Complete Fusion Cross Sections Research Articles

PLATYPUS: A code for reaction dynamics of weakly-bound nuclei at near-barrier energies within a classical dynamical model

A self-contained Fortran-90 program based on a classical trajectory model with stochastic breakup is presented, which should be a powerful tool for quantifying complete and incomplete fusion, and breakup in reactions induced by weakly-bound two-body projectiles near the Coulomb barrier. The code calculates complete and incomplete fusion cross sections and their angular momentum distribution, as well as breakup observables (angle, kinetic energy and relative energy distributions).

Study of reactions with the weakly bound projectile9Be with89Y

With the aim to investigate the in∞uence of the breakup channel on difierent reaction channels, the elastic scattering and fusion of 9 Be with the medium mass target 89 Y has been stud- ied at near barrier energies. Optical model analysis of the elastic data has been carried out and a dispersion relation applied to the real and imaginary potentials to investigate their energy depen- dence from which the presence of breakup threshold anomaly has been observed. Complete fusion (CF) cross sections, obtained for 9 Be+ 89 Y system, are found to be suppressed by (20 § 5)% as compared to the coupled-channels calculations without breakup coupling. This observation has been further conflrmed by comparing these cross sections with those for the 4 He+ 93 Nb and 12 C+ 89 Y systems, where fusion is induced by a tightly bound projectile and forms a nearby compound nu- cleus to that formed by 9 Be+ 89 Y. Results from the breakup coupling done in continuum discretized coupled-channels calculations show that the elastic cross sections thus obtained, which also flt the experimental elastic cross sections, are enhanced compared to the uncoupled calculations which im- plies a reduction in absorption/fusion cross sections. These enhanced cross sections suggest that the dynamic polarization potential produced due to breakup coupling is repulsive in nature. Thus the efiective (bare+polarization) potential around the barrier becomes less attractive leading to the absence of the normal threshold anomaly.

Systematic Results on Reactions and Scattering with Weakly Bound Nuclei at Near barrier Energies

We present a systematic interpretation of the results available in literature on the complete fusion, total fusion and total reaction cross sections induced by weakly bound nuclei and compare the results with those induced by tightly bound nuclei. We also investigate the behaviour of the energy dependence of the optical potential at near barrier energies for the same systems. We discuss the results of the systematic and present some experimental challenges on the future of this subject.

Study of fusion in6,7Li+197Au at near barrier energies

Excitation functions are measured for complete fusion and transfer reactions of 6 Li and 7 Li with 197 Au at energies around the Coulomb barrier. Coupled channel calculations including the couplings to both target and projectile excited states have been performed and are found to explain the data at energies below the barrier. At above barrier energies the complete fusion cross sections are found to be suppressed compared to the coupled channel calculations for both the systems. A systematic comparison of fusion cross-section for halo nuclei 6,8 He and weakly bound stable nuclei 6,7 Li on 197 Au target is also presented. Large neutron transfer cross-sections are observed for 6,7 Li as compared to tightly bound projectiles 12 C, 16 O.

Fusion cross sections for theBe9+Sn124reaction at energies near the Coulomb barrier

The complete and incomplete fusion cross sections for $^{9}\mathrm{Be}+^{124}\mathrm{Sn}$ reaction have been deduced using the online $\ensuremath{\gamma}$-ray measurement technique. Complete fusion at energies above the Coulomb barrier was found to be suppressed by $~28%$ compared to the coupled-channels calculations and is in agreement with the systematics of L. R. Gasques et al. [Phys. Rev. C 79, 034605 (2009)]. Study of the projectile dependence for fusion on a $^{124}\mathrm{Sn}$ target shows that, for $^{9}\mathrm{Be}$ nuclei, the enhancement at below-barrier energies is substantial compared to that of tightly bound nuclei.

Fusion of the weakly bound projectileBe9withY89

The excitation function for the complete fusion of $^{9}\mathrm{Be}$$+$$^{89}\mathrm{Y}$ has been measured at near-barrier energies, and the barrier distribution has been extracted from the fusion data. Coupled-channels calculations have been carried out to understand the effect of coupling of both the projectile and target excitations on the above quantities. The complete fusion cross sections, especially at above-barrier energies, have been found to be suppressed by ($20\ifmmode\pm\else\textpm\fi{}5$)% compared to the ones predicted by the coupled-channels calculations that do not include the couplings to the projectile continuum, indicating the loss of flux from the entrance channel before fusion. This conclusion is also supported by a considerable incomplete fusion cross section observed for this system. Fusion measurements for two more systems have been carried out, namely, for $^{4}\mathrm{He}$$+$$^{93}\mathrm{Nb}$ and $^{12}\mathrm{C}$$+$$^{89}\mathrm{Y}$, which involve tightly bound projectiles and form compound nuclei nearby to that formed in $^{9}\mathrm{Be}$$+$$^{89}\mathrm{Y}$ fusion. Comparison of the fusion data obtained for all three systems further confirms the suppression of complete fusion in the $^{9}\mathrm{Be}$$+$$^{89}\mathrm{Y}$ system. Systematics of the suppression factor observed for $^{9}\mathrm{Be}$ induced fusion in different mass targets is discussed.

Influence of projectile breakup on complete fusion

Complete fusion excitation functions for 11,10B+159Tb and 6,7Li+159Tb have been reported at energies around the respective Coulomb barriers. The measurements show significant suppression of complete fusion cross-sections at energies above the barrier for 10B+159Tb and 6,7Li+159Tb reactions, when compared to those for 11B+159Tb. The comparison shows that the extent of suppression of complete fusion cross-sections is correlated with the α-separation energies of the projectiles. Also, the measured incomplete fusion cross-sections show that the α-particle emanating channel is the favoured incomplete fusion process. Inclusive measurement of the α-particles produced in 6Li+159Tb reaction has been carried out. Preliminary CDCC calculations carried out to estimate the α-yield following 6Li breaking up into α+d fail to explain the measured α-yield. Transfer processes seem to be important contributors.

MECHANISMS PRODUCING FISSIONLIKE BINARY FRAGMENTS IN HEAVY ION COLLISIONS

The mixing of the quasifission component to the fissionlike cross section causes ambiguity in the quantitative estimation of the complete fusion cross section from the observed angular and mass distributions of the binary products. We show that the partial cross section of quasifission component of binary fragments covers the whole range of the angular momentum values leading to capture. The calculated angular momentum distributions for the compound nucleus and dinuclear system going to quasifission may overlap: competition between complete fusion and quasifission takes place at all values of initial orbital angular momentum. Quasifission components formed at large angular momentum of the dinuclear system can show isotropic angular distribution and their mass distribution can be in mass symmetric region similar to the characteristics of fusion-fission components. As result the unintentional inclusion of the quasifission contribution into the fusion-fission fragment yields can lead to overestimation of the probability of the compound nucleus formation.

Suppression of fusion by breakup: Resolving the discrepancy between the reactions ofBe9withPb208andBi209

Complete fusion cross sections for $^{9}\mathrm{Be}$ incident on $^{208}\mathrm{Pb}$ and $^{209}\mathrm{Bi}$ have been measured at energies greater than the fusion barrier to investigate the large differences in their reported complete fusion cross sections. Relative $\mathit{xn}$ and fission cross sections are in good agreement. Thus, it is concluded that the differences arise from errors in absolute normalization in the previous measurements. The present measurements show that the above-barrier complete fusion cross sections for the reactions of $^{9}\mathrm{Be}$ with $^{209}\mathrm{Bi}$ and $^{208}\mathrm{Pb}$ are very similar, which resolves the previously observed anomaly. Complete fusion for the reaction of $^{9}\mathrm{Be}$ with $^{209}\mathrm{Bi}$ is found to be suppressed by $~32%$ compared to the expectations of a single-barrier penetration model, which is in close agreement with the value previously determined for the reaction with $^{208}\mathrm{Pb}$.

New Approach for Evaluating Incomplete and Complete Fusion Cross Sections with Continuum-Discretized Coupled-Channels Method

We propose a new method for evaluating incomplete and complete fusion cross sections separately using the Continuum-Discretized Coupled-Channels method. This method is applied to analysis of the deuteron induced reaction on a 7Li target up to 50 MeV of the deuteron incident energy. Effects of deuteron breakup on this reaction are explicitly taken into account. Results of the method are compared with those of the Glauber model, and the difference between the two is discussed. It is found that the energy dependence of the incomplete fusion cross sections obtained by the present calculation is almost the same as that obtained by the Glauber model, while for the complete fusion cross section, the two models give markedly different energy dependence. We show also that a prescription for evaluating incomplete fusion cross sections proposed in a previous study gives much smaller result than an experimental value.

Continuum-continuum coupling and polarization potentials for weakly bound systems

We investigate the influence of couplings among continuum states in collisions of weakly bound nuclei. For this purpose, we compare cross sections for complete fusion, breakup and elastic scattering evaluated by continuum discretized coupled channel (CDCC) calculations, including and not including these couplings. In our study, we discuss this influence in terms of the polarization potentials that reproduce the elastic wave function of the coupled coupled channel method in single channel calculations. We find that the inclusion of couplings among the continuum states renders the real part of the polarization potential more repulsive, whereas it leads to weaker apsorption to the breakup channel. We show that the non-inclusion of continuum-continuum couplings in CDCC calculations may not lead to qualitative and quantitative wrong conclusions.

Stability of superheavy nuclei produced in actinide-based complete fusion reactions: Evidence for the next magic proton number atZ⩾120

Using the experimental evaporation residue cross sections in the $^{48}\mathrm{Ca}$-induced complete fusion reactions and the complete fusion cross sections calculated within the dinuclear system model, the survival probabilities of superheavy nuclei with charge numbers $Z=112\text{\ensuremath{-}}116$ and 118 in the $\mathit{xn}$-evaporation channels are extracted. The effects of angular momentum and deformations of colliding nuclei are taken into account. The obtained dependence of the survival probability on $Z$ indicates the next doubly magic nucleus beyond $^{208}\mathrm{Pb}$ at $Z\ensuremath{\geqslant}120$.

Suppression of complete fusion in theLi6+Sm144reaction

Complete fusion excitation function for the $^{6}\mathrm{Li}+^{144}\mathrm{Sm}$ reaction has been measured at near barrier energies by the activation technique. Coupled-channel calculations show an enhancement in fusion cross section at energies below the barrier compared to the one-dimensional barrier penetration model calculation, but they overpredict it in the entire energy range compared to the experimental data. Reduced fusion cross sections for the present system at energies normalized to the Coulomb barrier were also found to be systematically lower than those with strongly bound projectiles forming a similar compound nucleus. These two observations conclusively show that the complete fusion cross section, at above barrier energies, is suppressed by $~32%$ in the $^{6}\mathrm{Li}+^{144}\mathrm{Sm}$ reaction. Reanalyses of existing fusion data for $^{7}\mathrm{Li}+^{165}\mathrm{Ho}$ and $^{7}\mathrm{Li}+^{159}\mathrm{Tb}$ also show a suppression compared to those with strongly bound projectiles, which contradicts earlier conclusions. The fusion suppression factor seems to exhibit a systematic behavior with respect to the breakup threshold of the projectile and the atomic number of the target nucleus.

Suppression of complete fusion due to breakup in the reactionsB10,11+Bi209

Above-barrier cross sections of fission and $\ensuremath{\alpha}$-active heavy reaction products were measured for the reactions of $^{10,11}\mathrm{B}$ with $^{209}\mathrm{Bi}$. Systematic analysis showed that the fission originates almost exclusively from complete fusion (CF). Existing measurements of above-barrier fusion products for the $^{30}\mathrm{Si}+^{186}\mathrm{W}$ reaction, assumed to proceed exclusively through CF, were extrapolated to the current systems using statistical model calculations. This extrapolation showed that the heavy reaction products from the $^{10,11}\mathrm{B}+^{209}\mathrm{Bi}$ reactions include substantial components from incomplete fusion as well as from CF. Compared with fusion calculations without breakup, the CF cross sections are suppressed by 15% for $^{10}\mathrm{B}$ and 7% for $^{11}\mathrm{B}$. A consistent and systematic variation of the suppression of CF for reactions of the weakly bound nuclei $^{6,7}\mathrm{Li}$, $^{9}\mathrm{Be}$, and $^{10,11}\mathrm{B}$ on targets of $^{208}\mathrm{Pb}$ and $^{209}\mathrm{Bi}$ is found as a function of the breakup threshold energy.

Calculation of the energy dependence of the fusion cross section and total cross sections for peripheral reactions on the basis of an analysis of data on elastic heavy-ion scattering: Strongly bound ions

A method is proposed for calculating the energy dependence of the fusion cross section (in general, the sum of the cross sections for complete and incomplete fusion, quasifission, and reactions of deep-inelastic scattering) σF(E) and the total cross section for peripheral (or quasielastic) reactions, σD(E). The method is based on an analysis of a limited set of angular distributions for the elastic scattering in a given pair of nuclei. The predictive power of the method is illustrated by considering the 16O + 208Pb, 16O + 40Ca, and 16O + 28Si systems. For each of these systems, the calculations were performed at energies in the range extending from subbarrier values to those exceeding the barrier height substantially. The results of the calculations are found to be in good agreement with relevant experimental data, whereby the reliability of the method is confirmed. By virtue of this, it is proposed to employ the method to study the energy dependences σF(E) and σD(E) in collisions involving unstable nuclei, for which it is difficult to determine experimentally the above dependences because of a low intensity of secondary beams.

Synthesis of transactinide nuclei using radioactive beams

The prospects for the synthesis of transactinide nuclei using radioactive beams are evaluated quantitatively for a modern radioactive beam facility. A simple formalism for calculating the complete fusion cross sections that reproduces the known heavy element production cross sections over six orders of magnitude is used to calculate the production rates for transactinide nuclei with $Z\ensuremath{\leqslant}120$. All possible projectile and target combinations are evaluated. Exciting new possibilities for studies of the atomic physics, chemistry, and nuclear spectroscopy of the heaviest elements should be realized at a modern radioactive beam facility. The synthesis of new heavy elements is best undertaken at stable beam accelerators.

Relating Breakup and Incomplete Fusion of Weakly Bound Nuclei through a Classical Trajectory Model with Stochastic Breakup

A classical dynamical model that treats breakup stochastically is presented for low energy reactions of weakly bound nuclei. The three-dimensional model allows a consistent calculation of breakup, incomplete, and complete fusion cross sections. The model is assessed by comparing the breakup observables with continuum discretized coupled-channel quantum mechanical predictions, which are found to be in reasonable agreement. Through the model, it is demonstrated that the breakup probability of the projectile as a function of its distance from the target is of primary importance for understanding complete and incomplete fusion at energies near the Coulomb barrier.

Calculation of complete fusion cross sections of heavy ion reactions using the Monte Carlo method

The nucleus-nucleus potential for the fusion reactions {sup 40}Ca+{sup 48}Ca, {sup 16}O+{sup 208}Pb, and {sup 48}Ca+{sup 48}Ca has been calculated using the Monte Carlo method. The results obtained indicate that the technique employed for the calculation of the nucleus-nucleus potential is an efficient one. The effects of the spin and the isospin terms have also been studied using the same technique. The analysis of the results obtained for the {sup 48}Ca+{sup 48}Ca reaction reveal that the isospin-dependent term in the nucleon-nucleon potential causes the nuclear potential to drop by an amount of 0.5 MeV. The analytical calculations of the fusion cross section, particularly those at energies less than the fusion barrier, are in good agreement with the experimental data. In these calculations the effective nucleon-nucleon potential chosen is of the M3Y-Paris potential form and no adjustable parameter has been used.

Fusion and direct reactions around the barrier for the systemsBe7,9,Li7+U238

We present new cross section data for the complete fusion of the weakly bound systems $^{7,9}\mathrm{Be}$ and $^{7}\mathrm{Li}$ on $^{238}\mathrm{U}$ at energies around the Coulomb barrier. In the same measurement, yields for direct processes and incomplete fusion are detected. For all systems, a suppression of the complete fusion cross section around and above the barrier is observed. At energies below the barrier, the fusion of the $^{7}\mathrm{Be}+^{238}\mathrm{U}$ system shows no enhancement with respect to simple model predictions.

Comprehensive study of reaction mechanisms for theBe9+Sm144system at near- and sub-barrier energies

The delayed x-ray detection technique was used to measure complete and incomplete fusion cross sections for the $^{9}\mathrm{Be}+^{144}\mathrm{Sm}$ reaction at sub- and near-barrier energies. Elastic and inelastic scattering for this system were also measured. Reaction cross sections were derived and the transfer cross sections of one neutron were calculated. The suppression of complete fusion above the barrier, of the order of 10%, is attributed to $^{9}\mathrm{Be}$ breakup and is considerably smaller than the value of 30% found for the $^{9}\mathrm{Be}+^{208}\mathrm{Pb}$ system.