at above-barrier energies. It is demonstrated that the increase of the temperature T enhances the complete fusion suppression at this energy range.

Using the empirical/experimental fusion barrier heights and positions, we perform a systematic study for large number of reactions having projectile/target masses 6 ≤ A ≤ 238 and present new parameterized form for fusion barrier heights and positions. A comparison with other well known parameterized forms is also made.

Excitation functions of reaction residues produced in the $^{14}\mathrm{N}+^{169}\mathrm{Tm}$ system have been measured to high precision at energies above the fusion barrier, ranging from $1.04{V}_{B}$ to $1.30{V}_{B}$, and analyzed in the framework of the statistical model code pace4. Analysis of $\ensuremath{\alpha}$-emitting channels points toward the onset of incomplete fusion even at slightly above-barrier energies where complete fusion is supposed to be one of the dominant processes. The onset and strength of incomplete fusion have been deduced and studied in terms of various entrance channel parameters. Present results together with the reanalysis of existing data for various projectile-target combinations conclusively suggest strong influence of projectile structure on the onset of incomplete fusion. Also, a strong dependence on the Coulomb effect $({Z}_{P}{Z}_{T})$ has been observed for the present system along with different projectile-target combinations available in the literature. It is concluded that the fraction of incomplete fusion linearly increases with ${Z}_{P}{Z}_{T}$ and is found to be more for larger ${Z}_{P}{Z}_{T}$ values, indicating significantly important linear systematics.

For the first time the influence of the surface energy coefficient $\gamma$ and temperature T on the parameterization of the fusion barriers is systematically analyzed within the framework of the proximity formalism, namely proximity 1977, proximity 1988 and proximity 2010 models. A total of 114 fusion reactions with the condition $39 \leq Z_{1} Z_{2} \leq 1520$ for the charge product of their participant nuclei have been studied. We present $\gamma$ -dependent and T -dependent pocket formulas which reproduce the theoretical and empirical data of the fusion barrier height and position for our considered reactions with good accuracy. It is shown that the quality of the $\gamma$ -dependent formula enhances by increasing the strength of the surface energy coefficient. Moreover, the obtained results confirm that imposing the thermal effects improves the agreement between the parameterized and empirical data of the barrier characteristics.

In this study, the role of bombarding energy in analyzing the interaction potentials and describing the densities of interacting nuclei during fusion is investigated. For this purpose, the fusion cross sections of the $^{40}\mathrm{Ca}+^{48}\mathrm{Ca}, ^{16}\mathrm{O}+^{92}\mathrm{Zr}$, and $^{40}\mathrm{Ca}+^{90}\mathrm{Zr}$ systems are calculated by the use of potentials derived from the semiclassical Skyrme energy density functional and the coupled-channel formalism. The comparisons drawn between the theoretical fusion data and the experimental ones demonstrate the energy-dependence behavior of the potentials employed in the calculations. Considering this dependence, we also show the variations of the density parameters of the colliding nuclei with the bombarding energy. The obtained results indicate that with increasing energy, the fusion barrier heights increase, while the diffuseness parameters of the densities decrease.

Fusion reactions near the barrier energy are studied in this proceedings with the Hartree-Fock (HF) method, on systems involving 40–54 Ca+116,132 Sn. Both static and time-dependent (TDHF) versions of the method are used to probe what structure effects play a role in the fusion barrier energy. In static HF calculations for fusion, ground state properties of the nuclei influence the barrier energy. When dynamics are added in with TDHF, some effects from static properties (for example, the neutron skin) disappear. To understand the role of vibrations in dynamic reactions, TDHF is used in conjunction with the coupled-channels approach. Discussion on the effects of transfer is also presented.

We study the results of the proximity approach in calculating the fusion barrier parameters (the height of Coulomb barrier V B and its radius R B ) compared with the results of double folding model (DFM). We considered five interaction systems as examples and made our study at several relative orientations for the interacting deformed nuclei. We found that V B and R B , evaluated by using the proximity approach, have nonphysical Φ -dependence when the value of hexadecapole deformation parameter β 4 0 or at least one nucleus has octupole deformation order, β 3 . The results almost agree with those of DFM when β 4 = 0 . For positive β 4 values the results of the two models almost agree in behavior but differ in values. The reason for failure when β 4 has negative value is due to the existence of concave region in the nuclear surface, which does not satisfy the requirement of proximity approach based on gently-curved surface. Since the existence of β 6 and β 8 induce irregularity and concave regions in the surface, we expect failure of proximity approach in this case, for an example, β 6 was given.

We study the heavy-ion reaction at sub-barrier energies for 16O+144,154Smsystems using full order coupled-channels formalism. We especially investigate the effect of fusion and quasi- elastic barrier distributions on the surface diffuseness and the coupling radius parameters of the nuclear potential for these systems. We found that the structure of fusion and quasi-elastic barrier distributions is more sensitive to the surface diffuseness and coupling radius parameters for the reaction with spherical target, 16O+144Sm systemcompared to the reaction that involves the deformed target, i.e., 16O+154Sm system. In more detail, the results of coupled-channels calculations for the fusion and the quasi-elastic barrier distributions for deformed target are not sensitive to the choice of the coupling radius and surface diffuseness parameters. In mark contrast, the structure of the fusion and the quasi-elastic barrier distributions for spherical target are very sensitive to the coupling radius and surface diffuseness parameters. We found that the small surface diffuseness parameter smeared out the fusion barrier distributions and the larger coupling radius smoothed the high energy peak of the quasi-elastic barrier distributions. We also found that the larger coupling radius, , is required by the experimental quasi-elastic barrier distribution for the 16O+144Sm system whereas the experimental fusion barrier distribution compulsory the small value, i.e., .

Fusion cross sections were measured for the systems 40Ar+144Sm, 40Ar+148Sm and 40Ar+ 154Sm above and under Coulomb barrier to understand the role of coupled channels effects involved in barriers fusion. The fusion barriers distributions and fusion probabilities were analyzed using the semiclassical mechanical code which called Sequential Complete Fusion (SCF) as well as Full Coupled Channel code (CCFULL). These calculations show that the observed fusion cross sections fusion barrier distribution and fusion probabilities for these systems are reproduced clearly in the semiclassical mechanical for all excitation states above and under Coulomb barrier.

The fusion barrier distribution (Dfus) for the systems 16O+144Sm and 16O+208Pb systems had been analyzed in this work to test the benefit of using second derivative of Wong’s formula for fusion cross section to extract Dfus from experimental data. The calculated Dfususing Wong’s formula compared with the result of three-point difference formula, which is the usual method for extract Dfus from experimental cross section. The results showed that this method generated the fusion barrier distribution for both systems in an acceptable approach with respect to the relative position of distribution peaks when it is compared with the theoretical calculations and three-point difference formula.

The effects of coupled-channels in heavy-ion fusion reaction for the system 40Ca + 192Os, 40Ca + 194Pt, and 48Ca + 197Au are discussed. The fusion cross-section σfus, the fusion barrier distribution Dfus and fusion probability Pfus are also discussed. The fusion barrier distribution is calculated using numerical three point, five point and Wong methods. Full quantum coupled-channels calculations are performed using CCFULL code with all order coupling to compare and with available experimental data. The χ² values for the case of no-coupling and coupling effects included shows clearly that the present calculations are in agreement with the experimental.

The relative yield of complete fusion and quasifission components for the $^{12}\mathrm{C}+^{204}\mathrm{Pb}, ^{19}\mathrm{F}+^{197}\mathrm{Au}, ^{30}\mathrm{Si}+^{186}\mathrm{W}$, and $^{48}\mathrm{Ca}+^{168}\mathrm{Er}$ reactions which all lead to the compound nucleus $^{216}\mathrm{Ra}$ are analyzed to calculate the entrance channel effects by comparison of capture, complete fusion, and quasifission cross sections, emission barriers (${B}_{\mathrm{fus}}^{*},{B}_{qf}$), as well as complete fusion probability estimated by statistical method within the framework of the dinuclear system model. The difference among complete fusion probabilities calculated by the dinuclear system model for different entrance channels can be explained by the hindrance to complete fusion due to the larger inner fusion barrier ${B}_{\mathrm{fus}}^{*}$ for the transformation of the dinuclear system into a compound nucleus and the increase of the quasifission contribution due to the decreasing of the emission barrier ${B}_{qf}$ of quasifission as a function of the angular momentum. Although these reactions with different entrance channels populate the same compound nucleus $^{216}\mathrm{Ra}$ at similar excitation energies, the model predicts the negligible quasifission probability for reactions having higher entrance channel mass asymmetry and the dominant decay channel is complete fission. For reactions induced by massive projectiles such as $\mathrm{Si}$ and $\mathrm{Ca}$ having lower entrance channel mass asymmetry, the quasifission component is dominant in the evolution of dinuclear system, and the fusion process is extremely hindered.

The difference between evaporation residue cross sections measured in the cold (X+ 208 Pb, 209 Bi) and hot ( 48 Ca+actinides) fusion reactions can be related to the stage of compound nucleus (CN) formation and/or to the stage of its survival against fission. The cold fusion reactions are favorable in synthesis of the superheavy elements (SHE) with charge numbers Z< 112 in comparison with the hot fusion reactions due to small excitation energy and large fission barrier of the CN formed in these reactions. The strong decrease of the cross sections of the synthesis of the SHE Z = 113 in the cold fusion reactions in comparison with the ones in the hot fusion reactions is the result of the increase of hindrance to the CN formation in the cold fusion reactions. The origin of the intrinsic fusion barrier, B ∗ , causing the strong decrease of the probability PCN in the cold fusion is discussed.