Calculated Fusion Cross Sections Research Articles

Fusion enhancement within a collective clusterization approach applied to the isotopic chain of neutron-rich light-mass compound nuclei

The dynamics of neutron-rich light-mass compound nuclei $^{24,25,26,27}\mathrm{Mg}^{*}$ formed in $^{12,13,14,15}\mathrm{C}+^{12}\mathrm{C}$ fusion reactions, respectively, is explored at different ${E}_{\mathrm{c}.\mathrm{m}.}$ values within the dynamical cluster decay model (DCM). DCM is based on the quantum mechanical fragmentation theory, which treats the binary fragmentation of emitting compound nucleus as light particles (LPs), intermediate mass fragments (IMFs), as well as symmetric mass fragments (SMFs), on equal footing, which is not the case with other fission and statistical models. All calculations are made for spherical considerations and angular momenta taken up to the $\ensuremath{\ell}$-critical value for the respective reactions. A fusion enhancement is observed as we go from compound nuclei (CN) having an even number of neutrons ($^{24,26}\mathrm{Mg}^{*}$) to CN with the odd number of neutrons ($^{25,27}\mathrm{Mg}^{*}$). Interestingly, we find that the only parameter of the DCM, the neck-length parameter $\mathrm{\ensuremath{\Delta}}R$ related to the barrier lowering, is in linear relation with ${\ensuremath{\sigma}}_{\mathrm{Fusion}}$ at chosen incident laboratory energy. The fusion enhancement is found to be larger for odd neutron number nuclei, which indicates the influence of unpaired neutrons on fusion cross sections. Within the formalism of DCM, the phenomenon of fusion enhancement finds its base in the process of collective clusterization, which is quite evident from the larger values of summed-up preformation probability for the reactions having odd mass projectiles or forming odd mass CN. The DCM calculated fusion cross sections are in good agreement with the available experimental data for the given reactions.

Microscopic study of the fusion reactions Ca40,48+Ni78 and the effect of the tensor force

We provide a microscopic description of the fusion reactions between $^{40,48}\mathrm{Ca}$ and $^{78}\mathrm{Ni}$. The internuclear potentials are obtained using the density-constrained (DC) time-dependent Hartree-Fock (TDHF) approach and fusion cross sections are calculated via the incoming wave boundary condition method. By performing DC-TDHF calculations at several selected incident energies, the internuclear potentials for both systems are obtained and the energy-dependence of fusion barrier are revealed. The influence of tensor force on internuclear potentials of $^{48}\mathrm{Ca}+^{78}\mathrm{Ni}$ is more obvious than those of $^{40}\mathrm{Ca}+^{78}\mathrm{Ni}$. By comparing the calculated fusion cross sections between $^{40}\mathrm{Ca}+^{78}\mathrm{Ni}$ and $^{48}\mathrm{Ca}+^{78}\mathrm{Ni}$, an interesting enhancement of subbarrier fusion cross sections for the former system is found, which can be explained by the narrow width of internuclear potential for $^{40}\mathrm{Ca}+^{78}\mathrm{Ni}$ while the barrier heights and positions are very close to each other. The tensor force suppresses the subbarrier fusion cross sections of both two systems.

Exploring the effects of breakup couplings for weakly bound projectile 9Be on various targets at around barrier energies

Here, the fusion excitation functions of reactions induced by 9Be on various heavy mass targets, 144Sm, 169Tm, 181Ta, 186W, 187Re, 197Au and 208Pb, at around barrier energies have been studied within the framework of the Continuum Discretized Coupled Channel (CDCC) approach. The inconsistency in the definitions of theoretical and experimental fusion cross section is properly accounted for which results in a fair agreement between data and predictions at near and above barrier energies for all the targets except Tungsten. The difference between the measured and the calculated fusion cross section is found to be independent of the targets.

Exploring the fusion hindrance phenomenon: the case of 32,34S + 89Y

The sub-barrier fusion data of 32,34S + 89Y colliding systems are analyzed using the coupled-channels (CC) calculations, including couplings to the low-lying 2+ and 3− states in reacting nuclei as well as mutual and multi-phonon excitations of these states, based on the proximity potential model. In this scheme, we focus upon the the effect of surface energy coefficient γ and also thermal properties of liquids and hot nuclei on the inner part of the nuclear potential and thus on the fusion cross sections at bombarding energies far below the Coulomb barrier. As expected, our primary calculations using the original proximity potential 1977 show that this model underestimates the measured fusion cross sections at the whole energy region. It is shown that the mentioned physical effects bring significant cross sections enhancements for both reactions. The indications of the fusion hindrance phenomenon in the fusion cross sections at energies far below the Coulomb barrier show up. The observed S factors for the above-mentioned systems develop a maximum at low energies which can also be predicted by the phenomenological extrapolations. Our results within the framework of the modified form of the proximity potential reveal that the calculated fusion cross sections, S factors, and logarithmic slopes for the two systems are in good agreement with the corresponding experimental data even at the lowest energies.

Systematic investigation of “hindrance” in heavy-ion fusion reactions at deep sub-barrier energies

In order to explore the influence of adiabatic process on fusion reactions, we employ 13 different phenomenological nuclear potentials to make a systematic comparison of the experimental and calculated fusion cross sections. After two colliding nuclei contact, the adiabatic process is introduced to calculate the fusion cross sections at the above- and sub- barrier energies for 16 fusion reactions. At deep sub-barrier energy region, a detailed investigation is made to study the fusion hindrance by taking Krappe-Nix-Sierk, Bass (1980), and Akyüz-Winther nuclear potentials as examples. For newly observed fusion systems 12C + 198Pt, 11B + 197Au, and 40Ca + 90Zr, the calculated fusion cross sections are in good agreement with experimental data by considering the damping of coupled-channels effect. The results of astrophysical S factor and logarithmic derivative at deep sub-barrier energies show a close dependence on the behavior of potentials inside the Coulomb barrier. For newly observed light mass system 12C + 30Si, the corresponding improvement by considering the damping factor is small owing to the weak coupling effect.

A comprehensive analysis of 9Li + 70Zn fusion cross section by using proximity potentials, temperature dependent density distributions and nuclear potentials

The fusion cross section of $^{9}$Li + $^{70}$Zn reaction is studiedin an extensive manner within the framework of different theoreticalapproaches. For this purpose, three different methods which consistof proximity potentials, temperature dependent densities andtemperature dependent nuclear potentials are used in order todetermine the real part of the nuclear potential. The imaginary partis considered as Woods-Saxon potential. The calculated fusion crosssections are compared with the experimental data. The theoreticalresults describe the experimental data very well. It is seen thatthe applied approaches present to be different ways to study thereactions involving fusion cross sections.

N/Z dependence of decay channels in A=80 compound nuclei

A comparative decay analysis of $^{80}\mathrm{Zr}^{*}$, $^{80}\mathrm{Sr}^{*}$, and $^{80}\mathrm{Kr}^{*}$ isobaric nuclear systems formed in $^{40}\mathrm{Ca}+^{40}\mathrm{Ca}$, $^{16}\mathrm{O}+^{64}\mathrm{Zn}$, and $^{32}\mathrm{S}+^{48}\mathrm{Ca}$ reactions, respectively, has been conducted to investigate the $N/Z$ dependence of different decay modes within a dynamical cluster-decay model based on the collective clusterization approach of quantum mechanical fragmentation theory. The comparative contributions of the emission of light particles (LPs), intermediate mass fragments (IMFs), and symmetric mass fragments (SMFs) in the total fusion cross-sections, ${\ensuremath{\sigma}}_{\mathrm{fusion}}$, have been calculated. The results show that LPs have a major contribution to ${\ensuremath{\sigma}}_{\mathrm{fusion}}$ in the decay of all three compound nuclei (CN). The percentage contribution of LPs is larger for CN with higher $N/Z$ ratio. The IMFs and SMFs cross-section are comparatively low in the total ${\ensuremath{\sigma}}_{\mathrm{fusion}}$ but their emissions are in competition in the decay process. The results show that the shape of mass distribution evolves from symmetric to asymmetric with increasing $N/Z$ ratio. The yield around SMFs is greater for the system having the lowest $N/Z$ ratio. This may be attributed to higher ${P}_{0}$ for the symmetric exit channel, particularly at higher $\ensuremath{\ell}$ values. The calculated fusion cross-sections for all three CN are in good agreement with the experimental data.

Improved nucleus–nucleus folding potential with a repulsive core due to the change of intrinsic kinetic energy

The change in the internal kinetic energy (KE) of two interacting nuclei grows by increasing their density overlap. We investigated to what extent the double-folding potential based on the density dependent M3Y nucleon–nucleon interaction can be improved by considering this repulsive KE. We adopted the α-decay of , the 24Ne decay of 232U, and the fusion cross section as examples of reactions involving density redistribution. We performed the α and cluster decay calculations based on solving the Schrödinger equation to find the wavefunction and the penetration probability. Upon normalizing the calculated KE by applying the Bohr–Sommerfeld quantization condition, the necessary missed pocket is physically developed in the internal region of the total folding potential. The folding potential improved by considering the pivotal repulsive KE reduced the uncertainty inherent in the decay calculations at small internuclear distances. The calculated fusion cross section is substantially improved and its steep falloff at sub-barrier energies is reasonably reproduced.

Sensitivity of the fusion cross section to the density dependence of the symmetry energy

It is the aim of this paper to discuss the impact of nuclear fusion on the EOS. This is a timely subject given the expected availability of increasingly exotic beams at rare isotope facilities\,\cite{balantekin2014}. In practice, we focus on $^{48}$Ca+$^{48}$Ca fusion. We employ three different approaches to calculate fusion cross-sections for a set of energy density functionals with systematically varying nuclear matter properties. Fusion calculations are performed using frozen densities, using a dynamic microscopic method based on density-constrained time-dependent Hartree-Fock (DC-TDHF) approach, as well as direct TDHF study of above barrier cross-sections. For these studies, we employ a family of Skyrme parametrizations with systematically varied nuclear matter properties. We find a slight preference for forces which deliver a slope of symmetry energy of $L\approx 50$\,MeV that corresponds to a neutron-skin thickness of $^{48}$Ca of $R_\mathrm{skin}\!=\!(0.180\!-\!0.210)$\,fm.

Semi-classical model of neutron rearrangement using quantum coupled-channel approach

A quantum coupled-channel approach with collective degrees of freedom (the rotation of deformed nuclei and/or their surface vibrations) is combined with an empirical coupled-channel model to add neutron rearrangement channels to vibrational and rotational excitations. The calculated fusion cross sections and the barrier distribution functions for several combinations of nuclei are in good agreement with experimental data.

The effect of breakup of 6Li on elastic scattering and fusion with 28Si at near barrier energies

Elastic scattering angular distributions for 6Li+[Formula: see text]Si system were measured at [Formula: see text] and analyzed along with the existing data from the previous measurements in the energy range of [Formula: see text]. The measured cross-sections and the existing data, forming a set of angular distributions over a range of E/[Formula: see text], were analyzed using the phenomenological optical model potential (OMP). Three different sets of potential parameters were used. The energy dependence of the real and the imaginary potential strengths were, subsequently, extracted at the radius of sensitivity ([Formula: see text]) for the system. Continuum Discretized Coupled Channel (CDCC) calculation was performed to explore the contribution of projectile break-up (BU) on the observed energy dependence of the effective potential for elastic scattering of 6Li from [Formula: see text]Si. The energy variation of the strength of the real potential with continuum coupling was found to agree with the energy dependence of the same extracted from the (OMP) analysis at energies around the barrier. But the behavior of the imaginary strength appeared to be different. The calculated fusion cross-sections, including the effect of BU, clearly overestimated the measured fusion excitation function data in the below and near barrier energies but compared well with the data at higher energies.

Quantum coupled-channels model of nuclear fusion with a semiclassical consideration of neutron rearrangement

Background: Significant enhancement of sub-barrier fusion cross sections owing to neutron transfer with positive $Q$ values was observed in many combinations of colliding nuclei. This degree of freedom has not yet been included into the rigorous quantum coupled-channels (QCC) approach. However, the empirical coupled-channels model with neutron rearrangement [Zagrebaev, Phys. Rev. C 67, 061601 (2003)] has already been successfully used in several papers to reproduce and predict cross sections for sub-barrier fusion reactions of stable nuclei.Purpose: The objective of this study is to combine the QCC approach and the empirical model to account for additional channels of neutron rearrangement.Method: Coupling of relative motion to collective degrees of freedom (rotation of nuclei and/or their surface vibrations) are taken into account within the QCC approach. The probability of transfer of $x$ neutrons with a given $Q$ value is estimated semiclassically.Results: The proposed new model was successfully tested on a few combinations of fusing nuclei $^{40}\text{Ca}+^{90,94,96}\text{Zr}, ^{32}\text{S}+^{90,94,96}\text{Zr}$, and $^{60,64}\text{Ni}+^{100}\text{Mo}$. The calculated fusion cross sections and barrier distribution functions agree well with experimental data.Conclusions: The model developed in this work confirms all the conclusions previously made within the empirical coupled-channels model with neutron rearrangement [see Rachkov et al., Phys. Rev. C 90, 014614 (2014)]. Moreover, it has an advantage of a more reliable microscopic account for the coupling between relative motion and the collective degrees of freedom. The proposed model can also be used to reproduce the structure of the barrier distribution function. This is a step forward to a complete solution of the long-term problem of accounting for neutron transfer channels in the QCC model.

Three-stage classical molecular dynamics model for simulation of heavy-ion fusion

A three-stage Classical Molecular Dynamics (3S-CMD) approach for heavy-ion fusion is developed. In this approach the Classical Rigid-Body Dynamics simulation for heavy-ion collision involving light deformed nucleus is initiated on their Rutherford trajectories at very large initial separation. Collision simulation is then followed by relaxation of the rigid-body constrains for one or both the colliding nuclei at distances close to the barrier when the trajectories of all the nucleons are obtained in a Classical Molecular Dynamics approach. This 3S-CMD approach explicitly takes into account not only the long range Coulomb reorientation of the deformed collision partner but also the internal vibrational excitations of one or both the nuclei at distances close to the barrier. The results of the dynamical simulation for 24 Mg+208 Pb collision show significant modification of the fusion barrier and calculated fusion cross sections due to internal excitations.

Barrier distributions and signatures of transfer channels in theCa40+Ni58,64fusion reactions at energies around and below the Coulomb barrier

Background: The nuclear structure of colliding nuclei is known to influence the fusion process. Couplings of the relative motion to nuclear shape deformations and vibrations lead to an enhancement of the sub-barrier fusion cross section in comparison with the predictions of one-dimensional barrier penetration models. This enhancement is explained by coupled-channels calculations including these couplings. The sub-barrier fusion cross section is also affected by nucleon transfer channels between the colliding nuclei.Purpose: The aim of the present experiment is to investigate the influence of the projectile and target nuclear structures on the fusion cross sections in the $^{40}\mathrm{Ca}+^{58}\mathrm{Ni}$ and $^{40}\mathrm{Ca}+^{64}\mathrm{Ni}$ systems.Methods: The experimental and theoretical fusion excitation functions as well as the barrier distributions were compared for these two systems. Coupled-channels calculations were performed using the ccfull code.Results: Good agreement was found between the measured and calculated fusion cross sections for the $^{40}\mathrm{Ca}+^{58}\mathrm{Ni}$ system. The situation is different for the $^{40}\mathrm{Ca}+^{64}\mathrm{Ni}$ system where the coupled-channels calculations with no nucleon transfer clearly underestimate the fusion cross sections below the Coulomb barrier. The fusion excitation function was, however, well reproduced at low and high energies by including the coupling to the neutron pair-transfer channel in the calculations.Conclusions: The nuclear structure of the colliding nuclei influences the fusion cross sections below the Coulomb barrier for both $^{40}\mathrm{Ca}+^{58,64}\mathrm{Ni}$ systems. Moreover, we highlighted the effect of the neutron pair-transfer channel on the fusion cross sections in $^{40}\mathrm{Ca}+^{64}\mathrm{Ni}$.

Measurements of fusion reactions of low-intensity radioactive carbon beams on 12C and their implications for the understanding of X-ray bursts.

The interaction between neutron-rich nuclei plays an important role for understanding the reaction mechanism of the fusion process as well as for the energy production through pycnonuclear reactions in the crust of neutron stars. We have performed the first measurements of the total fusion cross sections in the systems (10,14,15)C+(12)C using a new active target-detector system. In the energy region accessible with existing radioactive beams, a good agreement between the experimental and theoretical cross sections is observed. This gives confidence in our ability to calculate fusion cross sections for systems which are outside the range of today's radioactive beam facilities.

Classical simulations of heavy-ion fusion reactions and weakly-bound projectile breakup reactions

Heavy-ion collision simulations in various classical models are discussed. Heavy-ion reactions with spherical and deformed nuclei are simulated in a classical rigid-body dynamics (CRBD) model which takes into account the reorientation of the deformed projectile. It is found that the barrier parameters not only on the initial orientations of the deformed nucleus, but also on the collision energy and the moment of inertia of the deformed nucleus. Maximum reorientation effect occurs at near- and below-barrier energies for light deformed nuclei. Calculated fusion cross-sections for 24Mg + 208Pb reaction are compared with a static-barrier-penetration model (SBPM) calculation to see the effect of reorientation. Heavy-ion reactions are also simulated in a 3-stage classical molecular dynamics (3S-CMD) model in which the rigid-body constraints are relaxed when the two nuclei are close to the barrier thus, taking into account all the rotational and vibrational degrees of freedom in the same calculation. This model is extended to simulate heavy-ion reactions such as6Li + 209Bi involving the weakly-bound projectile considered as a weakly-bound cluster of deuteron and 4He nuclei, thus, simulating a 3-body system in 3S-CMD model. All the essential features of breakup reactions, such as complete fusion, incomplete fusion, no-capture breakup and scattering are demonstrated.

A model for explaining fusion suppression using the classical trajectory method

A two-dimensional classical trajectory model is used to explain the projectile breakup and above-barrier fusion suppression for the reactions 6Li+209Bi, 6Li+152Sm and 6Li+144Sm. To obtain the initial conditions of the equations of motion, a simplified model of the 6Li nucleus has been developed. Numerical solutions of the equations lead to the classification of orbits into breakup and no-breakup trajectories. The breakup fraction is studied as a function of the impact parameter. Using quantum mechanical arguments, the cut-off impact parameter for fusion is determined by proposing a sharp cut-off model which assumes that there is an angular momentum limit to fusion. We introduce a simple formula for the explanation of fusion suppression, according to which fusion suppression is given by the average of the breakup fractions evaluated at impact parameters ranging from head-on collision up to the cut-off impact parameter. We find that there is excellent agreement between the experimental fusion cross section (σexp) and the calculated fusion cross section (σcal) for the systems studied.

Effects of the entrance channel mass asymmetry in fusion reactions

The symmetric and asymmetric fusion reaction systems forming the same compound nuclei 26Al, 30Si, 38Ar and 170Hf are investigated with the frame of improved isospin dependent quantum molecular dynamics model. The entrance channel mass asymmetry dependence of compound nucleus formation is found by analyzing the shell correction energies, the Coulomb barriers and the fusion cross sections. The calculated fusion cross sections agree quantitatively with the experimental data. The results indicate that compound nucleus formation is favorable for the systems with larger mass asymmetry because of the smaller Coulomb contribution to the fusion barrier.

Coulomb reorientation effect on near-barrier heavy-ion fusion reactions in rigid-body rotational dynamics calculation

A classical rigid-body dynamics model is used for study of Coulomb reorientation effect on the fusion dynamics. Model calculations show that barrier parameters depend on the initial orientations and also on the collision energy. Calculated fusion cross sections for 24Mg+ 208Pb and 16O+ 154Sm reactions show that reorientation effect is more pronounced in the case of 24Mg+ 208Pb reaction which involves a lighter deformed nucleus.

Fusion enhancement in the reactions of neutron-rich nuclei

The neutron-rich fusion reactions are investigated systematically using the improved isospin dependent quantum molecular dynamics model. By studying the systematic dependence of fusion barrier on neuron excess, we find the enhancement of the fusion cross sections for neutron-rich nuclear reactions that give the lowered static Coulomb barriers. The calculated fusion cross sections agree quantitatively with the experimental data. We further discuss the mechanism of the fusion enhancement of the cross sections for neutron-rich nuclear reactions by analyzing the dynamical lowering of the Coulomb barrier that is attributed to the enhancement of the N / Z ratio at the neck region.