Fusion Cross Sections For Reactions Research Articles

Investigation of dynamic effects on fusion cross sections for reactions $$^{16,18}$$O + $$^{112,116,118,124}$$Sn

Investigation of dynamic effects on fusion cross sections for reactions $$^{16,18}$$O + $$^{112,116,118,124}$$Sn

Theoretical study of dynamic effects on fusion cross sections for reactions S32,34,36+Pb204,206,208

The universal fusion function prescription and the empirical coupled-channel (ECC) model are used to analyze the dynamic effects on fusion cross sections for reactions $^{32,34,36}\mathrm{S}+^{204,206,208}\mathrm{Pb}$. An examination of the reduced fusion functions shows that the total dynamic effects on fusion cross sections in $^{36}\mathrm{S}+^{204,206,208}\mathrm{Pb}$ are almost the same as those in $^{34}\mathrm{S}+^{204,206,208}\mathrm{Pb}$. Furthermore, at sub-barrier energies of the reactions $^{32,34,36}\mathrm{S}+^{208}\mathrm{Pb}$, the largest enhancement of reduced fusion function is observed in the reaction $^{32}\mathrm{S}+^{208}\mathrm{Pb}$. Then the enhancement of fusion cross sections due to couplings to inelastic excitation channels and neutron transfer channels with positive $Q$ values is investigated by using the ECC model. The results show that the experimental data of the reactions $^{34,36}\mathrm{S}+^{204,206,208}\mathrm{Pb}$ and $^{32}\mathrm{S}+^{208}\mathrm{Pb}$ are reproduced well by the ECC model. In addition, it can be found that the effect of coupling to positive $Q$-value neutron transfer channels is necessary to reproduce the sub-barrier fusion data of the reaction $^{32}\mathrm{S}+^{208}\mathrm{Pb}$. Furthermore, for the two reactions $^{32}\mathrm{S}+^{204}\mathrm{Pb}$ and $^{32}\mathrm{S}+^{206}\mathrm{Pb}$, the effects of coupling to positive $Q$-value neutron transfer channels are predicted to be significant. The fusion cross sections for these two reactions are also predicted.

Effect of resonance states of the weakly bound 6Li on total fusion in reactions with targets 28Si, 96Zr and 209Bi

Continuum Discretized Coupled-Channel calculations of total fusion cross sections for reactions induced by the weakly bound nucleus 6Li with targets 28Si, 96Zr and 209Bi at energies around the Coulomb barrier are presented. In the cluster structure frame of 6Li → α+d, short-range absorption potentials are considered for the interactions between the α- and d-fragments with the targets. In the model, the effect of resonance (l = 2, Jπ = 3+, 2+, 1+) and non-resonance breakup states of 6Li on fusion is studied by using two approaches: (1) by omitting the resonance states from the full discretized CDCC breakup space and 2) by considering only the resonance discretized sub-space. Among other things, it is found that resonance breakup states produce strong repulsive polarization potentials that lead to fusion suppression. The particular effect on fusion of a single resonance is calculated. It is found that resonances 2+ and 1+ have a more significant role on incomplete fusion, while the 3+ on complete fusion.

Systematic continuum-discretized coupled-channels calculations of total fusion for Li6 with targets Si28, Co59, Zr96, Pt198 , and Bi209 : Effect of resonance states

Continuum discretized coupled-channel (CDCC) calculations of total fusion cross sections for reactions induced by the weakly bound nucleus $^{6}\mathrm{Li}$ with targets $^{28}\mathrm{Si}, ^{59}\mathrm{Co}, ^{96}\mathrm{Zr}, ^{198}\mathrm{Pt}$, and $^{209}\mathrm{Bi}$ at energies around the Coulomb barrier are presented. In the cluster structure frame of $^{6}\mathrm{Li}\ensuremath{\rightarrow}\ensuremath{\alpha}+d$, short-range absorption potentials are considered for the interactions between the $\ensuremath{\alpha}$ and $d$ fragments with the targets. The effect of resonance ($l=2, {J}^{\ensuremath{\pi}}={3}^{+},{2}^{+},{1}^{+}$) and nonresonance states of $^{6}\mathrm{Li}$ on fusion is studied by using two approaches: (1) by omitting the resonance states from the full discretized CDCC breakup space and (2) by considering only the resonance subspace. A systematic analysis of the effect on fusion from resonance breakup couplings is carried out from light to heavy mass targets. Among other things, it is found that resonance breakup states produce strong repulsive polarization potentials that lead to fusion suppression. Couplings from nonresonance states give place to weak repulsive potentials at high energies; however, these become attractive for the heavier targets at low energies.

CDCC calculations of fusion of 6Li with targets 144Sm and 154Sm: effect of resonance states**A. Gómez Camacho from CONACYT, México, J. Lubian from CNPq, FAPERJ, Pronex, Brazil. S.G.Z was partly supported by the NSF of China (11120101005, 11275248, 11525524, 11621131001, 11647601, 11711540016), 973 Program of China (2013CB834400) and the Key Research Program of Frontier Sciences of CAS. H.Q.Z. from NSF

Continuum Discretized Coupled-Channel (CDCC) model calculations of total, complete and incomplete fusion cross sections for reactions of the weakly bound 6Li with 144,154Sm targets at energies around the Coulomb barrier are presented. In the cluster structure frame of 6Li→α+d, short-range absorption potentials are considered for the interactions between the ground state of the projectile 6Li and α-d fragments with the target. In order to separately calculate complete and incomplete fusion and to reduce double-counting, the corresponding absorption potentials are chosen to be of different range. Couplings to low-lying excited states 2+, 3− of 144Sm and 2+, 4+ of 154Sm are included. So, the effect on total fusion from the excited states of the target is investigated. Similarly, the effect on fusion due to couplings to resonance breakup states of 6Li, namely, l=2, Jπ=3+,2+,1+ is also calculated. The latter effect is determined by using two approaches, (a) by considering only resonance state couplings and (b) by omitting these states from the full discretized energy space. Among other things, it is found that both resonance and non-resonance continuum breakup couplings produce fusion suppression at all the energies considered.

Quantitative analysis of the fusion cross sections using different microscopic nucleus-nucleus interactions

The fusion cross sections for reactions involving medium and heavy nucleus-nucleus systems are investigated near and above the Coulomb barrier using the one-dimensional barrier penetration model. The microscopic nuclear interaction potential is computed by four methods, namely: the double-folding model based on a realistic density-dependent M3Y NN interaction with a finite-range exchange part, the Skyrme energy density functional in the semiclassical extended Thomas-Fermi approximation, the generalized Proximity potential, and the Akyuz-Winther interaction. The comparison between the calculated and the measured values of the fusion excitation functions indicates that the calculations of the DFM give quite satisfactory agreement with the experimental data, being much better than the other methods. New parameterized forms for the fusion barrier heights and positions are presented. Furthermore, the effects of deformation and orientation degrees of freedom on the distribution of the Coulomb barrier characteristics as well as the fusion cross sections are studied for the reactions 16O + 70Ge and 28Si + 100Mo. The calculated values of the total fusion cross sections are compared with coupled channel calculations using the code CCFULL and compared with the experimental data. Our results reveal that the inclusion of deformations and orientation degrees of freedom improves the comparison with the experimental data.

Theoretical study of fusion reactions 32S + 94,96Zr and 40Ca + 94,96Zr and quadrupole deformation of 94Zr

The dynamic coupling effects on fusion cross sections for reactions $^{32}$S + $^{94,96}$Zr and $^{40}$Ca + $^{94,96}$Zr are studied with the universal fusion function formalism and an empirical coupled channel (ECC) model. An examination of the reduced fusion functions shows that the total effect of couplings to inelastic excitations and neutron transfer channels on fusion in $^{32}$S + $^{94}$Zr ($^{40}$Ca + $^{94}$Zr) is almost the same as that in $^{32}$S + $^{96}$Zr ($^{40}$Ca + $^{96}$Zr). The enhancements of the fusion cross section at sub-barrier energies due to inelastic channel coupling and neutron transfer channel coupling are evaluated separately by using the ECC model. The results show that effect of couplings to inelastic excitations channels in the reactions with $^{94}$Zr as target should be similar as that in the reactions with $^{96}$Zr as target. This implies that the quadrupole deformation parameters $\beta_2$ of $^{94}$Zr and $^{96}$Zr should be similar to each other. However, $\beta_2$'s predicted from the finite-range droplet model, which are used in the ECC model, are quite different. Experiments on $^{48}$Ca + $^{94}$Zr or $^{36}$S + $^{94}$Zr are suggested to solve the puzzling issue concerning $\beta_2$ for $^{94}$Zr.

Sub-barrier fusion calculations for the neutron star crust using the microscopic BruecknerG-matrix and Skyrme energy density functionals

Sub-barrier fusion cross sections for reactions involving stable and very neutron-rich nuclei, which may be important in determining the composition and heating of the crust of accreting neutron stars, are calculated using internuclear potentials derived from the microscopic Brueckner $G$-matrix and Skyrme SKM* and SLy4 energy density functionals. Microscopic Skyrme-Hartree-Fock proton and neutron density distributions are used. No parameters have been fit to fusion data. Calculations are performed for the isotopic reactions $^{16}\mathrm{O}+^{16}\mathrm{O},^{16}\mathrm{O}+^{24}\mathrm{O},^{16}\mathrm{O}+^{28}\mathrm{O},^{24}\mathrm{O}+^{24}\mathrm{O},^{12}\mathrm{C}+^{16}\mathrm{O},^{12}\mathrm{C}+^{24}\mathrm{O}$, and $^{12}\mathrm{C}+^{12}\mathrm{C}$, which are of great astrophysical importance for the understanding of the time scale and the nucleosynthesis during late stellar evolution. The coupling to the low lying excited states is considered through the ccfull code. I compare my results with the time-dependent-Hartree-Fock calculations and with the S\~ao Paulo model as well as the experimental data. I found a remarkable agreement with the fusion cross sections for stable nuclei.

Fusion cross sections for reactions involving medium and heavy nucleus-nucleus systems

Existing data on near-barrier fusion excitation functions of medium and heavy nucleus-nucleus systems have been analyzed using a simple diffused barrier formula derived assuming the Gaussian shape of the barrier height distributions. Fusion cross section is obtained by folding the Gaussian barrier distribution with the classical expression for the fusion cross section for a fixed barrier. The energy dependence of the fusion cross section, thus obtained, provides good description to the existing data on near-barrier fusion and capture excitation functions for medium and heavy nucleus-nucleus systems. The fusion or capture cross section predictions are especially important for planning experiments for synthesizing new super-heavy elements.

Calculation of penetration probability across an arbitrary potential barrier in fusion reactions

The penetration probability across an arbitrary nucleus-nucleus potential barrier is studied by using transfer matrix approach, including continuous variations of effective mass. The calculated penetration probabilities for reaction ${}^{16}$O+${}^{208}$Pb are closed to those of WKB and modified Numerov calculations based on the Bass potential. With the transfer matrix approach, the influence of the effective mass on the penetration probability are simultaneously investigated. The calculations imply that the effective mass is an important quantity for studying the hindrance of fusion cross sections of some reactions at deep sub-barrier energies. The fusion cross sections of heavy-ion fusion reactions and the resonance phenomena due to double-hump barriers are also studied with this approach.

Detailed determination of the nuclear fusion radius by a simultaneous optical model calculation of elastic scattering and fusion cross sections in reactions involving weakly bound projectiles

Within the optical model for direct reactions, simultaneous calculations of elastic scattering, complete fusion, and total reaction cross sections for energies around the Coulomb barrier are presented for reactions involving the weakly bound projectile $^{9}\mathrm{Be}$ on $^{64}\mathrm{Zn}$. Volume (${W}_{F}$) and surface (${W}_{\mathrm{DR}}$) Woods-Saxon optical potentials are used such that the former is responsible only for complete fusion reactions while the latter for all direct reactions plus incomplete fusion. Simultaneous fits can be obtained with several sets of potential parameters, but if we impose the condition that the strength of ${W}_{F}$ is smaller than the strength of ${W}_{\mathrm{DR}}$ at the tail region of the potential (this condition is discussed in detail), then values are required for ${r}_{F}$ and ${r}_{\mathrm{DR}}$ of around $1.6$ and 1.7--1.9 fm, respectively. These values are much larger than those frequently used in barrier penetration model calculations. Through the energy dependence of the real and imaginary parts of the polarization potentials, we show that the usual threshold anomaly does not show up for this system, but instead there is evidence of the presence of a breakup threshold anomaly.

Isotopic dependence of fusion cross sections in reactions with heavy nuclei

The dependence of fusion cross section on the isotopic composition of colliding nuclei is analysed within the dinuclear system concept for compound nucleus formation. Probabilities of fusion and surviving probabilities, ingredients of the evaporation residue cross sections, depend decisively on the neutron numbers of the dinuclear system. Evaporation residue cross sections for the production of actinides and superheavy nuclei, listed in table form, are discussed and compared with existing experimental data. In the Pb-based reactions neutron-rich radioactive projectiles are shown to lead to similar fusion cross sections as stable projectiles.