Heavy-ion Fusion Reactions Research Articles

Dynamical explanation for the anomaly in the diffuseness parameter of the nucleus-nucleus potential in heavy-ion fusion reactions

The abnormally large diffuseness parameter of the Woods-Saxon (WS) potential in heavy-ion fusion reactions is explained for the first time based on the microscopic dynamics simulations. With the improved quantum molecular dynamic (ImQMD) model, we systematically explore the dynamical processes in the fusion reactions $^{12}\mathrm{C}+^{92}\mathrm{Zr}$, $^{16}\mathrm{O}+^{92}\mathrm{Zr}$, $^{28}\mathrm{Si}+^{92}\mathrm{Zr}$, $^{35}\mathrm{Cl}+^{92}\mathrm{Zr}$, $^{40}\mathrm{Ca}+^{46}\mathrm{Ti}$, and $^{16}\mathrm{O}+^{154}\mathrm{Sm}$. Without introducing any free model parameters or additional assumptions, the microscopic ImQMD model can reproduce the measured fusion cross sections of all selected colliding systems with good accuracy. Due to the dynamical evolutions of the density distributions in the fusion processes, the energy dependence of nucleus-nucleus potential can be clearly observed. Based on the dynamical nucleus-nucleus potential of the ImQMD simulations, we extract the corresponding diffuseness parameters of the WS potential. The obtained values locate in a range between $\mathit{a}=0.83$ and $1.17\phantom{\rule{0.16em}{0ex}}\mathrm{fm}$ at different incident energies. In addition, the regular decreasing trend for the diffuseness parameter with the increase of the incident energies is also observed.

Experimental fission study using multi-nucleon transfer reactions

It is shown that the multi-nucleon transfer reactions is a powerful tool to study fission of exotic neutron-rich actinide nuclei, which cannot be accessed by particle-capture or heavy-ion fusion reactions. In this work, multi-nucleon transfer channels of the reactions of 18 O+232 Th, 18 O+238 U and 18 O+248 Cm are used to study fission for various nuclei from many excited states. Identification of fissioning nuclei and of their excitation energy is performed on an event-by-event basis, through the measurement of outgoing ejectile particle in coincidence with fission fragments. Fission fragment mass distributions are measured for each transfer channel. Predominantly asymmetric fission is observed at low excitation energies for all studied cases, with a gradual increase of the symmetric mode towards higher excitation energy. The experimental distributions are found to be in general agreement with predictions of the fluctuation-dissipation model. Role of multi-chance fission in fission fragment mass distributions is discussed, where it is shown that mass-asymmetric structure remaining at high excitation energies originates from low-excited nuclei by evaporation of neutrons.

Study of fission using multi-nucleon transfer reactions

It is shown that multi-nucleon transfer reaction is a powerful tool to study fission of exotic neutronrich actinide nuclei, which cannot be accessed by particle-capture or heavy-ion fusion reactions. In this work, multi-nucleon transfer channels of the reactions of 18O+232Th, 18O+238U, 18O+248Cm, and 18O+237Np were used to measure fission-fragment mass distribution for each transfer channel. Predominantly asymmetric fission is observed at low excitation energies for all the studied cases, with an increase of the symmetric fission towards high excitation energies. Experimental data are compared with predictions of the fluctuation-dissipation model, where effects of multi-chance fission (neutron evaporation prior to fission) was introduced. It is shown that mass-asymmetric structure remaining at high excitation energies originates from low-excited and less neutronrich excited nuclei due to higher-order chance fissions.

Semiclassical coupled channels calculations in heavy-ion fusion reaction

Semiclassical coupled channels calculations in heavy-ion fusion reaction

Dynamical Dipole mode in heavy-ion fusion reactions

The excitation of the Dynamical Dipole mode along the fusion path was investigated for the first time in the formation of a heavy compound nucleus in the A~190 mass region. The compound nucleus was formed at identical conditions of excitation energy and spin from two entrance channels having different charge asymmetry: the charge asymmetric 40 Ca + 152 Sm and the nearly charge symmetric 48 Ca + 144 Sm at Elab =11 and 10.1 MeV/nucleon, respectively. Both fusion–evaporation and fission events were studied simultaneously for the first time. The Dynamical Dipole mode excitation in the charge asymmetric channel was evidenced, in a model-independent way, by comparing the γ -ray multiplicity spectra and angular distributions of the two entrance channels with each other.

Evolving theoretical descriptions of heavy-ion fusion: from phenomenological to microscopic approaches

We overview the current status of theoretical approaches for heavy-ion fusion reactions at subbarrier energies. We particularly discuss theoretical challenges in the coupled-channels approach, that include i) a description of deep subbarrier hindrance of fusion cross sections, ii) the role of nuclear dissipation, iii) fusion of unstable nuclei, and iv) an interplay between fusion and multi-nucleon transfer processes. We also present results of a semi-microscopic approach to heavy-ion fusion reactions, that combines the coupled-channels approach with state-of-the-art microscopic nuclear structure calculations.

Fusion and the Discovery of Isotopes

Heavy-ion fusion-evaporation has been the most productive method to form and identify new isotopes. Of the presently known over 3200 isotopes, almost 25% were discovered with heavy-ion induced reactions. Since the development of the first heavy-ion beam at Berkeley in 1950 most of the nuclides on the neutron-deficient side of the line of stability and all isotopes of the superheavy elements were discovered utilizing fusion reactions. In addition, some isotopes were first produced in heavy-ion transfer, charge-exchange, incomplete fusion or deep inelastic reactions. The discovery of isotopes relies on new advances in accelerator and detector technology. The continuous development of pioneering and innovative separation and detection techniques have pushed the limit towards ‒ and in many cases beyond ‒ the proton-dripline. A review of the discovery of neutron-deficient and super-heavy nuclides in heavy-ion induced reactions as well as an outlook for the discovery potential in the future is presented.

Effect of pre-equilibrium emission on probing postsaddle nuclear dissipation with neutrons**Supported by National Nature Science Foundation of China (11575044)

Using the stochastic Langevin model coupled with a statistical decay model, we study the influence of pre-equilibrium (PE) emission on probing postsaddle friction (β) with neutrons. A postsaddle friction value of (14 − 16.5) × 1021 s−1 and (11 − 13) × 1021 s−1 is obtained from comparing calculated and measured prescission neutron multiplicities of heavy fissioning systems 248Fm and 256Fm in the absence and presence of the deformation factor. Moreover, it is found that a larger β is required to fit multiplicity data after the PE effect is accounted for, and that the effect becomes stronger when more energy is removed by PE particles. Our findings suggest that, to more accurately determine the postsaddle friction strength through the measurement of prescission neutrons, in addition to incorporating the contribution of PE evaporation source into the experimental multi-source analysis for particle energy spectra in coincidence with fission fragments, on the theoretical side, it is very important to make a precise evaluation of the energy that PE emission carries away from excited compound systems produced in heavy-ion fusion reactions.

Systematic study of probable projectile-target combinations for the synthesis of the superheavy nucleus120302

Probable projectile-target combinations for the synthesis of superheavy element $^{302}$120 have been studied taking Coulomb and proximity potential as the interaction barrier. The probabilities of compound nucleus formation, PCN for the projectile-target combinations found in the cold reaction valley of $^{302}$120 are estimated. At energies near and above the Coulomb barrier, we have calculated the capture, fusion and evaporation residue cross sections for the reactions of all the probable projectile-target combinations so as to predict the most promising projectile-target combinations for the synthesis of SHE $^{302}$120 in heavy ion fusion reactions. The calculated fusion and evaporation cross section for the more asymmetric (hotter) projectile-target combination is found to be higher than the less asymmetric (colder) combination. It can be seen from the nature of quasi-fission barrier height, mass asymmetry, probability of compound nucleus formation, survival probability and excitation energy, the systems $^{44}$Ar + $^{258}$No, $^{46}$Ar + $^{256}$No, $^{48}$Ca + $^{254}$Fm, $^{50}$Ca + $^{252}$Fm, $^{54}$Ti + $^{248}$Cf, $^{58}$Cr + $^{244}$Cm in the deep region I of cold reaction valley, and the systems $^{62}$Fe + $^{240}$Pu, $^{64}$Fe + $^{238}$Pu, $^{68}$Ni + $^{234}$U, $^{70}$Ni + $^{232}$U, $^{72}$Ni + $^{230}$U, $^{74}$Zn + $^{228}$Th in the other cold valleys are identified as the better projectile-target combinations for the synthesis of $^{302}$120. Our prediction on the synthesis of $^{302}$120 superheavy nuclei using the combinations $^{54}$Cr+$^{248}$Cm, $^{58}$Fe+$^{244}$Pu, $^{64}$Ni+$^{238}$U and $^{50}$Ti+$^{249}$Cf are compared with available experimental data and other theoretical predictions.

Fission fragments mass distributions of nuclei populated by the multinucleon transfer channels of the 18O +232Th reaction

Abstract It is shown that the multinucleon transfer reactions is a powerful tool to study fission of exotic neutron-rich actinide nuclei, which cannot be accessed by particle-capture or heavy-ion fusion reactions. In this work, multinucleon transfer channels of the 18O + 232Th reaction are used to study fission of fourteen nuclei 231,232,233,234Th, 232,233,234,235,236Pa, and 234,235,236,237,238U. Identification of fissioning nuclei and of their excitation energy is performed on an event-by-event basis, through the measurement of outgoing ejectile particle in coincidence with fission fragments. Fission fragment mass distributions are measured for each transfer channel, in selected bins of excitation energy. In particular, the mass distributions of 231,234Th and 234,235,236Pa are measured for the first time. Predominantly asymmetric fission is observed at low excitation energies for all studied cases, with a gradual increase of the symmetric mode towards higher excitation energy. The experimental distributions are found to be in general agreement with predictions of the fluctuation–dissipation model.

Sub-barrier fusion excitation function data and energy dependent Woods–Saxon potential

This paper analyzed the role of intrinsic degrees of freedom of colliding nuclei in the enhancement of sub-barrier fusion cross-section data of various heavy ion fusion reactions. The influences of inelastic surface vibrations of colliding pairs are found to be dominant and their couplings result in the significantly larger fusion enhancement over the predictions of the one dimensional barrier penetration model at sub-barrier energies. The theoretical calculations are performed by using energy dependent Woods–Saxon potential model (EDWSP model) in conjunction with the one dimensional Wong formula. The effects of dominant intrinsic channels are entertained within framework of the coupled channel calculations obtained by using the code CCFULL. It is quite interesting to note that the energy dependence in Woods–Saxon potential simulates the effects of inelastic surface vibrational states of reactants wherein significantly larger value of diffuseness parameter ranging from a = 0.85fm to a = 0.95fm is required to address the observed fusion excitation function data of the various heavy ion fusion reactions.

Investigating multichannel quantum tunneling in heavy-ion fusion reactions with Bayesian spectral deconvolution

Excitations of colliding nuclei during a nuclear reaction considerably affect fusion cross sections at energies around the Coulomb barrier. It has been demonstrated that such channel coupling effects can be represented in terms of a distribution of multiple fusion barriers. I here apply a Bayesian approach to analyze the so-called fusion barrier distributions. This method determines simultaneously the barrier parameters and the number of barriers. I particularly investigate the $^{16}\mathrm{O}+^{144}\mathrm{Sm}$ and $^{16}\mathrm{O}+^{154}\mathrm{Sm}$ systems in order to demonstrate the effectiveness of the method. The present analysis indicates that the fusion barrier distribution for the former system is most consistent with three fusion barriers, even though the experimental data show only two distinct peaks.

Experimental study of the 13C+12C fusion reaction at deep sub-barrier energies

Heavy-ion fusion reactions between light nuclei such as carbon and oxygen isotopes have been studied because of their significance for a wide variety of stellar burning scenarios. One important stellar reaction is 12C+12C, but it is difficult to measure it in the Gamow window because of very low cross sections and several resonances occurring. Hints can be obtained from the study of 13C+12C reaction. We have measured this process by an activation method for energies down to Ecm=2.5 MeV using 13C beams from the Bucharest 3 MV tandetron and gamma-ray deactivation measurements in our low and ultralow background laboratories, the latter located in a salt mine about 100 km north of Bucharest. Results obtained so far are shown and discussed in connection with the possibility to go even further down in energy and with the interpretation of the reaction mechanism at such deep sub-barrier energies.

Microscopic study ofCa40+Ni58,64fusion reactions

Background: Heavy-ion fusion reactions at energies near the Coulomb barrier are influenced by couplings between the relative motion and nuclear intrinsic degrees of freedom of the colliding nuclei. The time-dependent Hartree-Fock (TDHF) theory, incorporating the couplings at the mean-field level, as well as the coupled-channels (CC) method are standard approaches to describe low energy nuclear reactions. Purpose: To investigate the effect of couplings to inelastic and transfer channels on the fusion cross sections for the reactions $^{40}$Ca+$^{58}$Ni and $^{40}$Ca+$^{64}$Ni. Methods: Fusion cross sections around and below the Coulomb barrier have been obtained from coupled-channels (CC) calculations, using the bare nucleus-nucleus potential calculated with the frozen Hartree-Fock method and coupling parameters taken from known nuclear structure data. The fusion thresholds and neutron transfer probabilities have been calculated with the TDHF method. Results: For $^{40}$Ca+$^{58}$Ni, the TDHF fusion threshold is in agreement with the most probable barrier obtained in the CC calculations including the couplings to the low-lying octupole $3_1^{-}$ state for $^{40}$Ca and to the low-lying quadrupole $2_1^{+}$ state for $^{58}$Ni. This indicates that the octupole and quadrupole states are the dominant excitations while neutron transfer is shown to be weak. For $^{40}$Ca+$^{64}$Ni, the TDHF barrier is lower than predicted by the CC calculations including the same inelastic couplings as those for $^{40}$Ca+$^{58}$Ni. TDHF calculations show large neutron transfer probabilities in $^{40}$Ca+$^{64}$Ni which could result in a lowering of the fusion threshold. Conclusions: Inelastic channels play an important role in $^{40}$Ca+$^{58}$Ni and $^{40}$Ca+$^{64}$Ni reactions. The role of neutron transfer channels has been highlighted in $^{40}$Ca+$^{64}$Ni.

Systematic study ofαdecay using various versions of the proximity formalism

Finding the best model to describe the {\alpha}-decay process is an old and ongoing challenge in nuclear physics. The present work systematically studied {\alpha}-decay half-lives for the favored ground-state-to-ground-state transitions of 344 isotopes of nuclei with 52 <= Z <= 107 using 28 versions of the proximity potential model in the framework of the WKB approximation. The present study introduces the best proximity versions with the fewest deviations with respect to experimental values. The models for Prox. 77-set 4, Prox. 77-set 5, and Dutt 2011 with the root-mean-square deviations (RMSDs) of <1 were found to predict {\alpha}-decay half-lives better than the other models. Comparison with fusion studies shows that Dutt 2011 is an appropriate model both for {\alpha}-decay studies and for prediction of the barrier characteristic in heavy-ion fusion reactions. The calculation of {\alpha}-decay half-lives were repeated for even-even, even-odd, odd-even, and odd-odd nuclei. This detailed comparative study reveals that for these versions the half-lives of the even-even nuclei with RMSDs of <0.6 show less deviation than the even-odd, odd-even, and odd-odd nuclei.

Absence of isotopic dependence of sub-barrier fusion enhancement in the formation of Sn-isotopes via different entrance channels

The roles of the intrinsic degrees of freedom of the colliding pairs, the entrance channel mass asymmetry effects and variation of the N/Z ratio in the formation of the Sn-isotopes via different channels are analyzed within the view of coupled channel approach and the energy dependent Woods-Saxon potential model (EDWSP model). In the fusion of T2248i + N2858,60,64i, T2246i + N2864i, T2250i + N2860i, and F919 + N4193b reactions, which result in the formation of different Sn-isotopes, the effects of inelastic surface excitations and multi-nucleon transfer channels are found to be dominant while the entrance channel mass asymmetry and variation of the N/Z ratio with neutron richness show a weak influence on the sub-barrier fusion dynamics. With the increase of the N/Z ratio, the strong isotopic sub-barrier fusion enhancement is expected for neutron rich target isotope. But such effects are found to be absent in the fusion dynamics of these reactions and consequently display a weak isotopic fusion enhancement at below barrier energies. Both coupled channel approach and the EDWSP model reasonably describe the observed fusion dynamics of chosen reactions. In addition, the EDWSP model based calculations are capable of providing an agreement with the experimental fusion cross-section data within 10%. For six heavy ion fusion reactions, only at 7 fusion data points out of 54 fusion data points does the deviation exceed 5% while 47 fusion data points lie within 5%. Therefore, within the view of the EDWSP model, it is possible to recover the above barrier portion of the fusion cross-section data within 5% with a probability greater than 87%.

Comparative studies for different proximity potentials applied to sub-barrier fusion reactions

Coulomb barrier heights calculated by using 14 different versions of proximity potentials are studied and applied for experimental data of fusion in terms of a recently proposed energy scaling approach. The results show that the descriptions of proximity potentials 77 and 88 for the barrier heights seem to be closest to the values required by the systematics. On the basis of proximity potential 77, the parameterized formulas of the barrier height and radius are obtained. These formulas can calculate the barrier positions and barrier heights reasonably well within the error, respectively. Thus it provides a simple and direct way to calculate the barrier positions and barrier heights for heavy-ion fusion reactions.

Role of Projectile Degrees of Freedom in Sub-Barrier Fusion Dynamics

This work theoretically investigates the role of the projectile degrees of freedom on the fusion dynamics of various heavy-ion fusion reactions. The impact of the projectile breakup channel is studied for the fusion mechanism of the 4 9 Be + 39 89 Y, 6 12 C + 39 89 Y, and 16 32,34 S + 39 89 Y reactions within the view of the coupled channel approach and the energy-dependent Woods-Saxon potential model (EDWSP model). The above-barrier fusion cross-section data of the 4 9 Be + 39 89 Y reaction is suppressed by about 20 % with respect to the theoretical predictions of the coupled channel approach and the single barrier penetration model while this suppression factor is reduced to 10 % within the context of the EDWSP model calculations. Such fusion hindrance at above-barrier energies can be understood in terms of the projectile breakup effects that arise due to its low breakup threshold. However, the observed fusion enhancement of the 6 12 C + 39 89 Y and 16 32,34 S + 39 89 Y reactions, wherein the colliding pairs are stable against breakup, is adequately explained by the EDWSP model and the coupled channel approach in the whole range of energy around the Coulomb barrier. This reveals that the energy dependence in the nucleus-nucleus potential governs barrier modification effects (barrier height, barrier position, barrier curvature) in closely similar way as reflected from the coupled channel formulation.

Recent developments in heavy-ion fusion reactions around the Coulomb barrier

The nuclear fusion is a reaction to form a compound nucleus. It plays an important role in several circumstances in nuclear physics as well as in nuclear astrophysics, such as synthesis of superheavy elements and nucleosynthesis in stars. Here we discuss two recent theoretical developments in heavy-ion fusion reactions at energies around the Coulomb barrier. The first topic is a generalization of the Wong formula for fusion cross sections in a single-channel problem. By introducing an energy dependence to the barrier parameters, we show that the generalized formula leads to results practically indistinguishable from a full quantal calculation, even for light symmetric systems such as $^{12}$C+$^{12}$C, for which fusion cross sections show an oscillatory behavior. We then discuss a semi-microscopic modeling of heavy-ion fusion reactions, which combine the coupled-channels approach to the state-of-the-art nuclear structure calculations for low-lying collective motions. We apply this method to subbarrier fusion reactions of $^{58}$Ni+$^{58}$Ni and $^{40}$Ca+$^{58}$Ni systems, and discuss the role of anharmonicity of the low-lying vibrational motions.

Present status of coupled-channels calculations for heavy-ion subbarrier fusion reactions

The coupled-channels method has been a standard tool in analyzing heavy-ion fusion reactions at energies around the Coulomb barrier. We investigate three simplifications usually adopted in the coupled-channels calculations. These are i) the exclusion of non-collective excitations, ii) the assumption of coordinate independent coupling strengths, and iii) the harmonic oscillator approximation for multi-phonon excitations. In connection to the last point, we propose a novel microscopic method based on the beyond-mean-field approach in order to take into account the anharmonic effects of collective vibrations.