Heavy Fusion Research Articles

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.

Describing the heavy-ion above-barrier fusion using the bare potentials resulting from Migdal and M3Y double-folding approaches

Systematic calculations of the Coulomb barrier parameters for collisions of spherical nuclei are performed within the framework of the double folding approach. The value of the parameter (which estimates the Coulomb barrier height) varies in these calculations from 10 MeV up to 150 MeV. The nuclear densities came from the Hartree–Fock calculations which reproduce the experimental charge densities with good accuracy. For the nucleon-nucleon effective interaction two analytical approximations known in the literature are used: the M3Y and Migdal forces. The calculations show that Migdal interaction always results in the higher Coulomb barrier. Moreover, as BZ increases the difference between the M3Y and Migdal barrier heights systematically increases as well. As the result, the above barrier fusion cross sections calculated dynamically with the M3Y forces and surface friction are in agreement with the data. The cross sections calculated with the Migdal forces are always below the experimental data even without accounting for the dissipation.

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.

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.

Indirect Study of the16O+16O Fusion Reaction Toward Stellar Energies by the Trojan Horse Method

The 16 O+ 16 O fusion reaction is important in terms of the explosive oxygen burning process during late evolution stage of massive stars as well as understanding of the mechanism of low-energy heavy-ion fusion reactions. We aim to determine the excitation function for the most major exit channels, α + 28 Si and p + 31 P, toward stellar energies indirectly by the Trojan Horse Method via the 16 O( 20 Ne , α 28 Si) α and 16 O( 20 Ne , p 31 P) α three-body reactions. We report preliminary results involving reaction identification, and determination of the momentum distribution of α - 16 O intercluster motion in the projectile 20 Ne nucleus.

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.

Heavy-ion fusion probability and nuclear fission rate in a quantum non-ohmic environment

Heavy-ion fusion probability and nuclear fission rate in a quantum non-ohmic environment

Analysis of fusion dynamics of colliding systems involving stable, loosely bound and halo nuclei

This article analyzed the fusion dynamics of stable nuclei, loosely bound nuclei and halo nuclei within the view of coupled channel approach and the energy dependent Woods–Saxon potential model (EDWSP model). The different projectiles ( and are bombarded onto common spherical target isotope ( wherein target isotope exhibits inelastic surface excitations as dominant mode of coupling. The fusion dynamics of reactions, wherein there is no signature of fusion suppression at above barrier energies, are adequately explained by both theoretical approaches in domain of Coulomb barrier. In case of reactions, the couplings of inelastic surface excitations of colliding systems remove the discrepancies between below barrier fusion data and expectations of one-dimensional barrier penetration model. However, at above barrier energies, the fusion excitation function data are suppressed in comparison to the theoretical predictions of both approaches. Interestingly, this suppression of above barrier fusion data is minimized by the present model calculation by a factor of 7% with respect to a value reported in literature. Within the view of the EDWSP model calculations, the above barrier fusion data of reaction are hindered by a factor of 25% and by a factor of 17% for reaction which is smaller than a value as pointed out in literature. The observed sub-barrier fusion dynamics of and reactions are reasonably described by the coupled channel model and the EDWSP model. Furthermore, the applicability of the EDWSP model has been tested for exploration of the fusion of reaction and hence due to barrier modification effects, the EDWSP model successfully explains the observed fusion enhancement of reaction. The present calculations clearly indicate that different theoretical approaches (coupled channel formulation and EDWSP model) induce similar kinds of barrier modification effects in the heavy ion fusion reactions.

Nuclear dynamical octupole deformation in heavy-ion reactions

Within the quantum molecular dynamics (QMD) model, the dynamical octupole deformation is studied as a function of the central distance between the projectile and target in the approaching process of heavy-ion fusion reactions. The dependence of the maximum dynamical octupole deformations on the incident energies is also investigated. The dynamical octupole deformations can be observed during the approaching process, and the maximum dynamical octupole deformations become more significant with decreasing incident energies. The distributions of the proton and neutron centers in the projectile and target are also investigated, respectively. In the approaching process of heavy-ion fusion reactions, the separation between proton centers for two nuclei is larger than that between neutron centers because of the strong Coulomb potential.

Configuration transition effect in heavy-ion fusion reactions with deformed nuclei

Fusion reactions of 16O + 24Mg are investigated with the three-dimensional time-dependent Hartree-Fock (TDHF) method. The resultant fusion excitation functions show some novel features that are beyond the current understandings and the predictions of various theoretical models. We will demonstrate that these phenomena cannot be explained by a density rearrangement effect but by the configuration transition mechanism in the dynamical process.

Well-defined atomic hydrogen target driven by electromagnetic shock wave for stopping power measurement

AbstractThe precise estimation of stopping power is crucial to predict the beam energy loss in the target for heavy-ion fusion and heavy-ion-driven high-energy density physics experiments. The electromagnetic shock wave has been proposed to generate a well-defined atomic hydrogen target for the stopping power measurement with dissociation effects. We measured the angular distribution profile of the discharge plasma and the plasma velocity in the electromagnetic shock tube by high-speed framing cameras. To improve the uniformity of the discharge plasma and the velocity, an external magnetic field was applied in the electromagnetic shock tube. The plasma velocity was up to approximately 40 km/s for an initial hydrogen gas pressure of 100 Pa and the velocity decreased with the initial pressure and the propagation length. The framing cameras showed that angular distributions of the discharge plasmas were not uniform and the initial angular distributions were important for the development of plasma profiles. The interaction of the plasma with the external magnetic field was estimated using the ratio of the plasma dynamic pressure to the magnetic pressure. The estimations offer more magnetic fields to improve the discharge uniformity due to the interaction.

Investigation of physical parameters in ion-beam-heated converters

The conversion of ion beam energy into thermal X-ray radiation by means of stretched cylindrical volumes is discussed. Converting the kinetic energy of heavy ion beam into radiation energy at high efficiency is important for heavy ion fusion. The conversion efficiency between different materials, low-Z and high-Z material, is compared and simulations have been performed by SRIM code. Our results show high-z materials are superior converters. It is found to achieve a high conversion efficiency, a deposition power higher than 1016 W/cm2 is required.

Effects of intrinsic degrees of freedom in enhancement of sub-barrier fusion excitation function data and energy-dependent one-dimensional barrier penetration model

We have analyzed the role of barrier modification effects (barrier height, barrier position, barrier curvature) introduced due to the energy-dependent Woods–Saxon potential model (EDWSP model) and the coupled channel model on the sub-barrier fusion dynamics of $$ {}_{16}^{32,36} {\text{S}} + {}_{40}^{90,96} {\text{Zr}} $$ reactions. The influence of inelastic surface excitations of colliding pairs and multi-neutron transfer channels is found to be a dominant mode of couplings. The coupling of relative motion of colliding nuclei to these dominant intrinsic degrees of freedom leads to a substantially large fusion enhancement at below-barrier energies over the expectations of one-dimensional barrier penetration model. The coupled channel calculations based upon static Woods–Saxon potential must include the internal nuclear structure degrees of freedom of colliding nuclei for complete description of experimental data. On the other hand, theoretical calculations based upon the EDWSP model along with Wong formula provide a complete description of sub-barrier fusion enhancement of various heavy-ion fusion reactions. In EDWSP model calculations, significantly larger values of diffuseness parameter ranging from a = 0.98 fm to a = 0.85 fm are required to address the observed sub-barrier fusion enhancement of $$ {}_{16}^{32,36} {\text{S}} + {}_{40}^{90,96} {\text{Zr}} $$ reactions. Furthermore, within the context of EDWSP model, it is possible to achieve an agreement with the experimental fusion cross-sectional data within 10 %. For four heavy-ion fusion reactions, only at 4 fusion data points out of 90 fusion data points deviates exceeding 5 %, while 86 fusion data points lie within 5 % and hence the EDWSP model is able to account the above-barrier portion of the fusion cross-sectional data within 5 % with a probability greater than 90 %.

Fusion measurements for the O+ reaction and search for neutron shell closure effects

Evaporation residue (ER) and fission cross sections were measured for the reaction O+ forming the compound nucleus 212Rn. Fission fragment angular distributions and anisotropies are consistent with the saddle point model predictions. Measured ER cross sections were fitted with statistical model calculations assuming shell-corrected free energy fission barrier height. The non-zero dissipation strength required to fit the ER cross section supports the dissipative nature of fission dynamics in heavy ion fusion. In the present study shell closure effects are not observed in the dissipation strength.

Uniformity of fuel target implosion in heavy ion fusion

AbstractIn inertial confinement fusion the target implosion non-uniformity is introduced by a driver beams’ illumination non-uniformity, a fuel target alignment error in a fusion reactor, the target fabrication defect, etc. For a steady operation of a fusion power plant the target implosion should be robust against the implosion non-uniformities. In this paper the requirement for the implosion uniformity is first discussed. The implosion uniformity should be less than a few percent. A study on the fuel hotspot dynamics is also presented and shows that the stagnating plasma fluid provides a significant enhancement of vorticity at the final stage of the fuel stagnation. Then non-uniformity mitigation mechanisms of the heavy-ion beam (HIB) illumination are also briefly discussed in heavy ion inertial fusion (HIF). A density valley appears in the energy absorber, and the large-scale density valley also works as a radiation energy confinement layer, which contributes to a radiation energy smoothing. In HIF a wobbling HIB illumination was also introduced to realize a uniform implosion. In the wobbling HIBs illumination, the illumination non-uniformity oscillates in time and space on a HIF target. The oscillating-HIB energy deposition may contribute to the reduction of the HIBs’ illumination non-uniformity by its smoothing effect on the HIB illumination non-uniformity and also by a growth mitigation effect on the Rayleigh–Taylor instability.

Microscopic analysis of fusion hindrance in heavy nuclear systems

Background: Heavy-ion fusion reactions involving heavy nuclei at energies around the Coulomb barrier exhibit fusion hindrance, where the probability of compound nucleus formation is strongly hindered compared with that in light- and medium-mass systems. The origin of this fusion hindrance has not been well understood from a microscopic point of view. Purpose: Analyze the fusion dynamics in heavy systems by a microscopic reaction model and understand the origin of the fusion hindrance. Method: We employ the time-dependent Hartree-Fock (TDHF) theory. We extract nucleus--nucleus potential and energy dissipation by the method combining TDHF dynamics of the entrance channel of fusion reactions with one-dimensional Newton equation including a dissipation term. Then, we analyze the origin of the fusion hindrance using the properties of the extracted potential and energy dissipation. Results: Extracted potentials show monotonic increase as the relative distance of two nuclei decreases, which induces the disappearance of an ordinary barrier structure of the potential. This is different from those in light- and medium-mass systems and from density-constraint TDHF calculations. Extracted friction coefficients show sizable energy dependence and universal value of their magnitude, which are rather similar to those in light- and medium-mass systems. Using these properties, we analyze the origin of the fusion hindrance and find that contribution of the increase in potential to the extra-push energy is larger than that of the accumulated dissipation energy in most systems studied in this article. Conclusions: By the analysis of the origin of the fusion hindrance, we conclude that, as the system becomes heavier, the dynamical increase in potential at small relative distances plays a more important role than the dissipation during the fusion reaction for understanding the origin of the fusion hindrance.

Semimicroscopic modeling of heavy-ion fusion reactions with multireference covariant density functional theory

Semimicroscopic modeling of heavy-ion fusion reactions with multireference covariant density functional theory

Observation of mass-asymmetric fission of mercury nuclei in heavy ion fusion

Background: Mass-asymmetric fission has been observed in low energy fission of $^{180}\mathrm{Hg}$. Calculations predicted the persistence of asymmetric fission in this region even at excitation energies of 30--40 MeV.Purpose: To investigate fission mass distributions by populating different isotopes of Hg using heavy ion fusion reactions.Methods: Fission fragment mass-angle distributions have been measured for two reactions, $^{40}\mathrm{Ca}+^{142}\mathrm{Nd}$ and $^{13}\mathrm{C}+^{182}\mathrm{W}$, populating $^{182}\mathrm{Hg}$ and $^{195}\mathrm{Hg}$, respectively, using the Heavy Ion Accelerator Facility and CUBE spectrometer at the Australian National University. Measurements were made at beam energies around the capture barrier for the two reactions and mass ratio distributions were obtained using the kinematic reconstruction method.Results: Asymmetric fission has been observed following the population of $^{182}\mathrm{Hg}$ at an excitation energy of 22.8 MeV above the saddle point. A symmetric peaked mass ratio distribution was observed for $^{195}\mathrm{Hg}$ nuclei at a similar excitation energy above the saddle point.Conclusions: Mass-asymmetric fission has been observed in neutron deficient Hg nuclei populated via heavy ion fusion for the first time. The results are consistent with observations from beta-delayed fission measurements and provide a proof-of-principle for expanding experimental studies of the influence of shell effects on the fission processes.