Deep Sub-barrier Energies Research Articles

Laser-assisted deuterium-tritium fusion: A quantum dynamical model

Deuterium-tritium (D-T) fusion is a key to generating safe, clean, and limitless energy on Earth in future fusion power plants. Its understanding at low collision energies is incomplete, as D-T fusion is a quantum tunneling process affected by resonances whose origin is linked to properties of not fully understood nuclear forces. Simplified quantum dynamical calculations of laser-assisted D-T fusion are presented, suggesting that laser-nucleus interaction can enhance the average D-T fusion probability by 7–70% at deep subbarrier energies using laser fields of intensity 1027–1029 Wcm−2 and a photon energy of 1 eV. Published by the American Physical Society 2024

Breakup dynamics of a neutron-halo projectile on heavy target at deep sub-barrier energies

By studying the total fusion and breakup cross-sections in the interaction of the neutron-halo 11Be projectile on the lead target 208Pb, it is shown that, even for the neutron-halo projectile, the breakup channel remains the most dominant reaction channel at sub-barrier energies, following a characteristic behavior that was also previously verified for the case of the proton-halo projectile 8B. This feature is found to emanate from the enhancement of the breakup cross-section, due to the continuum–continuum couplings (CCC) coming exclusively from its Coulomb component. We further speculate that the enhancement of the Coulomb breakup cross-section at sub-barrier incident energies by the CCC could be associated with the projectile breaking up on the outgoing trajectory, provided these couplings can be proven to delay the breakup process.

A study the 16 O + 166 E R , 16 O + 197 Au Systems Using Calculations of Quasi-elastic Scattering

Specific systematic studies on the nuclear potential parameter for the heavy-ion reactions which includes the systems have been achieved by using large-angle quasi elastic scattering at deep sub-barrier energies close to the Coulomb barrier height. The elastic scattering barrier distribution Dqelas a function of energy has also been calculated in this theoretical study. The single-channel (SC) and coupled-channels calculations have been carried out to elicit the nuclear potential. The chi-square method X2 has been used find the best value of the nuclear potential in comparison with the experimental data. The best values of the nuclear potential were found from the calculations of the single channels for systems: 16O+166ER , 16O+197Au, which are equal to (60.5, 100) MeV, respectively.

Recent Results on Direct Measurement of the \(^{12}\)C+\(^{12}\)C Fusion Cross section at Deep Sub-barrier Energies with STELLA

Recent Results on Direct Measurement of the \(^{12}\)C+\(^{12}\)C Fusion Cross section at Deep Sub-barrier Energies with STELLA

Investigation of deep sub-barrier fusion in asymmetric systems

Enhancement of fusion cross sections below the interaction barrier has been quite successfully explained by coupled-channels methods. However, extending the measurements to deep sub-barrier energies revealed a steeper descent of the excitation function which could not be explained by standard coupled-channels calculations. Though a large number of heavy-ion and light-ion induced reactions have been investigated to understand the dynamics of fusion deep below the barrier, the phenomenon of fusion hindrance has been studied only for a handful of asymmetric systems. We report new measurements of fusion excitation functions for the systems 16O+116Cd and 16O+142Ce. We also present comparisons of the same with the data for existing symmetric systems having nearly similar values of the ζ parameter, characterizing the size of the colliding system. We extracted the logarithmic derivatives of the energy-weighted cross sections and the astrophysical S -factors. Experimental results were reproduced well by coupled-channels calculations. We extrapolated our results, following the systematics, beyond the threshold energy for fusion hindrance for both the systems. From our investigation, we conclude that the present asymmetric systems, as well as the corresponding symmetric systems, show fusion hindrance and this feature is independent of the entrance channel mass asymmetry.

A Study the Nuclear Potential Using Quasi-Elastic Scattering Calculation for the 9,10,11Be+208Pb Reactions

Specific systematic studies on the nuclear potential parameter for the heavy-ion reactions, which includes the systems, have been achieved by using large-angle quasi-elastic scattering at deep sub-barrier energies close to the Coulomb barrier height. Single-channel (SC) and coupled-channel calculations have been carried out to elicit the nuclear potential. The chi-square method χ2 has been used to find the best value of the nuclear potential compared to the experimental data. The best values of the nuclear potential were found from the calculations of the coupled channels for an inert projectile and a vibrating target for systems: 9Be+208Pb,10Be+208Pb, 11Be+208Pb, which are equal to 45 MeV,65 MeV,53 MeV, respectively.

Carbon burning at stellar energies

Fusion reactions with light nuclei play an essential role in understanding the energy production, the nucleosynthesis of chemical elements and the evolution of massive stars. The measurement of key fusion reactions at stellar energies is thus of interest, but highly challenging since the associated cross sections are extremely small, of the sub-nanobarn range. Among these reactions, the fusion of carbon nuclei, which drives the stellar carbon burning phase, is deeply connected with essential microscopic features such as the impact of symmetries, the access to quantum states, emerging of resonances or Pauli repulsion effects. These may manifest themselves in exceptional behaviour of the S-factor of this particular system and the precision of extrapolations to deep sub-barrier energies is limited. The present contribution discusses recent experimental results of the nuclear astrophysics community on the measurement of the carbon + carbon fusion reaction down to the astrophysics region. The interplay between nuclear structure, nucleosynthesis and stellar evolution is addressed.

Global approach for the reactions Be7+Si28 and Be7+Pb208 at near- and sub-barrier energies

Elastic scattering, total reaction, and fusion cross section measurements for the radioactive $^{7}\mathrm{Be}$ nucleus on a light and a heavy target, are treated in a global approach at near and sub-barrier energies for probing the optical potential and describing fusion at low energies. Elastic scattering data of $^{7}\mathrm{Li}$ on the same target were analyzed under the same context to support this analysis. It is found that for low mass targets, dispersion relations are not adequate for describing the potential or the fusion. On the contrary this is possible for heavy targets, where the standard potential threshold anomaly and fusion enhancement is observed. The consequences of the above on fusion hindrance at deep sub-barrier energies is discussed.

Non-frozen process of heavy-ion fusion reactions at deep sub-barrier energies

Non-frozen process of heavy-ion fusion reactions at deep sub-barrier energies

Pauli blocking potential applied to heavy-ion fusion reactions * *Supported by the National Natural Science Foundation of China (12105080, 11822503, 11975091) and the Program for Innovative Research Team (in Science and Technology) in University of Henan Province (21IRTSTHN011), China

In this study, the Pauli blocking potential between two colliding nuclei in the density overlapping region is applied to describe the heavy nuclei fusion process. Inspired by the Pauli blocking effect in the -decay of heavy nuclei, the Pauli blocking potential of single nucleon from the surrounding matter is obtained. In fusion reactions with strong density overlap, the Pauli blocking potential between the projectile and target can be constructed using a single folding model. By considering this potential, the double folding model with a new parameter set is employed to analyze the fusion processes of 95 systems. A wider Coulomb barrier and shallower potential pocket are formed in the inner part of the potential between the two colliding nuclei, compared to that calculated using the Akyüz-Winther potential. The fusion hindrance phenomena at deep sub-barrier energies are described well for fusion systems O + Pb and Ni + Ni.

Density variation effects in α + Pb208 and O16 + Pb208 fusion reactions

We propose a hybrid approach between the sudden model and the adiabatic model to explain the fusion hindrance in heavy-ion fusion reactions at deep subbarrier energies. Due to the strong Pauli blocking effects at the density overlap region, the $\ensuremath{\alpha}$ particle approaching the target $^{208}\mathrm{Pb}$ becomes enlarged and its density distribution gets changed. By introducing energy dependence into this density variation effect, the potentials at different colliding energies are diverse. With the decrease of colliding energies, the significantly enhanced density variation effects make the nuclear potential more attractive and result in a deeper pocket in the inner part. A reasonable description of the experimental fusion cross sections is achieved for the $\ensuremath{\alpha} + ^{208}\mathrm{Pb}$ reaction. On account of highlighting the influence of density variation effects on the fusion process at deep subbarrier energies, we further investigate the density variation effects in the $^{16}\mathrm{O} + ^{208}\mathrm{Pb}$ fusion reaction based on the $\ensuremath{\alpha}$-cluster structures in $^{16}\mathrm{O}$ nuclei. The fusion hindrance at deep subbarrier energies is described well by considering the density variation effects. In addition, an astrophysical $S$ factor between the sudden model and adiabatic model is predicted at the energies below the experimental data.

Searching for treasures at sub-barrier energies: the case of 8B and 7Be

Unexpected and challenging experimental results, at below barrier energies for weakly bound nuclei, are briefly reviewed in this article. The emphasis will be on our recent breakup results for 8B+208Pb at deep sub-barrier energies, indicating a dominance of direct mechanisms at this low energy regime. We will also present, a preliminary analysis of the 4He and 3He - particle production events for the 7Be + 208Pb reaction. These data were collected at the same experiment and at similar deep sub-barrier energies, exhibiting large yields compatible with cluster transfer processes. To confirm these results a new experiment to be performed at TriSol is planned, as soon as the upgrading of this facility will be completed.

Fusion Hindrance and Pauli Blocking in 58Ni + 64Ni

58Ni +64Ni is the first case where the influence of positive Q-value transfer channels on sub-barrier fusion was evidenced, in a very well known experiment by Beckerman et al., by comparing with the two systems 58Ni +58Ni and 64Ni +64Ni. Subsequent measurements on 64Ni +64Ni showed that fusion hindrance is clearly present in this case. On the other hand, no indication of hindrance can be observed for 58Ni +64Ni down to the measured level of 0.1 mb. In the present experiment the excitation function has been extended by two orders of magnitude downward. The cross sections for 58Ni + 64Ni continue decreasing very smoothly below the barrier, down to ≃1 μb. The logarithmic slope of the excitation function increases slowly, showing a tendency to saturate at the lowest energies. No maximum of the astrophysical S-factor is observed. Coupled-channels (CC) calculations using a Woods-Saxon potential and including inelastic excitations only, underestimate the sub-barrier cross sections by a large amount. Good agreement is found by adding two-neutron transfer couplings to a schematical level. This behaviour is quite different from what already observed for 64Ni+64Ni (no positive Q-value transfer channels available), where a clear low-energy maximum of the S-factor appears, and whose excitation function is overestimated by a standard Woods-Saxon CC calculation. No hindrance effect is observed in 58Ni+64Ni in the measured energy range. This trend at deep sub-barrier energies reinforces the recent suggestion that the availability of several states following transfer with Q >0, effectively counterbalances the Pauli repulsion that, in general, is predicted to reduce tunneling probability inside the Coulomb barrier.

Microscopic description of fusion hindrance in symmetric Ni+Ni and asymmetric C12+Pt198 systems

Hindrance at deep subbarrier energies for the symmetric $^{58}\mathrm{Ni}+^{58}\mathrm{Ni}, ^{64}\mathrm{Ni}+^{64}\mathrm{Ni}$, and asymmetric $^{12}\mathrm{C}+^{198}\mathrm{Pt}$ systems is investigated using microscopic energy and the density-dependent $G$-matrix effective interaction. The proton and neutron density distributions of target and projectile are derived from Skyrme-Hartree-Fock calculations. A fair agreement with the data of the fusion excitation functions and astrophysical $S$ factors have been obtained without any fitting parameters. Hindrance is naturally reproduced at deep subbarrier energies, which is consistent with experimental observations.

Dominance of direct reaction channels at deep sub-barrier energies for weakly bound nuclei on heavy targets: The case B8+Pb208

Dominance of direct reaction channels at deep sub-barrier energies for weakly bound nuclei on heavy targets: The case <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">B</mml:mi><mml:mprescripts /><mml:none /><mml:mn>8</mml:mn></mml:mmultiscripts><mml:mo>+</mml:mo><mml:mmultiscripts><mml:mi>Pb</mml:mi><mml:mprescripts /><mml:none /><mml:mn>208</mml:mn></mml:mmultiscripts></mml:mrow></mml:math>

Pauli blocking effects in nα -nucleus-induced fusion reactions

The hindrances in the $n\ensuremath{\alpha}$-nucleus-induced fusion reactions at deep subbarrier energies are investigated by using the coupled-channels model. Inspired by the microscopic Pauli-blocking effects of $\ensuremath{\alpha}$-cluster decay in radioactive nuclei, a Pauli blocking potential is constructed in the $n\ensuremath{\alpha}$-nucleus-induced fusion reactions by using a single folding procedure, in which the $n\ensuremath{\alpha}$ nuclei are assumed to be consisted of $\ensuremath{\alpha}$ particles. A shallow pocket is formed in the inner part of the potential between two colliding nuclei as compared to the one obtained from the double-folding potential with standard Michigan-3-Yukawa effective nucleon-nucleon interaction. The experimental fusion cross sections are described well for fusion systems $^{12}\mathrm{C}+^{198}\mathrm{Pt}$, $^{16}\mathrm{O}+^{208}\mathrm{Pb}$, $^{12}\mathrm{C}+^{30}\mathrm{Si}$, $^{24}\mathrm{Mg}+^{30}\mathrm{Si}$, and $^{28}\mathrm{Si}+^{30}\mathrm{Si}$. At deep subbarrier energies, it is found that this shallow pocket potential reduces the partial fusion cross sections and shields the contributions of high-angular-momentum partial waves to fusion cross sections. In addition, a detailed comparison of fusion processes with different projectiles $^{12}\mathrm{C}$, $^{24}\mathrm{Mg}$, and $^{28}\mathrm{Si}$ on the same target $^{30}\mathrm{Si}$ shows the hindrance effect is stronger for heavier projectiles.

Advances in the Direct Study of Carbon Burning in Massive Stars.

The ^{12}C+^{12}C fusion reaction plays a critical role in the evolution of massive stars and also strongly impacts various explosive astrophysical scenarios. The presence of resonances in this reaction at energies around and below the Coulomb barrier makes it impossible to carry out a simple extrapolation down to the Gamow window-the energy regime relevant to carbon burning in massive stars. The ^{12}C+^{12}C system forms a unique laboratory for challenging the contemporary picture of deep sub-barrier fusion (possible sub-barrier hindrance) and its interplay with nuclear structure (sub-barrier resonances). Here, we show that direct measurements of the ^{12}C+^{12}C fusion cross section may be made into the Gamow window using an advanced particle-gamma coincidence technique. The sensitivity of this technique effectively removes ambiguities in existing measurements made with gamma ray or charged-particle detection alone. The present cross-section data span over 8 orders of magnitude and support the fusion-hindrance model at deep sub-barrier energies.

Status on $$^{\mathbf {12}}\mathbf {C}+{}^{\mathbf {12}}{\mathbf {C}}$$ fusion at deep subbarrier energies: impact of resonances on astrophysical $$S^{*}$$ factors

Since the discovery of molecular resonances in $^{12}$C+$^{12}$C in the early sixties a great deal of research work has been undertaken to study $\alpha$-clustering and resonant effects of the fusion process at sub-Coulomb barrier energies. The modified astrophysical $S^{*}$ factors of $^{12}$C+$^{12}$C fusion have been extracted from direct fusion measurements at deep sub-barrier energies near the Gamow window. They were also obtained by the indirect Trojan horse method (THM). A comparison of direct measurements and the THM, which elucidates problems in the analysis of the THM, is discussed in this Letter to the Editor.

Formula omitted] molecular resonances at deep sub-barrier energy

The existence of C12+16O molecular resonances at sub-barrier energy has been a significant problem in nuclear astrophysics because they strongly affect the C12+16O fusion reaction rate in type Ia supernovae and heavy stars. However, experimental surveys have been limited to 4 MeV and cannot access the deep sub-barrier energy due to a very small fusion cross section. Here we predict a couple of resonances with Jπ=0+, 2+, and 4+ in the deep sub-barrier energy based on the antisymmetrized molecular dynamics calculation that reproduces the known resonances and low-lying spectrum of Si28.

Fusion hindrance and Pauli blocking in Ni58+Ni64

Background: $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$ is the first case where the influence of positive $Q$-value transfer channels on subbarrier fusion was evinced, in a very well known experiment by Beckerman et al. [Phys. Rev. Lett. 45, 1472 (1980)], by comparing with the two systems $^{58}\mathrm{Ni}+^{58}\mathrm{Ni}$ and $^{64}\mathrm{Ni}+^{64}\mathrm{Ni}$. Subsequent measurements on $^{64}\mathrm{Ni}+^{64}\mathrm{Ni}$ showed that fusion hindrance is clearly present in this case. On the other hand, no indication of hindrance can be observed for $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$ down to the measured level of 0.1 mb.Purpose: Measuring deep subbarrier fusion cross sections for $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$, where the influence of positive $Q$-value transfer channels on near-barrier fusion was evidenced previously, in order to investigate whether hindrance shows up.Methods: 167--200 MeV $^{58}\mathrm{Ni}$ beams from the XTU Tandem Accelerator of INFN-Laboratori Nazionali di Legnaro were used, bombarding thin metallic $^{64}\mathrm{Ni}\phantom{\rule{4pt}{0ex}}(50\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{g}/{\mathrm{cm}}^{2})$ enriched to $99.6%$ in mass 64. An electrostatic beam deflector allowed fusion evaporation residues to be detected at very forward angles in a detector telescope.Results: The excitation function has been extended by two orders of magnitude downward. The cross sections for $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$ continue decreasing very smoothly below the barrier, down to $\ensuremath{\simeq}1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{b}$. The logarithmic slope of the excitation function increases slowly, showing a tendency to saturate at the lowest energies. No maximum of the astrophysical $S$ factor is observed. Coupled-channel (CC) calculations using a Woods-Saxon potential and including inelastic excitations only underestimate the subbarrier cross sections by a large amount. Good agreement is found by adding two-nucleon transfer couplings to a schematical level. This behavior is quite different from what already observed for $^{64}\mathrm{Ni}+^{64}\mathrm{Ni}$ (no positive $Q$-value transfer channels available), where a clear low-energy maximum of the $S$ factor appears, and whose excitation function is overestimated by a standard Woods-Saxon CC calculation.Conclusions: No hindrance effect is observed in $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$ in the measured energy range. This trend at deep subbarrier energies reinforces the recent suggestion that the availability of several states following transfer with $Qg0$ effectively counterbalances the Pauli repulsion that, in general, is predicted to reduce tunneling probability inside the Coulomb barrier.