Experimental Fusion Cross Sections Research Articles

Sub-barrier capture with quantum diffusion approach

With the quantum diffusion approach the behavior of capture cross sections and mean-square angular momenta of captured systems are revealed in the reactions with deformed and spherical nuclei at sub-barrier energies. With decreasing bombarding energy under the barrier the external turning point of the nucleus-nucleus potential leaves the region of short-range nuclear interaction and action of friction. Because of this change of the regime of interaction, an unexpected enhancement of the capture cross section is found at bombarding energies far below the Coulomb barrier. This effect is shown its worth in the dependence of mean-square angular momentum on the bombarding energy. From the comparison of calculated capture cross sections and experimental capture or fusion cross sections the importance of quasifission near the entrance channel is demonstrated for the actinidebased reactions and reactions with medium-heavy nuclei at extreme sub-barrier energies.

Coupled–Channels Analyses For Heavy–Ion Fusion Reactions of <sup>16</sup>O+<sup>92</sup>Zr,<sup>144,148</sup>Sm Systems

We study in detail the fusion reaction of 16 O with 92 Zr and 144,148 Sm at sub-barrier energies with coupled-channels framework using the error function potential for the nuclear potential. In particular, we investigate the effects of multiphonon excitations in target nuclei on experimental fusion cross section and barrier distributions for these reactions. We show that the present coupled-channels calculations well account for the experimental data of the fusion cross section as well as the fusion barrier distributions. It is shown that the coupled-channels calculations taking into account the coupling up to double quadrupole phonon excitations in 92 Zr well reproduce the experimental fusion cross section as well as fusion barrier distribution for 16 O+ 92 Zr. However, for 16 O+ 144 Sm, coupling to single quadrupole and octupole phonon states in 144 Sm can well explain the experimental data. And the coupling up to triple quadrupole phonon states and double octupole phonon excitations in 144 Sm are needed in order to reproduce the experimental data. Our study indicates the error function potential is adequate for analyses of the heavy-ion fusion reactions. Received: 20 November 2009; Revised: 17 April 2010; Accepted: 18 April 2010

An electrostatic deflector for a fusion reaction

An electrostatic deflector for separating the fusion evaporation residues from the beam-like products in heavy ion reactions was installed. The evaporation residue separation and identification with the electrostatic deflector setup was tested with the reaction 32S+96Zr at several energies. The fusion evaporation residues and the beam-like particles were well separated after the electrical separation and the experimental fusion cross section obtained from the angular distribution is in good agreement with the calculated value well above the Coulomb barrier. This confirms the reliability of the setup.

Effect of the Drive Parameter on the Differential Fusion Products in Plasma Focus Devices

A moving-boiler model is employed to study the branching ratio of two D-D reaction channels in plasma focus (PF) devices. This model is based on the thermal spreading of the pinched plasma toward the axial direction of the device. In this way, the experimental fusion cross sections of D(d, n)3He and D(d, p)3H reactions are used to calculate the velocity-averaged cross sections due to the penetration of the confined particles into the thermal boiler. The results obtained represent an indispensable effect of the drive parameter on the differential fusion yields. Obviously, an increment of the drive parameter has a high impact on the yields. However, this impact is dominantly in favor of proton yield particularly at lower drift velocity. Furthermore, a saturated condition is obtained at high drift velocity of the boiler. These facts are important for the optimization of fusion emissions in PFs for future applications, particularly in the field of short-lived radioisotope production.

Interaction of loosely bound radioactive 7Be and stable 7Li with 9Be

Quasielastic scattering angular distributions have been measured for the 7Be + 9Be system at Elab = 17 , 19 and 21MeV in the angular range \( \theta_{{cm}}^{}\) = 24° - 57° . An optical model (OM) analysis of these data has been carried out in order to extract optical potential parameters and reaction cross-sections. One-proton stripping cross-sections were also measured for this system at Elab = 19 and 21MeV. These transfer angular-distribution data were compared with the finite-range distorted-wave Born approximation (FRDWBA) calculations. For the 7Li + 9Be system quasielastic scattering angular distributions were measured and emitted light charged particles were detected at Elab = 15.75 , 24.00 and 30.00MeV in the angular range \( \theta_{{cm}}^{}\) = 7° - 70° . Fusion cross-sections were obtained by reproducing the measured \( \alpha\) -evaporation spectra from the compound nucleus at backward angles with the statistical model calculations. The ratios of the experimental fusion cross-sections to the total reaction cross-sections (obtained from OM analysis) were found to be small. This result suggests that the break-up process has a strong influence on the fusion process leading to a reduction in the fusion cross-section.

Channel coupling effects on the fusion excitation functions forSi28+Zr90,94in sub- and near-barrier regions

Fusion excitation functions and angular distributions of evaporation residues (ERs) have been measured for $^{28}\mathrm{Si}+^{90,94}\mathrm{Zr}$ systems around the Coulomb barrier using the recoil mass spectrometer, Heavy Ion Reaction Analyzer (HIRA). For both systems, the experimental fusion cross sections are strongly enhanced compared to the predictions of the one-dimensional barrier penetration model (1-d BPM) below the barrier. Coupled channels formalism has been employed to theoretically explain the observed sub-barrier fusion cross section enhancement. The enhancement could be explained by considering the coupling of the low-lying inelastic states of the projectile and target in the $^{28}\mathrm{Si}+^{90}\mathrm{Zr}$ system. In the sub-barrier region, the measured fusion cross sections for $^{28}\mathrm{Si}+^{94}\mathrm{Zr}$ turned out to be about an order of magnitude higher than the ones for the $^{28}\mathrm{Si}+^{90}\mathrm{Zr}$ system, which could not be explained by coupling to inelastic states alone. This observation indicates the importance of multinucleon transfer reaction channels with positive $Q$ values in the sub-barrier fusion cross section enhancement, because $^{90,94}\mathrm{Zr}$ are believed to have similar collective strengths. This implies that no strong isotopic dependence of fusion cross sections is expected as far as the couplings to collective inelastic states are concerned. In addition, the role of projectile and multiphonon couplings in the enhancement has been explored.

Quasifission and difference in formation of evaporation residues in the 16O + 184W and 19F + 181Ta reactions

The role of the entrance channel has been studied to ascertain a cause of the observed difference between the evaporation residue cross sections normalized to the fusion cross sections in the 19F+181Ta and 16O+184W reactions at high excitation energies. The theoretical analysis performed in the framework of the dinuclear system and advanced statistical models showed that the more intense yield of evaporation residues in the 16O+184W reaction in comparison with that in the 19F+181Ta reaction was explained by the large capture and fusion cross sections in the former reaction, which is in agreement with the experimental data. The observed decrease in the evaporation residue cross section normalized to the fusion cross section in the 19F+181Ta reaction, in comparison with one in the 16O+184W reaction at large excitation energies, is caused by the unintentional inclusion of the quasifission and fast fission contributions in the fissionlike fragment yields that were used in reconstructing the experimental fusion cross section in the normalizing procedure. The range of the angular momentum distribution for both systems was similar, but the partial cross sections are different, showing the presence of a difference in the hindrance to complete fusion in both reactions.

The α-nucleus potential for fusion and decay

The α-nucleus fusion cross sections at energies around and below the barrier and the α-decay half lives are calculated in the semi-classical WKB approach using the same microscopic as well as empirical α-nucleus potentials. The microscopic potential is generated within the double-folding framework using M3Y nucleon–nucleon interaction along with the required neutron and proton density distributions calculated in the relativistic mean field theory. It is found that in spite of the excellent results for the half lives the fusion cross sections are underestimated by almost a factor of 3. However, the experimental fusion cross sections can be reproduced by introducing a norm factor (overall multiplicative factor to the potential) 1.3 but this then worsens the agreement for half lives. To verify this observation and for comparison the calculations are repeated using some of the representative empirical potentials available in the literature. The same conclusion emerged. The present study thus indicates that the same α-nucleus potential may yield accurate description for both the α-nucleus fusion cross sections and α-decay half lives only with the introduction of additional parameter(s).

Measurements of elastic scattering for 7Be, 7Li + 9Be systems and fusion cross sections for 7Li + 9Be system

Elastic scattering angular distributions have been measured for 7Be + 9Be system at Elab = 17, 19 and 21 MeV in the angular range θcm=26○–58°, and for 7Li + 9Be system at Elab= 15.75, 24 and 30 MeV. An optical model (OM) analysis of these data have been carried out. For the 7Li + 9Be system fusion cross sections were obtained at Elab = 15.75, 24 and 30 MeV by measuring the α-evaporation spectra from the compound nucleus at backward angles. The measured α-evaporation spectra were reproduced by the statistical model calculations and fusion cross sections were extracted therefrom. The ratios of the experimental fusion cross sections to the total reaction cross sections (obtained form OM analysis) were found to be rather small. This result suggests that break-up process has a strong influence on fusion process leading to a reduction in fusion cross section.

The finite size effects in fusion of deformed nuclei at incident energies near the barrier

By the end of the last century, the precision of heavy-ion-fusion cross-section measurement had been increased up to 1%. This allowed the measured cross sections to be converted into experimental fusion-barrier distributions. In the experimental analysis, the barrier distributions were analyzed using a Woods-Saxon shape for the nuclear part of the bare nucleus-nucleus potential. This potential was defined along the line joining the centers of the two nuclei (“centerline potential”), which, for deformed nuclei, contradicts the short-range character of the nucleon-nucleon (N N) nuclear interaction. We present the results of our theoretical study of the significant deviations of the simplified potential from a “realistic” nuclear potential. The finite-size effects on the potential for deformed nuclei were first investigated in an approximate geometrical way. Then a more rigorous approach, namely, a semimicroscopic double-folding model, was applied to calculate the nucleus-nucleus potential. The angle-dependent fusion barriers calculated with a simple delta-function-like exchange term of the N N M3Y interaction was found to be very similar to those calculated with a finite-range expression. This circumstance enables us to perform rather quick calculations of the fusion cross sections and the corresponding barrier distributions. Comparison of the results with the experimental data showed that the finite-size effects are substantial and cannot be ignored in a quantitative analysis of experimental fusion cross sections and barrier distributions.

Semi-microscopic calculations of the fusion barrier distributions for reactions involving deformed target nuclei

The double-folding model with an M3Y effective nucleon-nucleon (NN) interaction was applied to obtain the angle-dependent bare nucleus-nucleus potential for heavy-ion fusion reactions involving deformed target nuclei. The angular dependence with a zero-range exchange NN interaction is almost identical to that with a finite-range interaction, allowing quick calculations of the fusion cross sections and corresponding barrier distributions $D({E}_{c.m.})$. Since in the literature the experimental $D({E}_{c.m.})$ have been analyzed usually using a Woods-Saxon shape for the nuclear part of the nucleus-nucleus potential, we fitted the spherical double-folding potentials at the barrier radii with a Woods-Saxon (WS) form. The calculated $D({E}_{c.m.})$ with this fitted WS potential, but now accounting for the deformation of the target nuclei, are significantly different from the $D({E}_{c.m.})$ calculated directly using the double-folding potential. This indicates that the finite size effects are substantial and should not be ignored in the analysis of experimental fusion cross sections and barrier distributions for reactions with statically deformed nuclei.

Partial fusion of a weakly bound projectile with heavy target at energies above the Coulomb barrier

Partial-fusion cross-sections for the systems 6Li + 208Pb, 9Be + 209Bi have been determined. The effect of breakup on fusion for weakly bound projectiles 6Li and 9Be incident on 208Pb or 209Bi targets has been discussed comparing experimental fusion cross-section excitation functions to those evaluated with a semi-classical approach. It is shown that complete fusion of a weakly bound projectile with heavy target is reduced, whereas the breakup process has very little influence on the total-fusion cross-section for some of the studied systems at energies above the Coulomb barrier.

Fusion of heavy ions by means of the Langevin equation

The Langevin equation was used to describe fusion dynamics in two systems, $^{64}\mathrm{Ni}+^{100}\mathrm{Mo}$ and $^{64}\mathrm{Ni}+^{96}\mathrm{Zr}$. The corresponding fusion cross sections were calculated for different energies, and the mean angular momentum and its dependence on energy were also obtained. We were able to reproduce experimental fusion cross sections at high energies with the one-body dissipation mechanism. Attention was focused on the fusion barrier calculated with the Yukawa-plus-exponential method.

Consistent analysis of peripheral reaction channels and fusion for the 16,18O + 58Ni systems

We have measured elastic scattering and peripheral reaction channel cross sections for the 16,18O + 58Ni systems at E Lab = 46 MeV . The data were analyzed through extensive coupled-channel calculations. It was investigated the consistency of the present analysis with a previous one at sub-barrier energies. Experimental fusion cross sections for these systems are also compared with the corresponding predictions of the coupled-channel calculations.

How does breakup influence the total fusion ofLi6,7at the Coulomb barrier?

Total (complete + incomplete) fusion excitation functions of $^{6,7}$Li on $^{59}$Co and $^{209}$Bi targets around the Coulomb barrier are obtained using a new continuum discretized coupled channel (CDCC) method of calculating fusion. The relative importance of breakup and bound-state structure effects on total fusion is particularly investigated. The effect of breakup on fusion can be observed in the total fusion excitation function. The breakup enhances the total fusion at energies just around the barrier, whereas it hardly affects the total fusion at energies well above the barrier. The difference between the experimental total fusion cross sections for $^{6,7}$Li on $^{59}$Co is notably caused by breakup, but this is not the case for the $^{209}$Bi target.

Theory of fusion for superheavy elements

A new model is proposed for fusion mechanisms of massive nuclear systems, where so-called fusion hindrance exists. The model describes the whole process in two steps: two-body collision processes in an approaching phase and shape evolutions of an amalgamated system into the compound nucleus formation. It is applied to 48Ca-induced reactions and is found to reproduce the experimental fusion cross sections extremely well, without any free parameter. A schematic case is solved in an analytic way, the results of which shed light on fusion mechanisms. Combined with statistical decay theory, residue cross sections for superheavy elements can be readily calculated. Examples are given.

Two-step model of fusion for the synthesis of superheavy elements

A new model is proposed for fusion mechanisms of massive nuclear systems where so-called fusion hindrance exists. The model describes two-body collision processes in an approaching phase and shape evolutions of an amalgamated system into the compound nucleus formation. It is applied to $^{48}$Ca-induced reactions and is found to reproduce the experimental fusion cross sections extremely well, without any free parameter. Combined with the statistical decay theory, residue cross sections for the superheavy elements can be readily calculated. Examples are given.

Accuracy in the detemination of fusion barriers

Although there is no proof of the validity of the method, in a lot of papers, one computes the Second derivative of the the experimental fusion cross section multiplied by the energy to extract the fusion barriers directly from the experiment. The purpose of this paper is to check the consistency of the method, as experimental points are sandwiched inside their error bars. We therefore analysed the validity, by giving ourselves a cross section σ(E), resulting from the coupled channel calculation code ECIS, upon which, in spite of the complexity of the calculations, we have full control. We took these calculated points as the “experimental” ones and we altered them by multiplication by small random numbers. This is intended to simulate the error bars, of which we want to examine the influence on the fusion barriers. We find that in spite of the rough predictions yielded by the second derivative method, this task requires data with a precision difficult to reach. Furthermore, a careful check of the predictions of this method for coupled channels calculations shows that, due to the errors bars, this approach adds spurious results.

Subbarrier heavy ion fusion enhanced by nucleon transfer

We discuss a model for the description of subbarrier fusion of heavy ions which takes into account the coupling to the low-energy surface vibrational states and to the few-nucleon transfer with arbitrary reaction Q -value. The fusion reactions 28,30Si+58,62,64Ni, 40Ca+90,96Zr, 28S+94,100Mo, 58Ni+64Ni, 16,18,20,22,24O+58Ni and 28Si+124,126,128,130,132Sn are analyzed in detail. The model describes rather well the experimental fusion cross section and mean angular momentum for reactions between nuclei near the β-stability line. It is shown that these quantities are significantly enhanced by few-nucleon transfer with large positive Q-value. A shape independent parameterization of the heavy ion potential at distances smaller then the touching point is proposed.

Theoretical studies of atomic cluster - cluster collisions

A theoretical study on collisions between fullerenes for the systems , and is presented covering a wide range of collision energies (50 < E < 250 eV in the centre-of-mass frame). Quantum molecular dynamics (QMD) simulations enable a detailed insight into the underlying mechanism of the different reaction channels. The fusion barriers for the investigated systems are determined and compared with experimental data taking into account the finite temperature of the colliding fullerenes. Structural as well as energetic aspects of the reaction mechanism are discussed from a microscopic point of view. As a counterpart to the QMD simulations, a simple phenomenological fusion model is described and compared to the experimental fusion cross section as a function of the collision energy.